Computer Simulation of Quantum Dynamics in a Classical Spin Environment

Abstract

In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric phases in the evolution of the density matrix. It is shown that such geometric phases must also be considered in the quantum-classical Liouville equation for a classical bath with canonical phase space coordinates; this occurs whenever the adiabatics basis is complex (as in the case of a magnetic field coupled to the quantum subsystem). When the quantum subsystem is weakly coupled to the spin environment, non-adiabatic transitions can be neglected and one can construct an effective non-Markovian computer simulation scheme for open quantum system dynamics in classical spin environments. In order to tackle this case, integration algorithms based on the symmetric Trotter factorization of the classical-like spin propagator are derived. Such algorithms are applied to a model comprising a quantum two-level system coupled to a single classical spin in an external magnetic field. Starting from an excited state, the population difference and the coherences of this two-state model are simulated in time while the dynamics of the classical spin is monitored in detail. It is the author's opinion that the numerical evidence provided in this paper is a first step toward developing the simulation of quantum dynamics in classical spin environments into an effective tool. In turn, the ability to simulate such a dynamics can have a positive impact on various fields, among which, for example, nano-science.

To appear in Theoretical Chemistry Accounts (special issue in honor of Professor Gregory Sion Ezra)

References in corpus (7)

• Nonlinear thermodynamic quantum master equation: Properties and examples
• Deterministic constant-temperature dynamics for dissipative quantum systems
• The geometry and thermodynamics of dissipative quantum systems
• Symplectic integrators for classical spin systems
• Bulgac-Kusnezov-Nosé-Hoover thermostats
• Stochastic process behind nonlinear thermodynamic quantum master equation
• Quantum Dynamics in Classical Spin Baths

Cited by in corpus (4)

• Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths
• A Demonstration of Consistency between the Quantum Classical Liouville Equation and Berry's Phase and Curvature
• Dynamics of mixed quantum-classical spin systems
• Time-Irreversible Quantum-Classical Dynamics of Molecular Models in the Brain