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.     

Spin dynamics in a dissipative environment: from quantal to classical

We address the problem of spin dynamics in the presence of a thermal bath, by solving exactly the appropriate quantum master equations with continued-fraction methods. The crossover region between the quantum and classical domains is studied by increasing the spin value , and the asymptote for the classical absorption spectra is eventually recovered. Along with the recognized relevance of the coupling strength, we show the critical role played by the structure of the system-environment interaction in the emergence of classical phenomenology.     

Non-Markovian and Markovian Dynamics of a V-type Three-Level Atom

The reduced dynamics of a V-type three-level atom in a structure reservoir is presented,which has the exact solution in certain special condition.The Markovian and non-Markovian master equations for this composite system are solved and compared with the exact solution.The solving approach can be directly generalized to the solution of a V-type multilevel system dynamics interacting with a reservoir.The results further testify that these two kinds of master equations are exploited in different coupling regime,providing guidance for further application of these variants master equations to solve multilevel system dynamics without the exact solution.     

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.     

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.     

Analytical and Numerical Studies of the One-Dimensional Spin Facilitated Kinetic Ising Model

The one-dimensional spin facilitated kinetic Ising model is studied analytically using the master equation and by simulations. The local state of the spins (corresponding to mobile and immobile cells) can change depending on the state of the neighbored spins, which reflects the high cooperativity inherent in glassy materials. The short-time behavior is analyzed using a Fock space representation for the master equation. The hierarchy of evolution equations for the averaged spin state and the time dependence of the spin autocorrelation function are calculated with different methods (mean-field theory, expansion in powers of the time, partial summation) and compared with numerical simulations. The long-time behavior can be obtained by mapping the one-dimensional spin facilitated kinetic Ising model onto a one-dimensional diffusion model containing birth and death processes. The resulting master equation is solved by van Kampen's size expansion, which leads to a Langevin equation with Gaussian noise. The predicted autocorrelation function and the global memory offer in the long-time limit a screened algebraic decay and a stretched exponential decay, respectively, consistent with numerical simulations.     

Master Equation in Phase Space for a Uniaxial Spin System

A master equation, for the time evolution of the quasi-probability density function of spin orientations in the phase space representation of the polar and azimuthal angles is derived for a uniaxial spin system subject to a magnetic field parallel to the axis of symmetry. This equation is obtained from the reduced density matrix evolution equation (assuming that the spin-bath coupling is weak and that the correlation time of the bath is so short that the stochastic process resulting from it is Markovian) by expressing it in terms of the inverse Wigner-Stratonovich transformation and evaluating the various commutators via the properties of polarization operators and spherical harmonics. The properties of this phase space master equation, resembling the Fokker-Planck equation, are investigated, leading to a finite series (in terms of the spherical harmonics) for its stationary solution, which is the equilibrium quasi-probability density function of spin “orientations” corresponding to the canonical density matrix and which may be expressed in closed form for a given spin number. Moreover, in the large spin limit, the master equation transforms to the classical Fokker-Planck equation describing the magnetization dynamics of a uniaxial paramagnet.     

Description of far-from-equilibrium processes by mean-field lattice gas models

Mean-field kinetic equations are a valuable tool to study the atomic dynamics and spin dynamics of simple lattice gas and Ising models. They can be derived from the microscopic master equation of the system and contain analytical expressions for kinetic coefficients and thermodynamic quantities which are usually introduced phenomenologically. We review several methods to obtain such equations, and discuss applications to the dynamics of order–disorder transitions, spinodal decomposition, and dendritic growth in the isothermal or chemical model. In the case of dendritic growth we show that the mean-field kinetic equations are equivalent to standard continuum equations for this problem and derive expressions for macroscopic quantities, e.g. the surface tension and kinetic coefficients, as functions of the microscopic order parameters. In spinodal decomposition, we focus our attention on the vacancy mechanism, which is a more faithful picture of diffusion in solids than the more widely examined exchange mechanism. We study the interfaces between an unstable mixture and a stable ‘vapour’ phase, and analyse surface modes that lead to specific surface patterns. For order–disorder transitions, studied in the framework of a repulsive two-sublattice model, we derive sets of coupled equations for the mean concentration (a conserved quantity) and for the occupational difference between the two sublattices emerging from the symmetry breaking due to ordering (non-conserved order parameter). These equations are applied to transport in the presence of ordered domains. Finally, we discuss the possibilities of improving the simple mean-field approximation by density functional theories and various forms of the dynamic pair approximation, including the path-probability method.     

Analysis of the wave functions for accelerating Kerr-Newman metric

As is well-known, it is very difficult to solve wave equations in curved space-time. In this paper,we find that wave equations describing massless fields of the spins s≤2 in accelerating KerrNewman black holes can be written as a compact master equation. The master equation can be separated to radial and angular equations, and both can be transformed to Heun's equation,which shows that there are analytic solutions for all the wave equations of massless spin fields.The results not only demonstrate that it is possible to study the similarity between waves of gravitational and other massless spin fields, but also it can deal with other astrophysical applications, such as quasinormal modes, scattering, stability, etc. In addition, we also derive approximate solutions of the radial equation.     

