We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions....We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulations. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, the amplitude of scattered photons is high for lower modulation amplitude than higher modulation amplitude. We also found that the behavior of the plots are similar under strong and weak modulations for the quantized mirror motion.展开更多
While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null...While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect.展开更多
The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet str...The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.展开更多
The Casimir energy of massive scalar field with hybrid （Diriehlet-Neumann） boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green＇s function...The Casimir energy of massive scalar field with hybrid （Diriehlet-Neumann） boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green＇s function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field＇s mass. When the field is massless, the result is consistent with previous literatures.展开更多
We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field i...We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field in the presence of dielectricsl where the physical meaning of ＂evanescent mode＂ is discussed. The Lifshitz＇s formula is rederived using all the vacuum mode functions, which include the contribution of the ＇evanescent modes＇. Only in the case of the perfect, metallic plates will the evanescent modes become unimportant.展开更多
We discuss the Casimir effect for massless scalar fields subject to the Diriehlet boundary conditions on the parallel plates at finite temperature in the presence of one fraetal extra eompactified dimension. We obtain...We discuss the Casimir effect for massless scalar fields subject to the Diriehlet boundary conditions on the parallel plates at finite temperature in the presence of one fraetal extra eompactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sumciently high, the sign of the Casimir energy remains negative no matter how great the scale dimension 6 is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.展开更多
We present analytical solutions describing quantized vacuum field in a one-dimensional cavity with one of its two mirrors fixed and another vibrating in simple harmonic form. These solutions are accurate up to the sec...We present analytical solutions describing quantized vacuum field in a one-dimensional cavity with one of its two mirrors fixed and another vibrating in simple harmonic form. These solutions are accurate up to the second order of the oscillating magnitude and they are uniformly valid for all time. We obtain the simple analytical expression for the energy density of the field which explicitly manifests that for a cavity vibrating at its -th eigenfrequency, traveling wave packets emerge in the finite part of the field energy density, and their amplitudes grow while their widths shrink in time, representing a large concentration of energy. The finite part of the field energy density originating from the oscillations is shown to be proportional to the factor .展开更多
The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field wit...The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet and Neumann boundary conditions are also discussed.展开更多
A rigorous model for the electron is presented by generalizing the Coulomb’s Law or Gauss’s Law of electrostatics, using a unified theory of electricity and gravity. The permittivity of the free-space is allowed to ...A rigorous model for the electron is presented by generalizing the Coulomb’s Law or Gauss’s Law of electrostatics, using a unified theory of electricity and gravity. The permittivity of the free-space is allowed to be variable, dependent on the energy density associated with the electric field at a given location, employing generalized concepts of gravity and mass/energy density. The electric field becomes a non-linear function of the source charge, where the concept of the energy density needs to be properly defined. Stable solutions are derived for a spherically symmetric, surface-charge distribution of an elementary charge. This is implemented by assuming that the gravitational field and its equivalent permittivity function is proportional to the energy density, as a simple first-order approximation, with the constant of proportionality, referred to as the Unified Electro-Gravity (UEG) constant. The stable solution with the lowest mass/energy is assumed to represent a “static” electron without any spin. Further, assuming that the mass/energy of a static electron is half of the total mass/energy of an electron including its spin contribution, the required UEG constant is estimated. More fundamentally, the lowest stable mass of a static elementary charged particle, its associated classical radius, and the UEG constant are related to each other by a dimensionless constant, independent of any specific value of the charge or mass of the particle. This dimensionless constant is numerologically found to be closely related to the fine structure constant. This possible origin of the fine structure constant is further strengthened by applying the proposed theory to successfully model the Casimir effect, from which approximately the same above relationship between the UEG constant, electron’s mass and classical radius, and the fine structure constant, emerges.展开更多
