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Register a new userFluctuation-Dissipation Relation for a Quantum Brownian Oscillator in a Parametrically Squeezed Thermal Field
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In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh-DeWitt detector, coupled to a nonequilibrium, nonstationary quantum field and inquire whether a fluctuation-dissipation relation can exist after/if it approaches equilibration. This is a nontrivial issue since a squeezed bath field cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. B) The field is initially in a thermal state, but subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is met in cosmology and dynamical Casimir effect. The squeezing in the bath in both types of processes will affect the oscillators nonequilibrium evolution. We show that at late times it approaches equilibration, which warrants the existence of an FDR. The trait of squeezing is marked by the oscillators effective equilibrium temperature, and the factor in the FDR is only related to the stationary component of baths noise kernel. Setting C) is more subtle: A finite system-bath coupling strength can set the oscillator in a squeezed state even the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium systems.
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Continuing our work on the nature and existence of fluctuation-dissipation relations (FDR) in linear and nonlinear open quantum systems [1-3], here we consider such relations when a linear system is in a nonequilibrium steady state (NESS). With the model of two-oscillators (considered as a short harmonic chain with the two ends) each connected to a thermal bath of different temperatures we find that when the chain is fully relaxed due to interaction with the baths, the relation that connects the noise kernel and the imaginary part of the dissipation kernel of the chain in one bath does not assume the conventional form for the FDR in equilibrium cases. There exists an additional term we call the `bias current that depends on the difference of the baths initial temperatures and the inter-oscillator coupling strength. We further show that this term is related to the steady heat flow between the two baths when the system is in NESS. The ability to know the real-time development of the inter-heat exchange (between the baths and the end-oscillators) and the intra-heat transfer (within the chain) and their dependence on the parameters in the system offers possibilities for quantifiable control and in the design of quantum heat engines or thermal devices.
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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In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the nonequilibrium regime and cannot be ignored, making such processes difficult to understand and treat. Here we derive an emergent fluctuation relation that virtually guarantees the average heat produced to be dissipated into the reservoir either when the system or reservoir is large (or both) or when the temperature is high. The implication of our result is that for nonequilibrium processes, heat fluctuations away from its average value are suppressed independently of the underlying dynamics exponentially quickly in the dimension of the larger subsystem and linearly in the inverse temperature. We achieve these results by generalizing a concentration of measure relation for subsystem states to the case where the global state is mixed.
In this work, a physical system described by Hamiltonian $mathbf{H}_omega = mathbf{H}_0 + mathbf{V}_omega(mathbf{x},t)$ consisted of a solvable model $mathbf{H}$ and external random and time-dependent potential $mathbf{V}_omega(mathbf{x},t)$ is investigated. Under the conditions that the average external potential with respect to the configuration $omega$ is constant in time, and, for each configuration, the potential changes smoothly that the evolution of the system follows Schrodinger dynamics, the mean-dynamics can be derived from taking average of the equation with respect to configuration parameter $omega$. It provides extra contributions from the deviations of the Hamiltonian and evolved state along the time to the Heisenberg and Liouville-von Neumann equations. Consequently, the Kubos formula and the fluctuation-dissipation relation obtained from the construction is modified in the sense that the contribution from the information of randomness and memory effect from time-dependence are present.
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