Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations

Abstract

Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study non-canonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte-Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify non-canonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, non-canonical statistics enhances as temperature decreases but vanishes at high temperature.

8 pages, 6 figures, to appear in Phys. Rev. E

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• Improving the estimation of environment parameters via initial probe-environment correlations
• Quantum Control in Open and Periodically Driven Systems
• Non-canonical statistics of finite quantum system
• Effective-Hamiltonian theory: An approximation to the equilibrium state of open quantum systems
• Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle
• Preferred basis derived from eigenstate thermalization hypothesis
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
• The quantum Zeno and anti-Zeno effects with strong system-environment coupling