The Casimir effect is a term used for quantum effects resulting from the precise form and the finite extension of systems.
The continuing miniaturization of technical devices makes this effect increasingly more important.
In microelectromechanical systems it is known to be responsible for up to 10% of the forces encountered and an optimal design
needs to take the effect into account. Given this ubiquitous character, a complete understanding of the effect is warranted. However, presently the origin of the sign of the Casimir energy is not well understood, and the change of the Casimir energy is largely unknown when the shape of objects and their material properties are altered.
The goal of this proposal, which is a collaborative proposal with Klaus Kirsten of Baylor University, was two fold:
(1) Add bits of understanding to the knowledge of Casimir forces
based on specific calculations for specific configurations. Several configurations were considered within this grant including singular configurations such as inverse square law potentials.
(2) Analyze the change of the Casimir energy under a
deformation of the space. Analytical surgery, a geometric analysis method designed to analyze changes in spectral quantities, was newly employed in the field of the Casimir effect as part of this grant.
A better understanding of fundamental aspects of the Casimir effect is likely to help find an optimal design of microelectromechanical devices. Contributions arising out of this grant are expected to add information that will help to achieve this goal.
\n
The main publication during this grant period was the paper, joint with Klaus Kirsten, Analytic surgery of the zeta function, in the journal Communications in Mathematical Physics. The paper can be described as a preliminary result concerning analytical surgery as it was presented for the special case of smooth manifolds; this work in particular did not contain Casimir's original work. After this paper was published, I was able to solve the analytical surgery formula for the zeta function in full generality for manifolds with corners, which in particular contains Casimir's original work as a corollary, as well as scores of many other works as special cases.
I currently have three Ph.D. students and a younger student who has asked me to be his Ph.D. advisor. During the past couple years, all these students have been taking independent study classes with me to learn the basics of pseudodifferential operators and heat kernels, some of the main tools needed to understand the analytical surgery of zeta functions. The interest of these students is the first step to using this grant project as a springboard to attract new and current graduate students to study analysis here at Binghamton University.
Perhaps the most significant educational activity this grant has helped initiate is the start of a new graduate ``Analysis Program'' and ``Analysis Seminar'' here at Binghamton University. In order to recruit and retain students interested in analysis we need to provide courses in analysis. During this grant period, for the first time in a couple decades, we offered a two semester (Fall-Spring) course in ``Graduate Analysis.'' The objective was to teach a one year unified course in integration, functional analysis and complex analysis. To bring about this new curriculum, we had to write a report explaining why the current system was not working and why the new system is superior. Also, for the first time (to the best of my knowledge) in the history of Binghamton University we have an official ``Analysis Seminar''. I was the chairman of the seminar during its inaugural period. One purpose of the seminar is to present introductory talks on various research topics with the goal of recruiting graduate studen...","publicAccessMandate":"0","publicationResearch":["Comm. Math. Phys.~2011~310~Kirsten, K. and Loya, P.~181--215~Analytic surgery of the zeta function~","J. Math. Phys.~2010~51~Kirsten, K. and Loya, P.~053512, 2~Spectralfunctions for the Schr{\\\"o}dinger operator on $\\mathbb{R}^+$ with a singularpotential~","JOURNAL OF MATHEMATICAL PHYSICS~2010~51~Kirsten, K; Loya, P~10.1063/1.326393~http://wok-ws.isiknowledge.com/WoS?recid=189320881#000278182800044~Spectral functions for the Schrodinger operator on R+ with a singular potential~Y~","Adv. Appl.Clifford Algebr.~2010~20~Loya, P.~707--732~Semiclassical pseudodifferential operators and the{A}tiyah-{S}inger index theorem~","ADVANCES IN APPLIED CLIFFORD ALGEBRAS~2010~20~P. Loya~707-732~Semiclassical pseudodifferential operators and the Atiyah-Singer index theorem~N~"],"startDate":"09/01/2008","title":"Collaborative Research: The Casimir effect: Geometry and boundary condition dependence","transType":"Continuing Grant","ueiNumber":"NQMVAAQUFU53"},{"abstractText":"This Collaborative Research is proposed by Klaus Kirsten, BaylorUniversity, and Paul Loya, Binghamton University. Casimir effect is a term used for quantum effects resulting from the finite extension of systems. The continuing miniaturization of technical devices makes this effect increasingly more important; e.g. in microelectromechanical systems it is responsible for up to 10% of the forces encountered. Also on cosmological scales this effect is relevant to the dark energy and to the stabilization of extra dimensions of the universe. However, presently not even the origin of the sign of the Casimir energy is well understood. In addition, the change of the Casimir energy is largely unknown when the shape of small objects and their material properties are altered. The goal of the present proposal is to considerably improve this situation by employing two completely different strategies. 1.) For highly symmetric situations, e.g. spheres, cubes and tori, the Casimir energy is well understood. Using contour integral methods this pool will be significantly increased to include configurations related to any separable coordinate system. 