Quantum kicked harmonic oscillator in contact with a heat bath

Abstract

We consider the quantum harmonic oscillator in contact with a finite-temperature bath, modeled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos, on the one hand, and ballistic or diffusive energy absorption, on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase-space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high-resolution Wigner functions at long times, where the system approaches a quasistationary cyclic evolution. Thereby, we perform an accurate study of the thermodynamic properties of a nonintegrable, quantum chaotic system in contact with a heat bath at finite temperature. In particular, we find that the heat transfer between harmonic oscillator and heat bath is governed by Fourier's law

Floquet many-body engineering: topology and many-body physics in phase space lattices

“…y y y y p á ñ = á ñ + |ˆ|ˆ|ˆ|ˆ, the Q-functions are shifted by 2π in the P-dimension. The underlying topology of a quasienergy band is defined by the Chern number [97]…”

“…The two Lindblad terms in equation (3.9) represents relaxation and heating processes respectively. We notice that some authors also choose the non-Lindblad Caldeira-Leggett master equation to describe the dissipative dynamics [97]. Here, we choose the Lindblad master equation (3.9) since it can give the correct thermal equilibrium state of harmonic oscillator without kicking force while the non-Lindblad Caldeira-Leggett master equation cannot [101].…”

“…Then the master equation (3.9) without kicking can be transformed into the following Fokker-Planck equation [97] w k w s w n s k w 2 2 2…”

“…As the kicks act as delta-functions, we can separate the dissipative dynamics from the kicking dynamics. In order to solve the dissipative dynamics, we define the characteristic function of the Wigner distribution by [95] w(s, k) ≡ dx e ixk/λ x + s 2 |ρ|x − s 2 , Then the master equation (12) without kicking can be transformed into the following Fokker-Planck equation [96] The dissipative dynamics between two successive kicks is solvable from the above Fokker-Planck equation. Given the initial state at the moment right after n − 1 kicks w(s, k; τ + n−1 ), where τ + n−1 = (n − 1)τ + ∆ with a positive infinitesimal increment ∆, the final state at the moment right before n kicks w(s, k; τ − n ) with τ − n = nτ − ∆, is given by the following map [96] w(s, k;…”

Probing the dynamics of an open quantum system via a single qubit

“…Here, we are interested in the case of finite temperature and a finite coupling strength (dissipation rate), and instead of a quantum chaotic system as in Ref. [18], we study a simple harmonic oscillator. This allows us to obtain the dynamics of the full system analytically, and thereby study the relations between the dynamics of the oscillator and that of the quantum probe in every detail.…”