The Casimir effect results from the zero-point energy of vacuum. A spherical cavity can be divided into three regions, and we make an analysis of every region and then give a formal solution of Casimir energy. The zet...The Casimir effect results from the zero-point energy of vacuum. A spherical cavity can be divided into three regions, and we make an analysis of every region and then give a formal solution of Casimir energy. The zeta-function regularization is also used to dispel the divergence of the summation. At the end, we can see the Casimir effect of a single sphere is included in our results.展开更多
The zeta function regularization technique is used to study the Casimir effect for a scalar field of mass m satisfying Dirichlet boundary conditions on a spherical surface of radius a. In the case of large scalar mass...The zeta function regularization technique is used to study the Casimir effect for a scalar field of mass m satisfying Dirichlet boundary conditions on a spherical surface of radius a. In the case of large scalar mass, , simple analytic expressions are obtained for the zeta function and Casimir energy of the scalar field when it is confined inside the spherical surface, and when it is confined outside the spherical surface. In both cases the Casimir energy is exact up to order and contains the expected divergencies, which can be eliminated using the well established renormalization procedure for the spherical Casimir effect. The case of a scalar field present in both the interior and exterior region is also examined and, for , the zeta function, the Casimir energy, and the Casimir force are obtained. The obtained Casimir energy and force are exact up to order and respectively. In this scenario both energy and force are finite and do not need to be renormalized, and the force is found to produce an outward pressure on the spherical surface.展开更多
We investigate the possibility of observing in integrated solid-state systems the dynamical Casimir effect,in which photons are created out of vacuum.We use a transmission line resonator on a superconducting chip as t...We investigate the possibility of observing in integrated solid-state systems the dynamical Casimir effect,in which photons are created out of vacuum.We use a transmission line resonator on a superconducting chip as the microwave cavity and modulate its properties by coupling it to carefully designed Josephson devices.We evaluate the effect of main decoherence sources and show that our design offers a promising system for experimentally demonstrating the dynamical Casimir effect.Moreover,we also study the squeezing properties of the created photon field and how they depend on the dissipation.展开更多
We design dynamical Casimir arrays(DCA)consisting of giant atoms and coupled resonator waveguides(CRWs)to investigate the Einstein–Podolsky–Rosen(EPR)steering at finite temperatures.Our designed system exhibits an a...We design dynamical Casimir arrays(DCA)consisting of giant atoms and coupled resonator waveguides(CRWs)to investigate the Einstein–Podolsky–Rosen(EPR)steering at finite temperatures.Our designed system exhibits an asymmetry in its structure,which is caused by the differences in the sizes and the coupling positions of the giant atoms.The system achieves different types of EPR steering and the reversal of one-way EPR steering by modulating parameters.Furthermore,the symmetry and asymmetry of the system structure,in their responses to parameter modulation,both reveal the asymmetry of EPR steering.In this process,we discover that with the increase in temperature,different types of steering can be transferred from Casimir photons to giant atoms.We also achieve the monogamy of the multipartite system.These results provide important assistance for secure quantum communication,and further intuitively validating the asymmetry of EPR steering from multiple perspectives.展开更多
A basically topological interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. This new interpretation complime...A basically topological interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so called missing dark energy density of the cosmos. We start with a general outline of the theoretical principle and basic design concepts of a proposed Casimir dark energy nano reactor. In a nutshell the theory and consequently the actual design depends crucially upon the equivalence between the dark energy density of the cosmos and the faint local Casimir effect produced by two sides boundary condition quantum waves. This Casimir effect is then colossally amplified as a one sided quantum wave pushing from the inside on the one sided M?bius-like boundary with nothing balancing it from the non-existent outside. In view of the present theory, this one sided M?bius-like boundary of the holographic boundary of the universe is essentially what leads to the observed accelerated expansion of the cosmos. Thus in principle we will restructure the local topology of space using material nanoscience technology to create an artificial local high dimensionality with a Dvoretzky theorem like volume measure concentration. Needless to say the entire design is based completely on the theory of quantum wave dark energy proposed by the present author. The quintessence of the present theory is easily explained as the intrinsic Casimir topological energy where produced from the zero set of the quantum particle when we extract the empty set quantum wave from it and find by restructuring space via plates similar to that of the classical Casimir experiments but with some modification.展开更多
文摘We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulations. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, the amplitude of scattered photons is high for lower modulation amplitude than higher modulation amplitude. We also found that the behavior of the plots are similar under strong and weak modulations for the quantized mirror motion.
