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Register a new userThe reaction coordinate mapping in quantum thermodynamics
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We present an overview of the reaction coordinate approach to handling strong system-reservoir interactions in quantum thermodynamics. This technique is based on incorporating a collective degree of freedom of the reservoir (the reaction coordinate) into an enlarged system Hamiltonian (the supersystem), which is then treated explicitly. The remaining residual reservoir degrees of freedom are traced out in the usual perturbative manner. The resulting description accurately accounts for strong system-reservoir coupling and/or non-Markovian effects over a wide range of parameters, including regimes in which there is a substantial generation of system-reservoir correlations. We discuss applications to both discrete stroke and continuously operating heat engines, as well as perspectives for additional developments. In particular, we find narrow regimes where strong coupling is not detrimental to the performance of continuously operating heat engines.
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Quantum thermodynamics is a research field that aims at fleshing out the ultimate limits of thermodynamic processes in the deep quantum regime. A complete picture of quantum thermodynamics allows for catalysts, i.e., systems facilitating state transformations while remaining essentially intact in their state, very much reminding of catalysts in chemical reactions. In this work, we present a comprehensive analysis of the power and limitation of such thermal catalysis. Specifically, we provide a family of optimal catalysts that can be returned with minimal trace distance error after facilitating a state transformation process. To incorporate the genuine physical role of a catalyst, we identify very significant restrictions on arbitrary state transformations under dimension or mean energy bounds, using methods of convex relaxations. We discuss the implication of these findings on possible thermodynamic state transformations in the quantum regime.
We study electron pumping in the strong coupling and non-Markovian regime. Our model is a single quantum dot with periodically modulated energy and tunnelling amplitudes. We identify four parameters to control the direction of the current: the driving phase, the coupling strength, the driving frequency and the location of the maxima of the spectral density. In the high-frequency regime, we use a Markovian embedding strategy to map our model to three serial quantum dots weakly coupled to the reservoirs allowing us to use a Floquet master equation. We observe a rectification effect of the pumped charge that is exclusive to the non-Markovian character of our model. In the low-frequency regime, we apply an additional transformation to see our model as three independent transport channels. With the use of full counting statistics, we study charge fluctuations and validate that our model behaves as a single electron source.
The thermodynamics of a quantum system interacting with an environment that can be assimilated to a harmonic oscillator bath has been extensively investigated theoretically. In recent experiments, the system under study however does not interact directly with the bath, but though a cavity or a transmission line. The influence on the system from the bath is therefore seen through an intermediate system, which modifies the characteristics of this influence. Here we first show that this problem is elegantly solved by a transform, which we call the Vernon transform, mapping influence action kernels on influence action kernels. We also show that the Vernon transform takes a particularly simple form in the Fourier domain, though it then must be interpreted with some care. Second, leveraging results in quantum thermodynamics we show how the Vernon transform can also be used to compute the generating function of energy changes in the environment. We work out the example of a system interacting with two baths of the Caldeira-Leggett type, each of them seen through a cavity.
The entropy produced when a system undergoes an infinitesimal quench is directly linked to the work parameter susceptibility, making it sensitive to the existence of a quantum critical point. Its singular behavior at $T=0$, however, disappears as the temperature is raised, hindering its use as a tool for spotting quantum phase transitions. Notwithstanding the entropy production can be split into classical and quantum components, related with changes in populations and coherences. In this paper we show that these individual contributions continue to exhibit signatures of the quantum phase transition, even at arbitrarily high temperatures. This is a consequence of their intrinsic connection to the derivatives of the energy eigenvalues and eigenbasis. We illustrate our results in two prototypical quantum critical systems, the Landau-Zener and $XY$ models.
Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown. Here we present a systematic study of these interplays: we consider a variety of interaction (from non-interacting to strongly correlated) and dynamical (from sudden quench to quasi-adiabatic) regimes, and draw some general conclusions in relation to work extraction and entropy production. As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting. We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy variation, even when many-body correlations are significant.
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