Oscillating Casimir force between two slabs in a Fermi sea

The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures.It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas.In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas,the Casimir force in a Fermi gas oscillates as a function of L.The Casimir force can be either attractive or repulsive,depending sensitively on the magnitude of L.In addition,it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature,which also is contrary to the case in a Bose gas,since the bosonic Casimir force increases linearly with the increase of the temperature in the region T相似文献   

Magnetic field effects in the Casimir force between two parallel anti-ferromagnetic slabs

We study the Casimir force F$F$ between two parallel anti-ferromagnetic slabs taking into account an external magnetic field in the Voigt configuration. Using a frequency and magnetic field dependent magnetic permeability tensor and a frequency independent dielectric permittivity, to describe the slabs, we calculate the Casimir force using non-normal incidence reflectivity of the electromagnetic waves in the free space between the slabs. We determine the Casimir force by performing two-dimensional calculations. F$F$ is investigated as a function of the layer thickness d$d$, the vacuum gap width L$L$ between slabs, and the external magnetic field strength H$H$. Features of F$F$ as function of the external field include the presence of sharp dips and peaks, which appear in the vicinity of the resonance frequency, and are consequences of the interaction of the external magnetic field with the electron spin. In addition, an external field may diminish F$F$, which is an important effect not found in any other system.     

Dynamical Casimir Effect in a Cavity with a Resonantly Oscillating Boundary

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 q-th (q≥2) eigenfrequency, q traveling wave packets emerge in the finite part of the field energy density,and their amplitudes grow 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(q^2-1).     

Casimir force in presence of multi layer magnetodielectric slabs

By using the path-integral formalism, electromagnetic field in the presence of some linear, isotropic magnetodielectric slabs is quantized and related correlation functions are found. In the framework of path-integral techniques, Casimir force between two infinitely large, parallel and ideal conductors, with a different number of magnetodielectric slabs in between, is obtained by calculating the Green’s function corresponding to each geometry.     

Casimir force on a piston at finite temperature in Randall-Sundrum models

The Casimir effect for a three-parallel-plate system at finite temperature within the framework of five-dimensional Randall-Sundrum models is studied. In the case of the Randall-Sundrum model involving two branes we find that the Casimir force depends on the plate distance and temperature after one outer plate has been moved to a distant place. Further we discover that the sign of the reduced force is negative if the plate and piston are located close together, but the nature of reduced force becomes repulsive when the plate distance is not very small and finally the repulsive force vanishes with extremely large plate separation. A higher temperature causes a greater repulsive Casimir force. Within the framework of a one-brane scenario the reduced Casimir force between the piston and one plate remains attractive no matter how high the temperature is. It is interesting that a stronger thermal effect leads to a greater attractive Casimir force instead of changing the nature of the force.     

Generating large steady-state optomechanical entanglement by the action of Casimir force

In this paper,we study an optomechanical device consisting of a Fabry-P′erot cavity with two dielectric nanospheres trapped near the cavity mirrors by an external driving laser.In the condition where the distances between the nanospheres and cavity mirrors are small enough,the Casimir force helps the optomechanical coupling to induce a steady-state optomechanical entanglement of the mechanical and optical modes in a certain regime of parameters.We investigate in detail the dependence of the steadystate optomechanical entanglement on external control parameters of the system,i.e.,the effective detuning,the pump powers of the cavity,the cavity decay rate and the wavelength of the driving field.It is found that the large steady-state optomechanical entanglement,i.e.EN=5.76,can be generated with experimentally feasible parameters,i.e.the pump power P=18.2μW,the cavity decay rateκ=0.5 MHz and the wavelength of the laserλL=1064 nm,which should be checked by optical measurement.     

Parameter estimation in dynamic Casimir force measurements with known periodicity

It is important to have an accurate estimate of the unknown parameters such as the separation distance between interacting materials in Casimir force measurements. Current methods tend to produce large estimation errors. In this Letter, we present a novel method based on an adaptive control approach to estimate the unknown parameters using large amplitude dynamic Casimir measurements at separation distances of below 1 μm where both electrostatic force and Casimir force are significant. The estimate is proved to be accurate and the effectiveness of our method is demonstrated via a numerical example.     

Repulsive Casimir force between silicon dioxide and superconductor

We present a detailed investigation of the Casimir interaction between the superconductor Bi₂Sr₂CaCu₂O_8+δ (BSCCO) and silicon dioxide with bromobenzene present in between. We found that the dispersion force is repulsive and the magnitude of the force can be changed by varying the thickness of the object and the temperature. The repulsive force would provide a method to deal with stiction problems and provide much significant from the practical point of view. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polaron and molecular states of a spin–orbit coupled impurity in a spinless Fermi sea

We investigate the polaron and molecular states of a fermionic atom with one-dimensional spin–orbit coupling(SOC)coupled to a three-dimensional spinless Fermi sea. Because of the interplay among the SOC, Raman coupling and spinselected interatomic interactions, the polaron state induced by the spin–orbit coupled impurity exhibits quite unique features. We find that the energy dispersion of the polaron generally has a double-minimum structure, which results in a finite center-of-mass(c.m.) momentum in the ground state, different from the zero-momentum polarons where SOC are introduced into the majority atoms. By further tuning the parameters such as the atomic interaction strength, a discontinuous transition between the polarons with different c.m. momenta may occur, signaled by the singular behavior of the quasiparticle residue and effective mass of the polaron. Meanwhile, the molecular state as well as the polaron-to-molecule transition is also strongly affected by the Raman coupling and the effective Zeeman field, which are introduced by the lasers generating SOC on the impurity atom. We also discuss the effects of a more general spin-dependent interaction and mass ratio. These results would be beneficial for the study of impurity physics brought by SOC.     

