Ehrenfest theorem for inhomogeneous superconductors and supercurrent force on Andreev reflected quasiparticles

Quasiclassical equations of motion are derived for quasiparticle wave packets in inhomogeneous superconductors with electromagnetic fields. Besides the Lorentz forces on electrons and holes there are two off-diagonal pair potential forces. The first one is due to gradients of the modulus of the pair potential and responsible for electron-hole scattering from inhomogeneities of the pair potential. The second one results from interactions with the ground state condensate and is proportional to the gauge invariant Cooper pair velocity of surface supercurrents in the interfaces between normal and superconducting regions. The most favorable experimental conditions for the observation of this new force may be found inN-S junctions composed of clean normal metals and type II superconductors with high critical fields, large London penetration depths, and large energy gaps.     

用纠缠态表象推导广义Ehrenfest定理

利用两粒子相对坐标和总动量的共同本征态|η〉构成的连续变量纠缠态表象,推导了转动系统的Ehrenfest定理,从而说明了在满足某些近似的情况下,量子力学不但能够与经典物理完美自洽,而且利用量子力学的规律可以导出相应的经典物理规律.     

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

The [, , ]-Langevin equation describes the time evolution of a real stationary process withT-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [, , ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics.     

Confinement and superfluidity in one-dimensional degenerate fermionic cold atoms

The physical properties of arbitrary half-integer spins F = N - (1/2) fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for F > or = (3/2) depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular-superfluid instability made of 2N fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the Z(N) generalized Ising universality class. We discuss the possible Mott phases at (1/2) filling.     

Confinement limit of a Dirac particle in two and three dimensions

Consider a particle that is in a stationary state described by the Dirac equation with a finite-range potential. In two and three dimensions the particle can be confined to an arbitrarily small spatial region. This is in contrast to the one-dimensional case in which the confinement region cannot be much narrower than the Compton wavelength.     

A one-dimensional lattice model for a quantum mechanical free particle

Two types of particles, A and B with their corresponding antiparticles, are defined in a onedimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field of the other type of particle with nonlocal action but with an effect decreasing with the distance: . It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.     

Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola–Kanai oscillator driven by a time-dependent force

The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schr o¨dinger equation for the Caldirola–Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular,we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.     

Confinement of Bloch surface waves in a graphene-based one-dimensional photonic crystal and sensing applications

Bloch surface waves(BSWs) are excited in one-dimensional photonic crystals(Ph Cs) terminated by a graphene monolayer under the Kretschmann configuration. The field distribution and reflectance spectra are numerically calculated by the transverse magnetic method under transfer-matrix polarization, while the sensitivity is analyzed and compared with those of the surface plasmon resonance sensing method. It is found that the intensity of magnetic field is considerably enhanced in the region of the terminated layer of the multilayer stacks, and that BSW resonance appears only in the interface of the graphene and solution. Influences of the graphene layers and the thickness of a unit cell in Ph Cs on the reflectance are studied as well. In particular, by analyzing the performance of BSW sensors with the graphene monolayer,the wavelength sensitivity of the proposed sensor is 1040 nm/RIU whereas the angular sensitivity is 25.1?/RIU. In addition,the maximum of figure of merit can reach as high as 3000 RIU-1. Thus, by integrating graphene in a simple Kretschmann structure, one can obtain an enhancement of the light–graphene interaction, which is prospective for creating label-free,low-cost and high-sensitivity optical biosensors.     

一维Hulthén势场中Klein-Gordon粒子的透射共振

用Heaviside函数构造出一维对称的Hulthén势垒,求解了其满足的Klein-Gordon方程. 散射态的精确解可以由超几何函数表示, 透射系数T和反射系数R能由Klein-Gordon 方程满足的边界条件得到.并由流密度守恒推导出低动量粒子发生透射共振的条件. 关键词： Klein-Gordon方程 Hulthén势垒 散射态 透射共振     

The Ehrenfest model: a path-integral for spin

The Ehrenfest model, formulated as a continuous time Markov chain, is a representation of a spin with length j in a magnetic field. The equivalence is shown by the introduction of a Feynman-Kac functional on the sample paths of the Markov chain. A transformation is used to calculate the functional leading to the solution of a path-integral for spin without reference to coherent states.     

Typical Recurrence for the Ehrenfest Wind-Tree Model

We show that the typical wind-tree model, in the sense of Baire, is recurrent and has a dense set of periodic orbits. The recurrence result also holds for the Lorentz gas: the typical Lorentz gas, in the sense of Baire, is recurrent. These Lorentz gases need not be of finite horizon!     

Diffusion and Einstein relation for a massive particle in a one-dimensional free fas: Numerical evidence

A computer simulation is used to investigate the motion of a marked particle of massM in a free gas of particles with massm=1, for large times. Previous results seem to indicate a non-Wiener behavior for the rescaled trajectory whenMm. The results reported here, with better statistics, are compatible with the Wiener hypothesis. The Einstein relation between mobility and diffusion coefficient is also investigated. The results indicate that it holds both forM=m and forMm.