文摘While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect.
文摘The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.
基金supported by National Natural Science Foundation of China under Grant Nos.10773002 and 10875012the National Fundamental Research Program of China under Grant No.2003CB716302
文摘The Casimir energy of massive scalar field with hybrid （Diriehlet-Neumann） boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green＇s function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field＇s mass. When the field is massless, the result is consistent with previous literatures.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2003CB716300 and National Natural Science Foundation of China under Grant No. 10121503
文摘We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field in the presence of dielectricsl where the physical meaning of ＂evanescent mode＂ is discussed. The Lifshitz＇s formula is rederived using all the vacuum mode functions, which include the contribution of the ＇evanescent modes＇. Only in the case of the perfect, metallic plates will the evanescent modes become unimportant.
基金Supported by National Natural Science Foundation of China under Grant No.10875043partly by the Shanghai Research Foundation under Grant No.07dz22020
文摘We discuss the Casimir effect for massless scalar fields subject to the Diriehlet boundary conditions on the parallel plates at finite temperature in the presence of one fraetal extra eompactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sumciently high, the sign of the Casimir energy remains negative no matter how great the scale dimension 6 is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.
文摘We present analytical solutions describing quantized vacuum field in a one-dimensional cavity with one of its two mirrors fixed and another vibrating in simple harmonic form. These solutions are accurate up to the second order of the oscillating magnitude and they are uniformly valid for all time. We obtain the simple analytical expression for the energy density of the field which explicitly manifests that for a cavity vibrating at its -th eigenfrequency, traveling wave packets emerge in the finite part of the field energy density, and their amplitudes grow while their widths shrink in time, representing a large concentration of energy. The finite part of the field energy density originating from the oscillations is shown to be proportional to the factor .
基金The project supported partly by National Natural Science Foundation of China under Grant Nos. 10373003, 10475013, and NBRPC under Grant No. 2003CB716302
文摘The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet and Neumann boundary conditions are also discussed.
文摘A rigorous model for the electron is presented by generalizing the Coulomb’s Law or Gauss’s Law of electrostatics, using a unified theory of electricity and gravity. The permittivity of the free-space is allowed to be variable, dependent on the energy density associated with the electric field at a given location, employing generalized concepts of gravity and mass/energy density. The electric field becomes a non-linear function of the source charge, where the concept of the energy density needs to be properly defined. Stable solutions are derived for a spherically symmetric, surface-charge distribution of an elementary charge. This is implemented by assuming that the gravitational field and its equivalent permittivity function is proportional to the energy density, as a simple first-order approximation, with the constant of proportionality, referred to as the Unified Electro-Gravity (UEG) constant. The stable solution with the lowest mass/energy is assumed to represent a “static” electron without any spin. Further, assuming that the mass/energy of a static electron is half of the total mass/energy of an electron including its spin contribution, the required UEG constant is estimated. More fundamentally, the lowest stable mass of a static elementary charged particle, its associated classical radius, and the UEG constant are related to each other by a dimensionless constant, independent of any specific value of the charge or mass of the particle. This dimensionless constant is numerologically found to be closely related to the fine structure constant. This possible origin of the fine structure constant is further strengthened by applying the proposed theory to successfully model the Casimir effect, from which approximately the same above relationship between the UEG constant, electron’s mass and classical radius, and the fine structure constant, emerges.
