author={Yu. P. Kalmykov and William T. Coffey and Sergei V. Titov},
  journal={arXiv: Statistical Mechanics},
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is that only master equations for the phase-space distributions akin to Fokker-Planck equations for the evolution of classical phase-space distributions in configuration space are involved so that operators are unnecessary. The explicit solution of these… 

Truncated Wigner approximation as non-positive Kraus map

We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the

Quasiprobability currents on the sphere

We present analytic expressions for the s-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents

Generalized SU(2) covariant Wigner functions and some of their applications

We survey some applications of SU(2) covariant maps to the phase space quantum mechanics of systems with fixed or variable spin. A generalization to SU(3) symmetry is also briefly discussed in

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

The semi-classical limit of the generalized SO(3) map is applied for representation of variable-spin systems in a four-dimensional symplectic manifold and one of the classical dynamic variables is “quantized” and a discretized version of the Truncated Wigner Approximation is introduced.



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

Phase-space formulation of the nonlinear longitudinal relaxation of the magnetization in quantum spin systems.

A simple description in terms of a Bloch equation holds even for the nonlinear response of a giant spin.

Phase space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie group symmetries

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors @J. Phys. A 31 ,L 9 ~1998!#. This theory provides a unified phase-space

Spin quasi-distribution functions

Two-classes of phase-space spin quasi-distribution functions are introduced and discussed. The first class of these distributions is based on the delta function construction. It is shown that such a

Phase space approach to theories of quantum dissipation

Six major theories of quantum dissipative dynamics are compared: Redfield theory, the Gaussian phase space ansatz of Yan and Mukamel, the master equations of Agarwal,

Nonlinear dynamics of a quantum ferromagnetic chain: Spin-coherent-state approach.

The spin evolution equation of an isotropic, quantum ferromagnetic Heisenberg chain is analyzed in the continuum approximation using spin-coherent states and the energy-momentum dispersion relation for the nonlinear excitations is derived.

Wigner function approach to the quantum Brownian motion of a particle in a potential.

It is shown how Wigner's method of obtaining quantum corrections to the classical equilibrium Maxwell-Boltzmann distribution may be extended to the dissipative non-equilibrium dynamics governing the quantum Brownian motion in an external potential V(x), yielding a master equation for the Wigners distribution function W(x,p,t) in phase space.

Quantum mechanics as a statistical theory

  • J. E. Moyal
  • Physics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1949
An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the

Phase space equilibrium distribution function for spins

The equilibrium quasiprobability density function W(ϑ, φ) of spin orientations in a representation (phase) space of the polar and azimuthal angles (ϑ, φ) (analogous to the Wigner distribution for