The Quantum Dense Coding in a Two Atomic System Under the Non-Markovian Environment

The quantum dense coding in a two atomic system under the non-Markovian environment is investigated in detail. We mainly concentrate on the effects about the environment parameter Γ(or γ) and the purity r of the initial state on the dense coding capacity χ. It is found that the dense coding capacity χ is initially decreased and gradually trends to be a constant nonzero value with evolution of time for different environment parameter Γ(or γ). This constant value is determined the initial state and independent to the environment. In other word, environment noise only affects the process of quantum dense coding, but not affects the final result of dense coding capacity. The purity r of the initial state has a strong influence on the initial value of the χ. Besides, for one value r, dense coding capacity χ is decreased firstly, and then reaches a stable value for a long time, whatever the values of other parameters are, but when the purity r of the initial state increased, the initial value of dense coding capacity increased.

     

The evolution of the cluster size distribution in a coagulation system

The coagulation equation with kernelK _ij =A+B(i+j)+C _ij and arbitrary initial conditions is studied analytically and a simple expression for the solution is found. For monodisperse initial conditions, we recover the known size distribution expressed in terms of a degeneracy factorN _k, which is determined by a recursion relation. For polydisperse initial conditions, a similar solution form is found, which includes a degeneracy factorN _kl, also determined by a recursion relation. The physical meaning ofN _kl and the recursion relation is given. A method to get explicit expressions forN _k andN _kl is illustrated. Finally, the pre-gel solution is given explicitly and a general method to get the post-gel solution is proposed.     

Electron-electron bremsstrahlung in a non-equilibrium plasma

Electron-electron bremsstrahlung in a weakly ionized uniform non-stationary plasma is investigated. The respective problem is solved analytically for two initial electron-distributions: maxwellian with the temperatureT ₀, and the delta distribution. In the case of initial maxwellian distribution the radiation intensity is proportional to ^3/2, where=T+(T ₀–T) exp (–s),s=2mv ₁ t/M,v ₁ is the momentum transfer frequency, and the other symbols are standard. In the case of initial delta distribution the radiation intensity is proportional to [1 -exp (–s)]^3/2. The proportionality factors are known, and are expressed in terms of mathematical and physical constants.     

Study of bifurcations in a model Hartree-Fock calculation

The Hartree-Fock procedure is used to study the behaviour of the ground state of a system ofM spinless electrons distributed overN equivalent and equidistant sites (M ⩽N) as a function of the strength of the mutual repulsion between the electrons. Below a critical strength, all initial configurations are seen, after repeated iterations, to converge to a unique solution. Above this critical strength, in addition to the initial configurations which lead to a unique solution, there exist configurations which on repeated iterations give rise to stable two-period solutions. Although the number of independent stable two-period solutions depends on the coupling strength, for no value of the coupling are stable solutions of periodicity higher than two seen.     

Quenching dynamics of a quantum XY spin-1/2 chain in the presence of transverse field by the application of a generalized Landau-Zener formula

In this paper we review the quenching dynamics of a quantum XY spin-1/2 chain in the presence of a transverse field, when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. We also extend the results to the cases in which the system starts with any arbitrary initial condition as opposed to the initial fully magnetically aligned state which has been extensively studied earlier. The evolution is non-adiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to nonadiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem. We show that in one dimension the density of defects in the final state scales as 1/√τ irrespective of the initial condition, where τ is the quenching time-scale. However, the magnitude of density of defects is found to depend on the initial condition.      

Average position in quantum walks with a U（2） coin

We investigated discrete-time quantum walks with an arbitary unitary coin.Here we discover that the average position x=max(x) sin(α+γ),while the initial state is 1/2～(1/2)(|0L+i|0R).We verify the result,and obtain some symmetry properties of quantum walks with a U(2) coin with |0L and |0R as the initial state.     

The dynamical Cooperative Lamb Shift in a system of two-level atoms in a slab-geometry

Using the eigenmode analysis, we compute the Cooperative Lamb Shift (CLS) as a function of time from the vector photon model for a system of two-level atoms in a slab-geometry for forward and backward emission in two initial states of weak excitation and complete inversion.     

Entanglement dynamics of two qubits coupled by Heisenberg XY interaction under a nonuniform magnetic field in a spin bath

This paper investigates the entanglement dynamics of a Heisenberg XY model for a two-spin system in the presence of a nonuniform magnetic field.The master equations and the concurrence evolution equations for the initial α state are derived and analysed.It is shown that for the symmetric initial α state,only the nonuniform field can play a role in entanglement dynamics while the uniform field and the bath will not play such a role.For the asymmetric α state,the nonuniform field leads to the beat pattern oscillation of the concurrence evolution.The inhomogeneity of the field can enhance the entanglement by suppressing the decoherence effects of both the spin-orbit interaction and the spin bath.     