2.) At present, no practicable technique is known to find the change of the Casimir energy when the geometry of objects or their material properties are changed. This proposal entails a completely new approach. Analytical surgery, a geometric analysis method designed to analyze changes in spectral quantities, will be newly employed in the field of the Casimir effect. \r\nBroader Impacts. The deeper understanding of the Casimir effect is necessary \r\nfor the optimal design of microelectromechanical devices. Furthermore this project will involve the collaboration of undergraduate and graduate students from various backgrounds and different departments. The techniques that the PIs will use to study the Casimir effect are accessible to advanced undergraduate students with a complex analysis background. An undergraduate text book and class on complex analysis, path integrals, and zeta regularized determinants will be developed by the PIs within the next two years. The newly established mathematical physics seminar at Baylor University started by Kirsten will serve to communicate results obtained under this grant to attract Baylor graduate students. Loya as the adviser of the Undergraduate Math Club at SUNY Binghamton will inform those students. This project will serve as a springboard to attract graduate students to this field of research to both involved universities. Finally, coming from the areas of mathematical physics (Kirsten) and analysis (Loya), the collaboration of the PIs in this project is multidisciplinary and will be a seed for new ideas combining physics and analysis. \r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"BAYLOR UNIVERSITY","awardeeAddress":"700 S UNIVERSITY PARKS DR","awardeeCity":"WACO","awardeeCountryCode":"US","awardeeDistrict":"17","awardeeDistrictCode":"TX17","awardeeName":"Baylor University","awardeePhone":"2547103817","awardeeStateCode":"TX","awardeeZipCode":"767061003","cfdaNumber":"47.049","date":"08/27/2008","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"150000","expDate":"08/31/2012","fundAgencyCode":"4900","fundProgramName":"MATHEMATICAL PHYSICS","fundsObligated":["FY 2008 = $50,000.00","FY 2009 = $50,000.00","FY 2010 = $50,000.00"],"fundsObligatedAmt":"150000","histAwd":"false","id":"0757791","initAmendmentDate":"08/27/2008","jrnl":[{"artPageNum":"374010 (1","artTitl":"Heat trace asymptotics and the Gauss-Bonnet theorem for general connections","auth":"C.G. 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\n
Casimir effect is a quantum effect first predicted by the Dutch physicist
Hendrik Casimir in 1948. It is known to have significant impact on
physical processes at very small scales. The continuing miniaturization of technical devices makes this effect increasingly more relevant, for instance in micromachines it is responsible for up to 10 percent of the forces
encountered and an optimal design needs to take the effect into
account. Not only on small, but also on cosmological scales its impact
might be extremely relevant. It relates to the dark energy and to the stabilization of extra dimensions of the universe. Given this ubiquitous character, a complete understanding of the Casimir effect is warranted. In particular, the question we need to answer is how the resulting Casimir force depends on the precise shape and properties of the systems involved.
\n
However, presently not even the origin of the negative or positive
sign of the Casimir energy, which decides between the attractive or repulsive nature of Casimir forces, is well understood. In addition, the change of the Casimir energy is largely unknown when the shape of small
objects and their material properties are altered. The goal of our
project has been to improve this situation by employing two completely different strategies. The first strategy is to compute the Casimir energy for as many as possible configurations such that a larger picture emerges. The second strategy uses techniques common in global analysis,
a mathematical discipline, to understand how Casimir energy changes under deformations of the geometry of objects, or systems.
\n
The most important outcome of the funded project is that we laid the mathematical foundation to understand how the Casimir energy changes under a specific deformation of systems. Furthermore, we enlarged considerably the category of treatable configurations. This was possible because we captured many of the important mathematical subtleties which are now understood at a deeper level. One of these configurations can be used to rule out inappropriate cosmological models based on current Casimir experiments making it a viable tool for physicists working on theories of the universe.
\n
This NSF grant allowed us to engage three PhD students and one postdoc at Baylor University in the research related to mathematical aspects of the Casimir effect. One dissertation has been successfully finished in 2012, the other two are expected to be completed in 2014. The PI has participated in eleven workshops and conferences, he has been co-editor of two books as well as co-organizer of two special sessions at conferences of the American Mathematical Society in a subject area related to the projects of our grant. This significantly helped to increase the much needed discussion and interaction about the Casimir effect among mathematicians and physicists.
\n
We gratefully acknowledge that the above research and related activities have fully or partially been made possible by our NSF grant.
\n
\n\t\t\t\t \tLast Modified: 12/21/2012
\n\t\t\t\t\tModified by: Klaus Kirsten
\n
\n
\n
