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We consider a thermal quantum harmonic oscillator weakly coupled to a heat bath at a different temperature. We analytically study the quantum heat exchange statistics between the two systems using the quantum-optical master equation. We exactly compute the characteristic function of the heat distribution and show that it verifies the Jarzynski-Wojcik fluctuation theorem. We further evaluate the heat probability density in the limit of long thermalization times, both in the low and high temperature regimes, and investigate its time evolution by calculating its first two cumulants.
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We consider the quantum harmonic oscillator in contact with a finite temperature bath, modelled 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 quasi-stationary cyclic evolution. Thereby, we are able to perform an accurate study of the thermodynamic properties of a non-integrable, quantum chaotic system in contact with a heat bath.
Using Schwinger Variational Principle we solve the problem of quantum harmonic oscillator with time dependent frequency. Here, we do not take the usual approach which implicitly assumes an adiabatic behavior for the frequency. Instead, we propose a new solution where the frequency only needs continuity in its first derivative or to have a finite set of removable discontinuities.
In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperature, which are coupled to opposite ends of the lattice, with focus on the validity of Fouriers law of heat conduction. We provide analytical solutions of the heat current through the quantum system in the non-equilibrium steady state using the rotating-wave approximation and bath interactions described by a master equation of Lindblad form. The influence of local dephasing in the transition of ballistic to diffusive transport is investigated.
To investigate a system coupled to a harmonic oscillator bath, we propose a new approach based on a phonon number representation of the bath. Compared to the method of the hierarchical equations of motion, the new approach is computationally much less expensive in a sense that a reduced density matrix is obtained by calculating the time evolution of vectors, instead of matrices, which enables one to deal with large dimensional systems. As a benchmark test, we consider a quantum damped harmonic oscillator, and show that the exact results can be well reproduced. In addition to the reduced density matrix, our approach also provides a link to the total wave function by introducing new boson operators.
In this paper we examine some foundational issues of a class of quantum engines where the system consists of a single quantum parametric oscillator, operating in an Otto cycle consisting of 4 stages of two alternating phases: the isentropic phase is detached from any bath (thus a closed system) where the natural frequency of the oscillator is changed from one value to another, and the isothermal phase where the system (now rendered open) is put in contact with one or two squeezed baths of different temperatures, whose nonequilibrium dynamics follows the Hu-Paz-Zhang (HPZ) master equation for quantum Brownian motion. The HPZ equation is an exact nonMarkovian equation which preserves the positivity of the density operator and is valid for a) all temperatures, b) arbitrary spectral density of the bath, and c) arbitrary coupling strength between the system and the bath. Taking advantage of these properties we examine some key foundational issues of theories of quantum open and squeezed systems for these two phases of the quantum Otto engines. This include, i) the nonMarkovian regimes for non-Ohmic, low temperature baths, ii) what to expect in nonadiabatic frequency modulations, iii) strong system-bath coupling, as well as iv) the proper junction conditions between these two phases. Our aim here is not to present ways for attaining higher efficiency but to build a more solid theoretical foundation for quantum engines of continuous variables covering a broader range of parameter spaces hopefully of use for exploring such possibilities.
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