Rigorous Results on Spontaneous Symmetry Breaking in a One-Dimensional Driven Particle System

We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting from an empty initial lattice, the system enters a symmetry broken state after some time T ₁ through an amplification loop of initial fluctuations. It remains in the symmetry broken state for a time T ₂ through a traffic jam effect. Applying a simple martingale argument, we obtain rigorous asymptotic estimates for the expected times 〈 T ₁〉 ∝ Lln L and ln 〈 T ₂〉 ∝ L, where L is the system size. The actual value of T ₁ depends strongly on the initial fluctuation in the amplification loop. Numerical simulations suggest that T ₂ is exponentially distributed with a mean that grows exponentially in system size. For the phase transition line we argue and confirm by simulations that the flipping time between sign changes of the difference of particle numbers approaches an algebraic distribution as the system size tends to infinity.     

Mixing Properties for Mechanical Motion¶of a Charged Particle in a Random Medium

We study a one-dimensional semi-infinite system of particles driven by a constant positive force F which acts only on the leftmost particle of mass M, called the heavy particle (the h.p.), and all other particles are mechanically identical and have the same mass m < M. Particles interact through elastic collisions. At initial time all neutral particles are at rest, and the initial measure is such that the interparticle distances ξ _i are i.i.d. r.v. Under conditions on the distribution of ξ which imply that the minimal velocity obtained by each neutral particle after the first interaction with the h.p. is bigger than the drift of an associated Markovian dynamics (in which each neutral particle is annihilated after the first collision) we prove that the dynamics has a strong cluster property, and as a consequence, we prove existence of the discrete time limit distribution for the system as seen from the first particle, a ψ-mixing property, a drift velocity, as well as the central limit theorem for the tracer particle. Received: 22 March 2000 / Accepted: 8 December 2000     

Quenching Evolution in a Quantum-Classical Hybrid System

The adiabatic theorem, an important theory in quantum mechanics, tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In this paper, we study the quench evolution that is another extreme circumstance where the external conditions vary rapidly such that the quantum system can not follow the change and remains in its initial state (or wavefunction). We examine the matter-wave pressure and derive the requirement for such an evolution. The study is conducted by considering a quantum particle in an infinitely deep potential, the potential width Q is assumed to be change rapidly. We show that the total energy of the quantum subsystem decreases as Q increases, and this rapidly change exerts a force on the wall which plays the role of boundary of the potential. For Q < Q₀ (Q₀ is the initial width of the potential), the force is repulsive, and for Q > Q₀, the force is positive. The condition for the quenching evolution evolution is given via a spin-\( \frac{1}{2} \) in a rotating magnetic field.

     

Quasi-adiabatic compression of a plasma column by a longitudinal magnetic field

Approximate 1.5-dimensional MHD equations are derived that describe the quasi-adiabatic compression of a thin plasma column by a longitudinal magnetic field. The parameters of the compressed plasma are obtained analytically as functions of the initial conditions and longitudinal field. The stability of plasma compression against the Rayleigh-Taylor instability is investigated. It is shown that, in the Z-Θ-pinch geometry, increasing the longitudinal magnetic field makes it possible to achieve radial compression ratios of 20–30 without violating the cylindrical symmetry of the column. The possibility of thermonuclear ignition in a thin plasma column in a Z-Θ-pinch configuration is studied. The ranges of the initial plasma densities and temperatures and the initial lengths of the plasma column that are needed to achieve ignition in a plasma compressed by a factor of 20–30 are determined. The parameters of the electromagnetic energy source required to achieve such a high plasma compression are estimated.     

Effect of time reversal in the magnetization of an atom by a resonant light pulse

It is shown that the even dependence of the light-induced magnetic moment on the detuning ω-ω _ba from resonance in the case of a circularly polarized pulse and an isotropic initial state of the atom and the odd dependence on ω-ω _ba in the case of a linearly polarized pulse and an anisotropic initial state in the form of alignment of the atom are consequences of the symmetry under time reversal t→−t and of the initial conditions at time t=0. In a number of cases, this fundamental law makes it possible to determine the vector properties of a light-induced magnetic moment and its dependence on the time t and ω-ω _ba without solving the equation for the density matrix in detail and without calculating the sum over the projections of the angular momenta in the formula for the magnetization of an atom by light. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 231–236 (10 February 1997)     

A WKB treatment of diffusion in a multidimensional bistable potential

We extend to the case of a finite set of stochastic variables whose distributionP obeys a nonlinear Fokker-Planck equation our previous treatment of diffusion in a bistable potentialU, in the limit of small, constant diffusion coefficient. This is done with the help of an extended WKB approximation due to Gervais and Sakita. The treatment is valid if there exists a well-defined most probable path connecting the minima ofU, and if the valley ofU along that path has a slowly varying width, and weak curvature and twisting. We find that: (i) the final approach to equilibrium is governed by Eyring's generalization of the Kramers high-viscosity rate, which we rederive; (ii) for intermediate times, if the initial distribution is concentrated in the region of instability (close vicinity of the saddle point ofU),P has, along the most probable path, the behavior described by Suzuki's scaling statement for a one-dimensional system. In a second part of this time domain,P enters the diffusive regions around the minima ofU and relaxes toward local longitudinal equilibrium on a time comparable with Suzuki's time scale. The time for relaxation toward transverse local equilibrium may, depending on the initial conditions, compete with these longitudinal times.We dedicate this work to our colleague, Yuri Orlov.     