","publicAccessMandate":"0","publicationResearch":["Journal of Physics A: Math. Theor.~2012~45~C.G. Beneventano, P. Gilkey, K. Kirsten and E.M. 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Kirsten~1260008 (~The Casimir effect for generalized piston geometries~N~","JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL~2011~44~Harrison, JM; Kirsten, K~10.1088/1751-8113/44/23/23530~http://wok-ws.isiknowledge.com/WoS?recid=197622389#000290518800007~Zeta functions of quantum graphs~Y~","Journal of Physics A: Math. Theor.~2012~45~J.M. Harrison, K. Kirsten and C. Texier~125206 (1~Spectral determinants and zeta functions of Schroedinger operators on metric graphs~N~","PHYSICAL REVIEW D~2009~79~Kirsten, K; Fulling, SA~10.1103/PhysRevD.79.06501~http://wok-ws.isiknowledge.com/WoS?recid=178856752#000264762500102~Kaluza-Klein models as pistons~Y~","JOURNAL OF MATHEMATICAL PHYSICS~2010~51~Kirsten, K; Loya, P~10.1063/1.326393~http://wok-ws.isiknowledge.com/WoS?recid=189320881#000278182800044~Spectral functions for the Schrodinger operator on R+ with a singular potential~Y~","Communications in Mathematical Physics~2012~310~K. Kirsten and P. Loya~181~Analytic surgery of the zeta function~N~","PHYSICAL REVIEW D~2009~80~Milton, KA; Wagner, J; Kirsten, K~10.1103/PhysRevD.80.12502~http://wok-ws.isiknowledge.com/WoS?recid=185758495#000273233300148~Casimir effect for a semitransparent wedge and an annular piston~Y~","Journal of Functional Analysis~2011~261~M. van den Berg, P. Gilkey and K. Kirsten~2293~Growth of heat trace and heat content asymptotic coefficients~N~","Journal of Geometric Analysis~2011~21~M. van den Berg, P. Gilkey and K. Kirsten~Heat trace asymptotics with singular weight functions II~N~","Communications in partial differential equations~2012~37~M. van den Berg, P. Gilkey, G. Grigor'yan and K. Kirsten~8~Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data~N~","Journal of Physics A: Math. Theor.~2012~45~T.D. Jeffres, K. Kirsten and T. 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This force and the corresponding effect, now known as the Casimir effect, results from the alteration by the plates (boundaries) of the zero point electromagnetic energy that pervades all of space as predicted by quantum field theory. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as a function of the size, geometry and topology of the boundary. This study will build on the rapid theoretical advances in the area of simple geometry dependencies in the last two years. Investigations into the geometry dependence of the lateral Casimir force for surfaces with periodic corrugation on nanometer length scales, which will incorporate cooperative diffraction like effects for the zero-point photons will be carried out. Additionally, the role of thermal photons in the Casimir effect will be explored. The role of thermal photons is not completely understood due to problems effectively incorporating the dielectric losses of the material and interesting predictions of non-trivial geometry dependence have also been advanced for thermal photons. Finally a preliminary investigation of the role of negative index of refraction materials in the Casimir force will be launched. The results of this complete study will also allow the setting of stringent limits on modern unification theories which predict the presence of new forces or compactified extra dimensions. \r\nEven though the Casimir effect originates from quantum fluctuations, it results in large forces on macroscopic objects separated by distances less than a micron. The role of Casimir forces in the fabrication, function and yield of micromechanical devices has recently become well recognized. This investigation will lead to improved nano-electromechanical devices such as nano actuators, micro mirrors for optical communication and nano tweezers. The research program also involves the training of a graduate student and a minority undergraduate student in laboratory research and nanotechnology. \r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"THE REGENTS OF THE UNIVERSITY OF CALIFORNIA","awardeeAddress":"900 UNIVERSITY AVE","awardeeCity":"RIVERSIDE","awardeeCountryCode":"US","awardeeDistrict":"39","awardeeDistrictCode":"CA39","awardeeName":"University of California-Riverside","awardeePhone":"9518275535","awardeeStateCode":"CA","awardeeZipCode":"925219800","cfdaNumber":"47.049","date":"06/04/2007","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"382210","expDate":"07/31/2010","fundAgencyCode":"4900","fundProgramName":"OPTICAL PHYSICS","fundsObligated":["FY 2007 = $142,210.00","FY 2008 = $120,000.00","FY 2009 = $120,000.00"],"fundsObligatedAmt":"382210","histAwd":"false","id":"0653657","initAmendmentDate":"06/04/2007","jrnl":[{"artPageNum":"036102","artTitl":"Comment on \"Precision measurement of the Casimir-Lifshitz force in a fluid\"","auth":"B. 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Klimchitskaya, U. Mohideen and V.M. Mostepanenko","authIndCode":"N","jrnlTitl":"Reviews of Modern Physics","jrnlVol":"81","jrnlYr":"2009"},{"artPageNum":"9","artTitl":"Thermal Casimir-Polder force between an atom and a dielectric plate: thermodynamics and experiment","auth":"G.L. Klimchitskaya, U. Mohideen, and V.M. Mostepanenko","authIndCode":"N","jrnlTitl":"Journal of Physics A","jrnlVol":"41","jrnlYr":"2008"},{"artPageNum":"164022","artTitl":"Experimental procedures for precision measurements of the Casimir force with an atomic force microscope","auth":"H-C. Chiu, C.C. Chang , R. Castillo-Garza, F. Chen, U. Mohideen","authIndCode":"N","jrnlTitl":"Journal of Physics A","jrnlVol":"41","jrnlYr":"2008"},{"artPageNum":"121402","artTitl":"Demonstration of the assymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime","auth":"H.C. Chiu, G.L. Klimchitskaya, V.N. Marachevsky, V.M. Mostepanenko, and U. Mohideen","authIndCode":"N","jrnlTitl":"Physical Review B (Rapid Communication)","jrnlVol":"80","jrnlYr":"2009"},{"artPageNum":"115417","artTitl":"Lateral Casimir force between sinusoidally corrugated surfaces: Asymmetric profiles, deviations from the proximity force approximation, and comparison with exact theory","auth":"HC. Chiu, G.L. Klimchitskaya, V.N. Marachevsky, V.M. Mostepanenko, U. Mohideen","authIndCode":"N","jrnlTitl":"Physical Review B","jrnlVol":"81","jrnlYr":"2010"},{"artPageNum":"F339","artTitl":"Kramers-Kronig relations for plasma-like permittivities and the Casimir force","auth":"Klimchitskaya, GL; Mohideen, U; Mostepanenko, VM","authIndCode":"Y","dgtlObjId":"10.1088/1751-8113/40/17/F0","endPageNum":"F346","jrnlTitl":"JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL","jrnlVol":"40","jrnlYr":"2007","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=156001631#000246085400004"},{"artPageNum":"F841","artTitl":"Pulsating Casimir