Physical Review

Quasiclassical Methods in Spin Dynamics

D. M. Kaplan, George C. Summerfield

Published Nov 10, 1969• 27 citations

Abstract

We present an extension of the concept of the Wigner distribution to include spin. The results are then used to indicate a method by which classical approximations to spin dynamics emerge naturally from the exact quantum theory, and estimates of the accuracy of these classical approximations can be computed.

DOI: 10.1103/physrev.187.639

Related papers

Quasiclassical Equation of Motion for the Heisenberg Spin System

Yao-Chung Chang, George C. Summerfield

Previous results of quasiclassical spin dynamics are extended by presenting a new approximation for quantum corrections to the classical equation of motion for the Heisenberg model. The accuracy of the equation with these corrections is determined by comparing computer calculations based on this formalism with exact quantum and classical results for spin pair correlation functions for a six-spin linear chain at infinite temperatures.

Physical review. B, Solid stateDec 1, 19714 citations

Quasiclassical Spin Dynamics for the Heisenberg Model

Yao-Chung Chang, George C. Summerfield, D. M. Kaplan

The Wigner method is employed to develop explicit relationships among quantum-mechanical and classical equations of motion and quantum-mechanical and classical pair-correlation functions of spin operators. In this method, quantum corrections to the classical theory can be accurately estimated. The formalism is applied to a spin-\textonehalf{} Heisenberg model at high temperatures. The most attractive feature of this method is that many of the results are intuitively satisfying. Finally, we make a connection between our results and the classical calculations made by several other authors.

Physical review. B, Solid stateMay 1, 19719 citations

A mapping of spin matrices on polynomials

D. M. Kaplan

A mapping between spin matrices and polynomial functions is exhibited. Matrix multiplication is replaced by specific left-right differential operators. The procedure supplies the natural extension of the method of Wigner distributions to include spin.

Transport Theory and Statistical PhysicsJan 1, 197110 citations

On quasi-classical nature of spin

Tamara P. Ershova, Natalia N. Gorobey, Alexander S. Lukyanenko

A special form of a quasiclassical approximation in non-relativistic and relativistic quantum mechanics is considered. It consists in the demand of classical interpretation for a natural time of the theory. As the consequence, in passing to quantum level, there arises the necessity of introduction of half-integer spin.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEApr 3, 20060 citations

Quasiclassical approach to the nonlinear Kerr dynamics

Mojdeh S. Najafabadi, A. B. Klimov, Luis Lorenzo Sánchez-Soto +1 more

We examine the quasiclassical approximation to the self-Kerr nonlinear effect. The corresponding dynamics appears as classical trajectories, with the quantumness of the state included via its Wigner function. We obtain analytical estimates of the optimal squeezing attainable that compare fairly well with the numerical quantum solution. We delimit the range of parameters for which the quasiclassical solution retains relevant quantum features.

Optics CommunicationsJun 28, 20235 citations

Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space

Johannes Schachenmayer, Alexander Pikovski, A. M. Rey

Following the time evolution of a large and high-dimensional quantum system is often computationally intractable. A new semiclassical method of modeling quantum dynamics yields surprisingly good results for nonequilibrium dynamics.

arXiv:1408.4441Physical Review XFeb 25, 2015205 citations