基金Supported by the Major Project of Knowledge Innovation Project of the Chinese Acedamy of Sciences(No.KJCX2-SW-N02
文摘The Casimir effect results from the zero-point energy of vacuum. A spherical cavity can be divided into three regions, and we make an analysis of every region and then give a formal solution of Casimir energy. The zeta-function regularization is also used to dispel the divergence of the summation. At the end, we can see the Casimir effect of a single sphere is included in our results.
文摘The zeta function regularization technique is used to study the Casimir effect for a scalar field of mass m satisfying Dirichlet boundary conditions on a spherical surface of radius a. In the case of large scalar mass, , simple analytic expressions are obtained for the zeta function and Casimir energy of the scalar field when it is confined inside the spherical surface, and when it is confined outside the spherical surface. In both cases the Casimir energy is exact up to order and contains the expected divergencies, which can be eliminated using the well established renormalization procedure for the spherical Casimir effect. The case of a scalar field present in both the interior and exterior region is also examined and, for , the zeta function, the Casimir energy, and the Casimir force are obtained. The obtained Casimir energy and force are exact up to order and respectively. In this scenario both energy and force are finite and do not need to be renormalized, and the force is found to produce an outward pressure on the spherical surface.
基金supported by the National Natural Science Foundation of China(Grant No.11174270)the National Basic Research Program of China(Grant Nos.2011CB921204 and 2011CBA00200)+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB01000000)ZHOU Zheng Wei gratefully acknowledges the support of theK.C.Wong Education Foundation,Hong Kong
文摘We investigate the possibility of observing in integrated solid-state systems the dynamical Casimir effect,in which photons are created out of vacuum.We use a transmission line resonator on a superconducting chip as the microwave cavity and modulate its properties by coupling it to carefully designed Josephson devices.We evaluate the effect of main decoherence sources and show that our design offers a promising system for experimentally demonstrating the dynamical Casimir effect.Moreover,we also study the squeezing properties of the created photon field and how they depend on the dissipation.
基金Project supported by the Education Department of Jilin Province,China(Grant No.JJKH20231291KJ)。
文摘We design dynamical Casimir arrays(DCA)consisting of giant atoms and coupled resonator waveguides(CRWs)to investigate the Einstein–Podolsky–Rosen(EPR)steering at finite temperatures.Our designed system exhibits an asymmetry in its structure,which is caused by the differences in the sizes and the coupling positions of the giant atoms.The system achieves different types of EPR steering and the reversal of one-way EPR steering by modulating parameters.Furthermore,the symmetry and asymmetry of the system structure,in their responses to parameter modulation,both reveal the asymmetry of EPR steering.In this process,we discover that with the increase in temperature,different types of steering can be transferred from Casimir photons to giant atoms.We also achieve the monogamy of the multipartite system.These results provide important assistance for secure quantum communication,and further intuitively validating the asymmetry of EPR steering from multiple perspectives.
文摘A basically topological interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so called missing dark energy density of the cosmos. We start with a general outline of the theoretical principle and basic design concepts of a proposed Casimir dark energy nano reactor. In a nutshell the theory and consequently the actual design depends crucially upon the equivalence between the dark energy density of the cosmos and the faint local Casimir effect produced by two sides boundary condition quantum waves. This Casimir effect is then colossally amplified as a one sided quantum wave pushing from the inside on the one sided M?bius-like boundary with nothing balancing it from the non-existent outside. In view of the present theory, this one sided M?bius-like boundary of the holographic boundary of the universe is essentially what leads to the observed accelerated expansion of the cosmos. Thus in principle we will restructure the local topology of space using material nanoscience technology to create an artificial local high dimensionality with a Dvoretzky theorem like volume measure concentration. Needless to say the entire design is based completely on the theory of quantum wave dark energy proposed by the present author. The quintessence of the present theory is easily explained as the intrinsic Casimir topological energy where produced from the zero set of the quantum particle when we extract the empty set quantum wave from it and find by restructuring space via plates similar to that of the classical Casimir experiments but with some modification.