force","auth":"Klimchitskaya, GL; Mohideen, U; Mostepanenko, VM","authIndCode":"Y","dgtlObjId":"10.1088/1751-8113/40/34/F0","endPageNum":"F847","jrnlTitl":"JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL","jrnlVol":"40","jrnlYr":"2007","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=157408067#000248786600003"},{"artPageNum":"012005","artTitl":"Customized silicon cantilevers for Casimir force experiments using focused ion beam milling","auth":"R.C. Castillo-Garza, C.C. Chang, Y. Dong, and U. Mohideen","authIndCode":"N","jrnlTitl":"Journal of Physics: Conference Series","jrnlVol":"161","jrnlYr":"2009"},{"artPageNum":"1721","artTitl":"Why screening effects do not influence the Casimir force","auth":"V.M. Mostepanenko, R.S. Decca, E. Fischbach, B. Geyer, G.L. Klimchitskaya, D.E. Krause, D. Lopez and U. Mohideen","authIndCode":"N","jrnlTitl":"Internation Journal of Modern Physics A","jrnlVol":"24","jrnlYr":"2009"}],"latestAmendmentDate":"04/29/2009","managingPec":"129000","orgCodeDir":"03000000","orgCodeDiv":"03010000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Physics","orgUrl":"http://www.nsf.gov/div/index.jsp?div=phy","parentUeiNumber":"GH98ZGGP6RR5","pdPIName":"Umar Mohideen","perfAddress":"900 UNIVERSITY AVE","perfCity":"RIVERSIDE","perfCountryCode":"US","perfDistrict":"39","perfDistrictCode":"CA39","perfLocation":"University of California-Riverside","perfStateCode":"CA","perfZipCode":"925219800","pi":["Umar Mohideen umar.mohideen@ucr.edu"],"piEmail":"umar.mohideen@ucr.edu","piFirstName":"Umar","piId":"000235517","piLastName":"Mohideen","poEmail":"","poName":"Wendell Talbot Hill","poPhone":"","primaryProgram":["app-0107","01000910DB NSF RESEARCH & RELATED ACTIVIT","01000809DB NSF RESEARCH & RELATED ACTIVIT"],"progEleCode":"129000","program":"UNASSIGNED, NANO NON-SOLIC SCI & ENG AWD, OTHER RESEARCH OR EDUCATION","progRefCode":"0000, 7237, OTHR","publicAccessMandate":"0","publicationResearch":["PHYSICAL REVIEW A~2008~77~B. Geyer, G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko~036102~Comment on \"Precision measurement of the Casimir-Lifshitz force in a fluid\"~N~","PHYSICAL REVIEW A~2007~75~Castillo-Garza, R; Chang, CC; Jimenez, D; Klimchitskaya, GL; Mostepanenko, VM; Mohideen, U~10.1103/PhysRevA.75.06211~http://wok-ws.isiknowledge.com/WoS?recid=158690904#000247624300031~Experimental approaches to the difference in the Casimir force due to modifications in the optical properties of the boundary surface~Y~","PHYSICAL REVIEW B~2007~76~Chen, F; Klimchitskaya, GL; Mostepanenko, VM; Mohideen, U~10.1103/PhysRevB.76.03533~http://wok-ws.isiknowledge.com/WoS?recid=157495457#000248500800113~Control of the Casimir force by the modification of dielectric properties with light~Y~","OPTICS EXPRESS~2007~15~Chen, F; Klimchitskaya, GL; Mostepanenko, VM; Mohideen, U~4823~4829~http://wok-ws.isiknowledge.com/WoS?recid=155852965#000245782500042~Demonstration of optically modulated dispersion forces~Y~","Reviews of Modern Physics~2009~81~G.L. Klimchitskaya, U. Mohideen and V.M. Mostepanenko~1827~The Casimir force between real materials: experiment and theory~N~","Journal of Physics A~2008~41~G.L. Klimchitskaya, U. Mohideen, and V.M. Mostepanenko~9~Thermal Casimir-Polder force between an atom and a dielectric plate: thermodynamics and experiment~N~","Journal of Physics A~2008~41~H-C. Chiu, C.C. Chang , R. Castillo-Garza, F. Chen, U. Mohideen~164022~Experimental procedures for precision measurements of the Casimir force with an atomic force microscope~N~","Physical Review B (Rapid Communication)~2009~80~H.C. Chiu, G.L. Klimchitskaya, V.N. Marachevsky, V.M. Mostepanenko, and U. Mohideen~121402~Demonstration of the assymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime~N~","Physical Review B~2010~81~HC. Chiu, G.L. Klimchitskaya, V.N. Marachevsky, V.M. Mostepanenko, U. Mohideen~115417~Lateral Casimir force between sinusoidally corrugated surfaces: Asymmetric profiles, deviations from the proximity force approximation, and comparison with exact theory~N~","JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL~2007~40~Klimchitskaya, GL; Mohideen, U; Mostepanenko, VM~10.1088/1751-8113/40/17/F0~F339~F346~http://wok-ws.isiknowledge.com/WoS?recid=156001631#000246085400004~Kramers-Kronig relations for plasma-like permittivities and the Casimir force~Y~","JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL~2007~40~Klimchitskaya, GL; Mohideen, U; Mostepanenko, VM~10.1088/1751-8113/40/34/F0~F841~F847~http://wok-ws.isiknowledge.com/WoS?recid=157408067#000248786600003~Pulsating Casimir force~Y~","Journal of Physics: Conference Series~2009~161~R.C. Castillo-Garza, C.C. Chang, Y. Dong, and U. Mohideen~012005~Customized silicon cantilevers for Casimir force experiments using focused ion beam milling~N~","Internation Journal of Modern Physics A~2009~24~V.M. Mostepanenko, R.S. Decca, E. Fischbach, B. Geyer, G.L. Klimchitskaya, D.E. Krause, D. Lopez and U. Mohideen~1721~Why screening effects do not influence the Casimir force~N~"],"startDate":"08/01/2007","title":"Investigation of the role of geometry, thermal photons and their interplay in the electromagnetic Casimir force","transType":"Continuing Grant","ueiNumber":"MR5QC5FCAVH5"},{"abstractText":"This award supports a research project to study the implications of a very unusual form of energy. The existence of this so-called ``negative energy'' is allowed by the laws of quantum field theory, which describe the behavior of matter and energy on microscopic scales. Negative energy would also have repulsive gravitational effects. Situations involving negative energy, such as the Casimir effect and squeezed states of light, have been produced in the laboratory. However, the amounts of negative energy generated in these experiments are extremely tiny and hence not directly measurable. However, if the laws of physics impose no constraints on negative energy, then one might be able to create large amounts of it and thereby produce bizarre macroscopic effects. Such effects could include: traversable wormholes (tunnels connecting otherwise distant regions of space and time), warp drives (for faster-than-light travel), time machines for travel into the past, violations of the second law of thermodynamics (e.g., refrigerators requiring no power sources), and the destruction of black holes (the remains of collapsed dead stars). However, research by L. Ford (Tufts U.) and the PI over more than a decade has shown that quantum field theory does impose some rather strong restrictions on negative energy. These constraints have come to be known as ``quantum inequalities,'' and yield severe limitations on the possible macroscopic effects mentioned above because they imply that large negative energies can exist for only short periods of time. The theoretical results obtained to date indicate that negative energy must be subtly intertwined with positive energy in space. An unanswered question is to what extent this must be true in general. Part of the research will be focused on narrowing the gap between distributions of negative energy which can be ruled out and those which are definitely allowed. The primary emphasis will be on a study of quantum states which involve negative energy and which can be produced using the techniques of quantum optics. A related, but smaller, part of the research will aim to study the connections between negative energy, energy conservation, and the evaporation and possible destruction of black holes.\r\nThis work lies at the intersection of, and deeply impacts, three important areas of physics: quantum field theory, Einstein's theory of gravity (general relativity), and thermodynamics. A primary goal of this research is to establish closer ties between this work on negative energy and the rapidly growing field of quantum optics. Such a link between these two areas of physics might allow experimental tests of at least the indirect effects of negative energy. The last ten years have seen the growth of a small but very active international group of researchers on the subject of negative energy. It is planned to involve undergraduates in this project.","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"CENTRAL CONNECTICUT STATE UNIVERSITY","awardeeAddress":"1615 STANLEY ST","awardeeCity":"NEW BRITAIN","awardeeCountryCode":"US","awardeeDistrict":"05","awardeeDistrictCode":"CT05","awardeeName":"Central Connecticut State University","awardeePhone":"8608322365","awardeeStateCode":"CT","awardeeZipCode":"060532439","cfdaNumber":"47.049","date":"08/02/2007","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"90000","expDate":"07/31/2011","fundAgencyCode":"4900","fundProgramName":"Gravity Theory","fundsObligated":["FY 2007 = $60,000.00","FY 2009 = $30,000.00"],"fundsObligatedAmt":"90000","histAwd":"false","id":"0652904","initAmendmentDate":"08/02/2007","jrnl":[{"artTitl":"Energy density-flux correlations in an unusual quantum state and in the vacuum","auth":"Ford, LH; Roman, TA","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevD.76.06401","jrnlTitl":"PHYSICAL REVIEW D","jrnlVol":"76","jrnlYr":"2007","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=158783967#000249786900050"},{"artPageNum":"2294","artTitl":"Effects of Vacuum Fluctuation Suppression on Atomic Decay Rates","auth":"L.H. Ford and T.A. Roman","authIndCode":"N","jrnlTitl":"Annals of Physics","jrnlVol":"326","jrnlYr":"2011"},{"artTitl":"Probability distributions of smeared quantum stress tensors","auth":"Fewster, CJ; Ford, LH; Roman, TA","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevD.81.12190","jrnlTitl":"PHYSICAL REVIEW D","jrnlVol":"81","jrnlYr":"2010","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=189349873#000278204700001"},{"artTitl":"Negative energy density in superposition and entangled states","auth":"Ford, LH; Roman, TA","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevD.77.04501","jrnlTitl":"PHYSICAL REVIEW D","jrnlVol":"77","jrnlYr":"2008","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=161461034#000253764800109"},{"artPageNum":"121901(R)","artTitl":"Probability Distributions of Smeared Quantum Stress-Tensors","auth":"Christopher J. Fewster, L.H. Ford and Thomas A. Roman","authIndCode":"N","dgtlObjId":"10.1103/PhysRevD.045018","jrnlTitl":"Physical Review D","jrnlVol":"81","jrnlYr":"2010"},{"artPageNum":"045018-1","artTitl":"Negative energy density in superposition and entangled states","auth":"L.H. Ford and Thomas A. Roman","authIndCode":"N","dgtlObjId":"10.1103/PhysRevD.045018","jrnlTitl":"Physical Review D","jrnlVol":"77","jrnlYr":"2008"},{"artPageNum":"064012","artTitl":"Energy density-flux correlations in an unusual quantum state and in the vacuum","auth":"L.H. Ford and Thomas A. Roman","authIndCode":"N","jrnlTitl":"Physical Review D","jrnlVol":"76","jrnlYr":"2007"}],"latestAmendmentDate":"04/30/2009","managingPec":"124400","orgCodeDir":"03000000","orgCodeDiv":"03010000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Physics","orgUrl":"http://www.nsf.gov/div/index.jsp?div=phy","parentUeiNumber":"","pdPIName":"Thomas A Roman","perfAddress":"1615 STANLEY ST","perfCity":"NEW BRITAIN","perfCountryCode":"US","perfDistrict":"05","perfDistrictCode":"CT05","perfLocation":"Central Connecticut State University","perfStateCode":"CT","perfZipCode":"060532439","pi":["Thomas A Roman roman@ccsu.edu"],"piEmail":"roman@ccsu.edu","piFirstName":"Thomas","piId":"269679179","piLastName":"Roman","piMiddeInitial":"A","poEmail":"pmarrone@nsf.gov","poName":"Pedro Marronetti","poPhone":"7032927372","primaryProgram":["01000910DB NSF RESEARCH & RELATED ACTIVIT","app-0107"],"progEleCode":"124400","program":"UNASSIGNED, PHYSICS OF THE UNIVERSE, RES IN UNDERGRAD INST-RESEARCH, OTHER RESEARCH OR EDUCATION","progRefCode":"0000, 7483, 9229, OTHR","publicAccessMandate":"0","publicationResearch":["PHYSICAL REVIEW D~2007~76~Ford, LH; Roman, TA~10.1103/PhysRevD.76.06401~http://wok-ws.isiknowledge.com/WoS?recid=158783967#000249786900050~Energy density-flux correlations in an unusual quantum state and in the vacuum~Y~","Annals of Physics~2011~326~L.H. Ford and T.A. Roman~2294~Effects of Vacuum Fluctuation Suppression on Atomic Decay Rates~N~","PHYSICAL REVIEW D~2010~81~Fewster, CJ; Ford, LH; Roman, TA~10.1103/PhysRevD.81.12190~http://wok-ws.isiknowledge.com/WoS?recid=189349873#000278204700001~Probability distributions of smeared quantum stress