Statistical description of small quantum systems beyond weak-coupling limit

Abstract

An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is given by a renormalized self-Hamiltonian of the studied system, which appropriately takes into account the influence of the system-environment interaction. In the case that the system has a narrow spectrum and the environment is sufficiently large, the modification to the self-Hamiltonian usually has a mean-field feature, given by an environmental average of the interaction Hamiltonian. In other cases, the modification may be beyond the mean-field approximation.

9 pages, published version

References in corpus (12)

• Thermalization and its mechanism for generic isolated quantum systems
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Strong and weak thermalization of infinite non-integrable quantum systems
• Strongly correlated fermions after a quantum quench
• Absence of Thermalization in Nonintegrable Systems
• Thermalization in Nature and on a Quantum Computer
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Finite quantum dissipation: the challenge of obtaining specific heat
• Entanglement-induced Decoherence and Energy Eigenstates
• Preferred States of Decoherence under Intermediate System-Environment Coupling
• The approach to typicality in many-body quantum systems

Cited by in corpus (9)

• Nonequilibrium quantum criticality in open systems: The dissipation rate as an additional indispensable scaling variable
• Entropy for Quantum Pure States and Its Dynamical Relaxation
• Non-canonical statistics of finite quantum system
• Equilibration of quantum chaotic systems
• Statistically preferred basis of an open quantum system: Its relation to the eigenbasis of a renormalized self-Hamiltonian
• Quantum thermalization and equilibrium state with multiple temperatures
• Closeness of the reduced density matrix of an interacting small system to the Gibbs state
• Preferred basis derived from eigenstate thermalization hypothesis
• Internal temperature of quantum chaotic systems at the nanoscale and its detection by a microscopic thermometer