Dynamic nuclear spin resonance in n-GaAs

The dynamics of optically detected nuclear magnetic resonance is studied in n-GaAs via time-resolved Kerr rotation using an on-chip microcoil for rf field generation. Both optically allowed and optically forbidden NMR are observed with a dynamics controlled by the interplay between dynamic nuclear polarization via hyperfine interaction with optically generated spin-polarized electrons and nuclear spin depolarization due to magnetic resonance absorption. Comparing the characteristic nuclear spin relaxation rate obtained in experiment with master equation simulations, the underlying nuclear spin depolarization mechanism for each resonance is extracted.     

周期场作用下自旋的主方程及其稳定态

用Robertson理论推导一个在纵磁场和横周期场作用下的自旋的运动方程。得到了阻尼和自旋稳定态对外场强度、频率及与热库的耦合系数的依赖关系。讨论了自旋稳定态的结构及其形成原因。 关键词：     

Field-induced spin mixing in ultrathin superconducting Al and be films in high parallel magnetic fields

We report spin-dependent electron density of states (DOS) studies of ultrathin superconducting Al and Be films in high parallel magnetic fields. Superconductor-insulator-superconductor (SIS) tunneling spectra are presented in which both the film and the counterelectrode are in the paramagnetic limit. This SIS configuration is exquisitely sensitive to spin mixing and/or spin flip processes which are manifest as DOS singularities at eV=2 Delta(0)+/-eV(z). Both our Al and Be data show a well defined subgap peak whose magnitude grows dramatically as the parallel critical field is approached. Though this feature has previously been attributed to spin-orbit scattering, it is more consistent with fluctuations into a field induced mixed-spin state.     

Gauge theory approach for diffusive and precessional spin dynamics in a two-dimensional electron gas

We develop a gauge theory for diffusive and precessional spin dynamics in a two-dimensional electron gas. Our approach reveals a direct connection between the absence of the equilibrium spin current and a strong anisotropy in the spin relaxation: both effects arise if spin-orbit coupling is reduced to a pure gauge SU(2) field. In this case, the spin-orbit coupling can be removed by a gauge transformation in the form of a local SU(2) spin rotation. The resulting spin dynamics is exactly described in terms of two kinetic coefficients: the spin diffusion and electron mobility. After the inverse transformation, full diffusive and precessional spin density dynamics, including the anisotropic spin relaxation, formation of stable spin structures, and spin precession induced by a macroscopic current are restored. Explicit solutions of the spin evolution equations are found for the initially uniform spin density and for stable, nonuniform structures. Our analysis demonstrates a universal relation between the spin relaxation rate and spin-diffusion coefficient.     

Transverse spin dynamics of a spin-polarized Fermi liquid

A microscopic derivation of the equations of transverse spin dynamics of a spin-polarized Fermi liquid at zero temperature is given in the leading-order approximation in the frequencies and wave vectors characterizing the spin motion. The equations are applicable for arbitrary degree of polarization and arbitrary deviations of the spin direction from the equilibrium orientation. The solutions describing a coherently precessing two-domain structure and spin waves are examined. In contrast to the assertion discussed in the literature that spin waves are damped at zero temperature, spin waves are found to be undamped in the long-wavelength limit. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 717–721 (10 May 1997)     

Nakajima-Zwanzig and Time-Convolutionless Master Equations for a One-Qubit System in a Non-Markovian Layered Environment

Quantum operations, are completely positive (CP) and trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of one-qubit open quantum system in layered environment which is a generalized spin star model. The Nakajima-Zwanzig and time-convolutionless projection operators technique are applied for deriving the master equations. Finally, a simple example will be studied to consider the relation between completely positive maps and initial quantum correlation and show that vanishing quantum discord is not necessary for CP maps.     

Master equations for time correlation functions of a quantum system interacting with stochastic perturbations and applications to emission and absorption line shapes

The stochastic and quantum dynamics of open quantum systems interacting with stochastic perturbations in considered. The master equations for one time and multi-time correlation functions of such a system are derived to all orders in the interaction with the stochastic perturbations. The importance of the non-markovian character of such equations in the study of various problems in optical resonance is discussed. The simplified form of the non-markovian master equations in Born approximation is also given. It is shown that such non-markovian master equations in Born approximation are exact if there is only one random perturbation, of the telegraphic signal type, acting on the system. The master equations for the linear response functions of an open system interacting with stochastic perturbations are also derived. The non-markovian master equations for multitime correlations are used to study the behaviour of two level atoms interacting with fluctuating laser fields. Both amplitude and phase fluctuations are taken into account. Explicit results are presented for the spectrum of resonance fluorescence, absorption spectrum, photon antibunching effects etc. The calculations are done for arbitrary values of the relaxation parameters and intial conditions. In general the fluorescence spectrum is found to be asymmetric for off resonant fields.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.