tensors~Y~","PHYSICAL REVIEW D~2008~77~Ford, LH; Roman, TA~10.1103/PhysRevD.77.04501~http://wok-ws.isiknowledge.com/WoS?recid=161461034#000253764800109~Negative energy density in superposition and entangled states~Y~","Physical Review D~2010~81~Christopher J. Fewster, L.H. Ford and Thomas A. Roman~10.1103/PhysRevD.045018~121901(R)~Probability Distributions of Smeared Quantum Stress-Tensors~N~","Physical Review D~2008~77~L.H. Ford and Thomas A. Roman~10.1103/PhysRevD.045018~045018-1~Negative energy density in superposition and entangled states~N~","Physical Review D~2007~76~L.H. Ford and Thomas A. Roman~064012~Energy density-flux correlations in an unusual quantum state and in the vacuum~N~"],"startDate":"08/01/2007","title":"RUI: Impact of Negative Energy in General Relativity and Quantum Field Theory","transType":"Continuing Grant","ueiNumber":"VWQNND6KLQQ5"},{"abstractText":"This IMR award supports the acquisition of a scanning probe microscope (SPM) operating in vacuum of 10-7 torr. Acquisition of the SPM will create the infrastructure to perform a series of experiments to investigate the fundamental interactions between surfaces with separations at the nanometer scale, including Casimir forces and non-contact friction. The vacuum environment, in combination with custom alterations to the sample chamber, will enable the operation of microelectromechanical devices simultaneously with the scanning head in the environmental chamber. The approach and distance feedback mechanism of the SPM head will be utilized in the measurement of the Casimir force using a microelectromechanical oscillator. The SPM will also be used to characterize surface imperfections, including the spatial mapping of surface potential and roughness. Such a complete characterization of the surface is essential in the fundamental test of the theory of Casimir forces. In addition to Casimir force measurements, the SPM will also be used to investigate novel non-conservative effects when closely spaced objects are in relative motion. Students participating in the experiments will acquire invaluable experience in scanning probe microscopy and in the design, fabrication and operation of microelectromechanical devices.\r\n\r\n\r\nThis IMR award supports the acquisition of a scanning probe microscope (SPM) operating in vacuum of 10-7 torr. Acquisition of the SPM will create the infrastructure to perform a series of experiments to investigate the fundamental interactions between surfaces with separations at the nanometer scale, including Casimir forces and non-contact friction. The vacuum environment, in combination with custom alterations to the sample chamber, minimizes viscous damping and enables the operation of microelectromechanical devices simultaneously with the scanning head. One of the areas to be pursued with the SPM is the study of Casimir forces. The Casimir effect is the attraction between two neutral metallic surfaces arising from the quantum fluctuations of the electromagnetic field. The approach and distance feedback mechanism of the SPM head will be utilized in the measurement of the Casimir force using a microelectromechanical oscillator. Even though the Casimir force has been experimentally verified by a number of experimental teams, surface imperfections introduce non-negligible corrections to the Casimir force. The SPM will be used to characterize and optimize various surface imperfections. In addition to Casimir force measurements, the SPM will also be used to investigate novel non-conservative effects when closely spaced objects are in relative motion. Students participating in the experiments will acquire invaluable experience in scanning probe microscopy and in the design, fabrication and operation of microelectromechanical devices.\r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"UNIVERSITY OF FLORIDA","awardeeAddress":"1523 UNION RD RM 207","awardeeCity":"GAINESVILLE","awardeeCountryCode":"US","awardeeDistrict":"03","awardeeDistrictCode":"FL03","awardeeName":"University of Florida","awardeePhone":"3523923516","awardeeStateCode":"FL","awardeeZipCode":"326111941","cfdaNumber":"47.049","date":"08/24/2004","dirAbbr":"MPS","divAbbr":"DMR","estimatedTotalAmt":"157883","expDate":"08/31/2006","fundAgencyCode":"4900","fundProgramName":"MPS DMR INSTRUMENTATION","fundsObligated":["FY 2004 = $157,883.00"],"fundsObligatedAmt":"157883","histAwd":"false","id":"0414595","initAmendmentDate":"08/24/2004","latestAmendmentDate":"08/24/2004","managingPec":"175000","orgCodeDir":"03000000","orgCodeDiv":"03070000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Materials Research","orgUrl":"http://www.nsf.gov/div/index.jsp?div=dmr","parentUeiNumber":"","pdPIName":"Ho Bun Chan","perfAddress":"1523 UNION RD RM 207","perfCity":"GAINESVILLE","perfCountryCode":"US","perfDistrict":"03","perfDistrictCode":"FL03","perfLocation":"University of Florida","perfStateCode":"FL","perfZipCode":"326111941","pi":["Ho Bun Chan hochan@phys.ufl.edu"],"piEmail":"hochan@phys.ufl.edu","piFirstName":"Ho Bun","piId":"269745714","piLastName":"Chan","poEmail":"","poName":"Charles E. Bouldin","poPhone":"","primaryProgram":["app-0104"],"progEleCode":"175000","program":"SINGLE DIVISION/UNIVERSITY, ADVANCED MATERIALS & PROCESSING PROGRAM","progRefCode":"9161, AMPP","publicAccessMandate":"0","startDate":"09/01/2004","title":"IMR: Acquisition of a Scanning Probe Microscope for Investigating Fundamental Interactions between Surfaces and Student Training","transType":"Standard Grant","ueiNumber":"NNFQH1JAPEP3"},{"abstractText":"The research discussed here deals with the implications of a very unusual form of energy. The existence of this so-called \"negative energy\" is allowed by the laws of quantum field theory, which describe the behavior of matter and energy on microscopic scales. Since negative energy would have repulsive gravitational effects, this work lies at the intersection of quantum field theory and Einstein's theory of gravity, general relativity. The focus of the research is the extended investigation of restrictions imposed by the laws of physics on negative energy. These generalized restrictions would involve the placement of constraints on the distribution of negative energy in both time and space. In addition, the scope of the constraints would be extended to include the effects of gravitation. Regions of negative energy also appear to be accompanied by large fluctuations in energy density, which could perhaps lead to large fluctuations in the gravitational fields produced by the negative energy. How this would affect the description of gravity, given in Einstein's theory as the curvature of the geometry of space and time, in these circumstances is currently not well understood. It is hoped to investigate this issue as well.