硬球势中相对论费米气体的热力学性质

用量子统计与数值模拟相结合的方法,在广义外势中相对论费米系统的热力学量的基础上,研究硬球势中相对论费米气体的热力学性质.得到了考虑相对论效应时系统的内能和热容量的解析表达式,分析了相对论效应对内能和热容量的影响.研究表明:与非相对论比较,相对论费米气体的内能和热容量更高;相对论特征量越大,热容量的转折温度越低;随着温度的升高,特征量越大,内能就越大.     

Finite-size effects in a D-dimensional ideal Fermi gas

By using the Euler-MacLaurin formula,this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container.The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed.It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy.It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects,such as the nonextensivity of the system,the anisotropy of the pressure,and so on.     

Relativistic thermodynamic properties of a weakly interacting Fermi gas in a weak magnetic field

This paper derives the analytical expression of free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the methods of quantum statistics as well as considering the relativistic effect. Based on the derived expression, the thermodynamic properties of the system at both high and low temperatures are given and the relativistic effect on the properties of the system is discussed. It shows that, in comparison with a nonrelativistic situation, the relativistic effect changes the influence of temperature on the thermodynamic properties of the system at high temperatures, and changes the influence of particle-number density on them at extremely low temperature. But the relativistic effect does not change the influence of the magnetic field and inter-particle interactions on the thermodynamic properties of the system at both high and extremely low temperatures.     

Casimir force in dense confined electrolytes

ABSTRACT

Understanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an additional mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analytically within the random phase approximation, which assumes the ions to be point charges, that this fluctuation-induced force is attractive and also decays exponentially, albeit with a decay length that is half of the bulk correlation length. These predictions change dramatically when excluded volume effects are accounted for within the mean spherical approximation. At high ion concentrations the Casimir force is found to be exponentially damped oscillatory as a function of the distance between the confining surfaces. Our analysis does not resolve the riddle of the anomalously long screening length observed in experiments, but suggests that the Casimir force due to mode restriction in density fluctuations could be an hitherto under-appreciated source of surface–surface interaction.     

强磁场中超冷费米气体的相对论效应

由单粒子的弱相对论能谱及泊松公式,导出强磁场中费米气体的热力学势函数.在此基础上,运用热力学关系求解低温条件下系统的统计特征量的解析式,分析相对论效应对统计性质的影响机理.研究表明,磁场愈强,相对论效应愈明显.相对论效应引发的单调项与相应的振荡项的振幅相比,对总能,单调项远大于振幅;对化学势及磁矩,单调项与振幅几乎同一量级. 关键词： 强磁场 费米气体 相对论效应     

Pressure of the fluctuating vacuum: Interpretation of the attractive and repulsive Casimir force

We calculate the Casimir force between two magnetodielectric slabs. The force expression is expressed in terms of parameters with which the repulsive effect is more transparent and convenient for numerical analysis. Finally, we propose a physical interpretation of the effect which clarifies the sign of force properly.     

弱相互作用费米气体的相对论顺磁性

通过考虑单粒子的相对论能量并且应用量子统计方法，研究弱磁场中弱相互作用费米气体的相对论顺磁性，求解相对论性的最可几磁化率及平均磁化率，讨论相对论效应对最可几磁化率的影响，给出相对论性的粒子数的临界值. 结果显示, 与非相对论情况比较，当 时, 相对论情况下的最可几磁化率和粒子数的临界值都没有变化. 当 时，相对论效应使系统呈现顺磁性容易，而且相对论效应增加磁化率，同时也放大了相互作用对磁化率的影响.     

弱相互作用费米气体的相对论顺磁性

通过考虑单粒子的相对论能量并且应用量子统计方法,研究弱磁场中弱相互作用费米气体的相对论顺磁性,求解相对论性的最可几磁化率及平均磁化率,讨论相对论效应对最可几磁化率的影响,给出相对论性的粒子数的临界值. 结果显示, 与非相对论情况比较,当 时, 相对论情况下的最可几磁化率和粒子数的临界值都没有变化. 当 时,相对论效应使系统呈现顺磁性容易,而且相对论效应增加磁化率,同时也放大了相互作用对磁化率的影响.     

Unconventional interaction between vortices in a polarized Fermi gas

Recently, a homogeneous superfluid state with a single gapless Fermi surface was predicted to be the ground state of an ultracold Fermi gas with spin population imbalance in the regime of molecular Bose-Einstein condensation. We study vortices in this novel state using a symmetry-based effective field theory, which captures the low-energy physics of gapless fermions and superfluid phase fluctuations. This theory is applicable to all spin-imbalanced ultracold Fermi gases in the superfluid regime, regardless of whether the original fermion-pairing interaction is weak or strong. We find a remarkable, unconventional form of the interaction between vortices. The presence of gapless fermions gives rise to a spatially oscillating potential, akin to the RKKY indirect-exchange interaction in non-magnetic metals. We compare the parameters of the effective theory to the experimentally measurable quantities and further discuss the conditions for the verification of the predicted new feature. Our study opens up an interesting question as to the nature of the vortex lattice resulting from the competition between the usual repulsive logarithmic (2D Coulomb) and predominantly attractive fermion-induced interactions.     

The Casimir interaction of a massive vector field between concentric spherical bodies

The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, there are no TM discrete modes that vanish identically in the perfectly conducting spherical bodies. Numerical simulations show that the Casimir interaction force between the two bodies is always attractive.     

非平行导线型边界下Maxwell-Chern-Simons场的Casimir效应

在路径积分量子化框架下，利用复变函数论中的保角变换与Plana求和公式，计算了（2＋1）维空间中两个非平行导线型边界下Maxwell-Chern-Simons场的Casimir效应.不引入任何截断参数，而得出有限的解析表达式. 关键词： Casimir效应 路径积分 保角变换 Plana求和公式