Leader discharge over a water surface in a Lichtenberg figure geometry

A multichannel leader discharge over a water surface is investigated in a Lichtenberg figure geometry. It is established that the Ohmic conductivity of water causes nonlinearity of the R(t)C discharge circuit. A mutual one-to-one correspondence between the channel lengths and the currents flowing in them is established during the discharge, and the discharge has a selfconsistent character. A mechanism is proposed for the initiation of initial channels by maxima which arise in the charge structure of the planar double layer on the water surface during the development of Rayleigh-Bénard instability in the layer after the pulsed corona from the anode reaches the water. Zh. Tekh. Fiz. 68, 63–66 (November 1998)     

Development of stochastic oscillations in a one-dimensional dynamical system described by the Korteweg-de Vries equation

The behavior of the solution of the Korteweg-de Vries equation for large-scale oscillating periodic initial conditions prescribed on the entire x axis is considered. It is shown that the structure of small-scale oscillations arising in a Korteweg-de Vries system as t→∞ loses its dynamical properties as a consequence of phase mixing. This process can be called the generation of soliton turbulence. The infinite system of interacting solitons with random phases developing under these conditions leads to oscillations having a stochastic character. Such a system can be described using the terms applied to a continuous random process, the probability density and correlation function. It is shown that for this it suffices to determine from the prescribed initial conditions amplitude distribution function of the solitons and their mean spatial density. The limiting stochastic characteristics of the mixed state for problems with initial data in the form of an infinite sequence of isolated small-scale pulses are found. Also, the problem of stochastic mixing under arbitrary initial conditions in the dispersionless limit (the Hopf equation) is completely solved. Zh. éksp. Teor. Fiz. 115, 333–360 (January 1999)     

Dynamics of a Peierls system in a light field

Equations describing the temporal dynamics of the order parameter ξ(t) of a metal-semiconductor phase transition and the density n(t) of electron-hole pairs in a Peierls system in a light field are obtained on the basis of the Lagrange equation for the phonon mode and the Liouville equation for the density matrix of the electronic subsystem. The equations obtained are analyzed for a stationary state (with adiabatically slow variation of the light intensity I) and for a transient process near the initial and final states of dynamic equilibrium (with the light field switched on abruptly). It is shown that for adiabatically slow growth of the intensity I up to a certain critical value I _c the band gap of the electronic spectrum decreases but the semiconductor phase of the Peierls system remains stable. For I>I _c the stationary semiconductor state (ξ≠0) becomes unstable. When the light is switched on abruptly, the deviation of the system parameters from the initial values is described by an exponential law with a characteristic reciprocal of the rise time of the process linearly dependent on the irradiation intensity I. As a new position of equilibrium is approached, three qualitatively different regimes of behavior of the order parameter ξ and density n are possible. For low intensities I(I< I ₁) a purely relaxational aperiodic process occurs. For intermediate intensities I(I ₁<I<I _c) damped oscillations of ξ and n are observed near a new stationary semiconductor state with a smaller band gap. For I>I _c the stationary semiconductor state with ξ≠0 is absent. The experimental data on the irradiation of a vanadium dioxide film with a powerful laser pulse is interpreted on the basis of the theory developed. Zh. éksp. Teor. Fiz. 116, 2154–2175 (December 1999)     

Nonequilibrium dynamics of a diffusion-limited reaction driven by a cluster-memory mechanism

The diffusion-limited reaction A+AA+B is studied in general dimension. The asymptotic decay of the system is found to depend nontrivially upon the initial concentration of A particles for certain ranges of the diffusion constant, backward reaction rate, and total concentration of particles. This nonequilibrium behavior is due to the formation of clusters centered about the initial A particles. A perturbative analysis ind=1 shows that the transition to the nonequilibrium dynamics is sharp and is quite similar to another previously studied reaction A+AA. Ford>1, a scaling argument is presented which describes the dependence of the asymptotic decay on the initial concentration of A particles and the equilibrium concentration for large backward reaction rates. Monte Carlo data are shown which confirm the analytic work ind=1, 2, and 3.     

Entanglement of electronic subbands and coherent superposition of spin states in a Rashba nanoloop

The present work is concerned with an analysis of the entanglement between the electronic coherent superpositions of spin states and subbands in a quasi-one-dimensional Rashba nanoloop acted upon by a strong perpendicular magnetic field. We explicitly include the confining potential and the Rashba spin-orbit coupling into the Hamiltonian and then proceed to calculate the von Neumann entropy, a measure of entanglement, as a function of time. An analysis of the von Neumann entropy demonstrates that, as expected, the dynamics of entanglement strongly depends upon the initial state and electronic subband excitations. When the initial state is a pure one formed by a subband excitation and the z-component of spin states, the entanglement exhibits periodic oscillations with local minima (dips). On the other hand, when the initial state is formed by the subband states and a coherent superposition of spin states, the entanglement still periodically oscillates, exhibiting stronger correlations, along with elimination of the dips. Moreover, in the long run, the entanglement for the latter case undergoes the phenomenon of collapse-revivals. This behaviour is absent for the first case of the initial states. We also show that the degree of entanglement strongly depends upon the electronic subband excitations in both cases.