\r\n\r\nThese topics are of interest for several reasons. Situations involving negative energy, such as the Casimir effect and squeezed states of light, have been produced in the laboratory. The amounts of negative energy generated in these experiments are extremely tiny. However, if the laws of physics impose no constraints on negative energy, then one might be able to create large amounts of it and thereby produce bizarre macroscopic effects. Such effects could include: traversable wormholes (tunnels connecting otherwise distant regions of space and time), warp drives (for faster-than-light travel), time machines for travel into the past, violations of the second law of thermodynamics (e.g., refrigerators requiring no power sources), and the destruction of black holes (the remains of collapsed dead stars). However, research by Larry Ford and the author has shown that quantum field theory does impose some rather strong restrictions on negative energy. These constraints have come to be known as \"quantum inequalities\", and yield severe limitations on the macroscopic effects of negative energy mentioned above. Loosely speaking, they say that large negative energies can exist for only short periods of time. It has recently been realized that even the currently known quantum inequalities, although formulated as restrictions in time, can be used to rule out or constrain the ways in which negative energy can be distributed in space as well. These results, together with some explicit examples of spatial distributions of negative energy which are allowed by the laws of physics, indicate that negative energy must be subtly intertwined with positive energy in space. Must this always be the case? A major focus of the proposed investigation will be to narrow the gap between distributions which can be ruled out and those which are definitely allowed. The latter will involve the construction and analysis of additional explicit examples. This represents a continuation of my previous research and essentially aims to extend the scope of all of these results.\r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"CENTRAL CONNECTICUT STATE UNIVERSITY","awardeeAddress":"1615 STANLEY ST","awardeeCity":"NEW BRITAIN","awardeeCountryCode":"US","awardeeDistrict":"05","awardeeDistrictCode":"CT05","awardeeName":"Central Connecticut State University","awardeePhone":"8608322365","awardeeStateCode":"CT","awardeeZipCode":"060532439","cfdaNumber":"47.049","date":"05/21/2002","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"50000","expDate":"07/31/2005","fundAgencyCode":"4900","fundProgramName":"Gravity Theory","fundsObligated":["FY 2002 = $50,000.00"],"fundsObligatedAmt":"50000","histAwd":"false","id":"0139969","initAmendmentDate":"05/21/2002","latestAmendmentDate":"05/21/2002","managingPec":"124400","orgCodeDir":"03000000","orgCodeDiv":"03010000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Physics","orgUrl":"http://www.nsf.gov/div/index.jsp?div=phy","parentUeiNumber":"","pdPIName":"Thomas A Roman","perfAddress":"1615 STANLEY ST","perfCity":"NEW BRITAIN","perfCountryCode":"US","perfDistrict":"05","perfDistrictCode":"CT05","perfLocation":"Central Connecticut State University","perfStateCode":"CT","perfZipCode":"060532439","pi":["Thomas A Roman roman@ccsu.edu"],"piEmail":"roman@ccsu.edu","piFirstName":"Thomas","piId":"269679179","piLastName":"Roman","piMiddeInitial":"A","poEmail":"","poName":"Beverly K. Berger","poPhone":"","primaryProgram":["app-0102"],"progEleCode":"124400","program":"UNASSIGNED, RES IN UNDERGRAD INST-RESEARCH, OTHER RESEARCH OR EDUCATION","progRefCode":"0000, 9229, OTHR","publicAccessMandate":"0","startDate":"08/01/2002","title":"RUI: Constraints on Negative Energy in Field Theory and Gravitation","transType":"Standard Grant","ueiNumber":"VWQNND6KLQQ5"},{"abstractText":"The effects of a network of cosmic strings in our universe will examined in light of recent progress in understanding the formation of structure on these networks. The principle concerns are gravitational radiation emission, the perturbations in the temperature of the cosmic background radiation, and the formation of large-scale structure in the universe. Aspects of quantum gravity associated with noneuclidean topology, and related problems involving closed timelike curves, will be examined. The Casimir effect will be studied as a method for supporting the throat of a traversable wormhole against gravitational collapse. Research in general-relativistic astrophysics will include efforts to portray the spin-down of rapidly rotating neutron stars and to extend work on normal modes, stability and equilibrium configurations of relativistic stars and black holes. Observations during the next decade may well fix the upper limit on neutron star rotation, and comparison with the theoretical limit would then sharply constrain the equation of state of neutron star matter. The properties of matter compressed to very high densities by gravitational collapse will be studied as a possible mechanism for avoiding the formation of singularities in general relativity. New methods will be developed for the numerical integration of the generalized Einstein equations containing higher derivative perturbative terms.","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"UNIVERSITY OF WISCONSIN SYSTEM","awardeeAddress":"3203 N DOWNER AVE # 273","awardeeCity":"MILWAUKEE","awardeeCountryCode":"US","awardeeDistrict":"04","awardeeDistrictCode":"WI04","awardeeName":"University of Wisconsin-Milwaukee","awardeePhone":"4142294853","awardeeStateCode":"WI","awardeeZipCode":"532113153","cfdaNumber":"47.049","coPDPI":["John L Friedman friedman@csd.uwm.edu","Leonard E Parker leonard@uwm.edu"],"date":"06/19/1991","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"765010","expDate":"12/31/1995","fundAgencyCode":"4900","fundProgramName":"Gravity Theory","fundsObligated":["FY 1991 = $164,774.00","FY 1992 = $190,402.00","FY 1993 = $199,919.00","FY 1994 = $209,915.00"],"fundsObligatedAmt":"765010","histAwd":"false","id":"9105935","initAmendmentDate":"06/19/1991","latestAmendmentDate":"03/25/1994","managingPec":"124400","orgCodeDir":"03000000","orgCodeDiv":"03010000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Physics","orgUrl":"http://www.nsf.gov/div/index.jsp?div=phy","parentUeiNumber":"","pdPIName":"Bruce Allen","perfAddress":"","perfCity":"","perfCountryCode":"","perfDistrict":"","perfDistrictCode":"","perfLocation":"DATA NOT AVAILABLE","perfStateCode":"","perfZipCode":"","pi":["Bruce Allen ballen@uwm.edu"],"piEmail":"ballen@uwm.edu","piFirstName":"Bruce","piId":"000156403","piLastName":"Allen","poEmail":"","poName":"Richard Isaacson","poPhone":"","primaryProgram":["","app-0193","app-0194"],"progEleCode":"124400","program":"UNASSIGNED, OTHER RESEARCH OR EDUCATION","progRefCode":"0000, OTHR","publicAccessMandate":"0","startDate":"07/01/1991","title":"Classical and Quantum Gravitation and Cosmology","transType":"Continuing Grant","ueiNumber":"JBQ9M3PLFDP5"},{"abstractText":"The most promising area to detect long range forces and the Casimir effect lies in electromagnetic interactions. However, the hope of observing this interaction between a pair of atoms is extremely small. Recent precision experiments on the fine structure of helium Rydberg states has given rise to the hope of observing the Casimir interaction between the highly excited electron and the core atom even though for the states studied experimentally, the Rydberg electron is not quite in the asymptotic region where the Casimer effect manifests itself in a pronounced way. A thorough relativistic quantum field theoretic evaluation of the two photon exchange potential in the electron- ion interaction for all distances beyond a few Bohr radii has been carried out recently, and a variety of corrections comparable to the Casimir effect have been estimated. An accurate verification of the Casimir effect seems to be within reach of both theory and experiment. In this proposal, The principal investigator describes recent progress made and plans to improve on the calculations and extend the investigation to a variety of systems of interest.","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"UNIVERSITY OF SOUTH CAROLINA","awardeeAddress":"1600 HAMPTON ST","awardeeCity":"COLUMBIA","awardeeCountryCode":"US","awardeeDistrict":"06","awardeeDistrictCode":"SC06","awardeeName":"University of South Carolina at Columbia","awardeePhone":"8037777093","awardeeStateCode":"SC","awardeeZipCode":"292083403","cfdaNumber":"47.049","date":"07/22/1987","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"95000","expDate":"07/31/1991","fundAgencyCode":"4900","fundProgramName":"THEORETICAL PHYSICS","fundsObligated":["FY 1987 = $30,000.00","FY 1988 = $65,000.00"],"fundsObligatedAmt":"95000","histAwd":"false","id":"8710118","initAmendmentDate":"07/22/1987","latestAmendmentDate":"07/27/1988","managingPec":"124500","orgCodeDir":"03000000","orgCodeDiv":"03010000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Physics","orgUrl":"http://www.nsf.gov/div/index.jsp?div=phy","parentUeiNumber":"Q93ZDA59ZAR5","pdPIName":"Chi-Kwan Au","perfAddress":"","perfCity":"","perfCountryCode":"","perfDistrict":"","perfDistrictCode":"","perfLocation":"DATA NOT AVAILABLE","perfStateCode":"","perfZipCode":"","pi":["Chi-Kwan Au"],"piFirstName":"Chi-Kwan","piId":"000050225","piLastName":"Au","poEmail":"","poName":"name not available","poPhone":"","primaryProgram":[""],"progEleCode":"124500","program":"","progRefCode":"","publicAccessMandate":"0","startDate":"08/15/1987","title":"Long Range Electromagnetic Interaction and the Casimir Effect (Physics)","transType":"Continuing Grant","ueiNumber":"J22LNTMEDP73"},{"activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"UNIVERSITY OF SOUTH CAROLINA","awardeeAddress":"1600 HAMPTON ST","awardeeCity":"COLUMBIA","awardeeCountryCode":"US","awardeeDistrict":"06","awardeeDistrictCode":"SC06","awardeeName":"University of South Carolina at Columbia","awardeePhone":"8037777093","awardeeStateCode":"SC","awardeeZipCode":"292083403","cfdaNumber":"47.049","date":"07/26/1985","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"41000","expDate":"01/31/1988","fundAgencyCode":"4900","fundProgramName":"THEORETICAL PHYSICS","fundsObligated":["FY 1985 = $41,000.00"],"fundsObligatedAmt":"41000","histAwd":"false","id":"8510642","initAmendmentDate":"07/26/1985","latestAmendmentDate":"07/26/1985","managingPec":"124500","orgCodeDir":"03000000","orgCodeDiv":"03010000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Physics","orgUrl":"http://www.nsf.gov/div/index.jsp?div=phy","parentUeiNumber":"Q93ZDA59ZAR5","pdPIName":"Chi-Kwan Au","perfAddress":"","perfCity":"","perfCountryCode":"","perfDistrict":"","perfDistrictCode":"","perfLocation":"DATA NOT AVAILABLE","perfStateCode":"","perfZipCode":"","pi":["Chi-Kwan Au"],"piFirstName":"Chi-Kwan","piId":"000050225","piLastName":"Au","poEmail":"","poName":"name not available","poPhone":"","primaryProgram":[""],"progEleCode":"124500","program":"","progRefCode":"","publicAccessMandate":"0","startDate":"08/15/1985","title":"Two Photon Exchange Potential and the Casimir Effect in Rydberg States and in Between Atoms (Physics)","transType":"Standard Grant","ueiNumber":"J22LNTMEDP73"}],"metadata":{"offset":0,"rpp":25,"totalCount":24}}}
![\"Casimir](\"/por/images/Reports/POR/2022/2019288/2019288_10576079_1672511864212_Torque_image--rgov-66x44.jpg\")
\n\n\nDepiction of the Casimir torque.\nJeremy Munday\nCopyrighted\nJeremy Munday\nCasimir torque\n \n![\"Casimir](\"/por/images/Reports/POR/2022/2019288/2019288_10576079_1672511864212_Torque_image--rgov-214x142.jpg\")