We investigate the effects of noise-induced coherence on average current and current fluctuations in a simple model of a quantum absorption refrigerator with degenerate energy levels. We describe and explain the differences and similarities between the system behavior when it operates in the classical regime, where the populations and coherences in the corresponding quantum optical master equation decouple in a suitably chosen basis, and in the quantum regime, where such a transformation does not exist. The differences between the quantum and the classical cases are observable only close to the maximum current regime, where the system steady-state becomes nonunique. This allows us to approximate the system dynamics by an analytical model based on a dichotomous process that explains the behavior of the average current both in the classical and in the quantum cases. Due to the nonuniqueness, the scaled cumulant generating function for the current at the vicinity of the critical point exhibits behavior reminiscent of the dynamical first-order phase transition. Unless the system parameters are fine-tuned to a single point in the parameter space, the corresponding current fluctuations are moderate in the quantum case and large in the classical case.
We investigate the effects of noise-induced coherence on average current and current fluctuations in a simple model of a quantum absorption refrigerator with degenerate energy levels. We describe and explain the differences and similarities between the system behavior when it operates in the classical regime, where the populations and coherences in the corresponding quantum optical master equation decouple in a suitably chosen basis, and in the quantum regime, where such a transformation does not exist. The differences between the quantum and the classical cases are observable only close to the maximum current regime, where the system steady-state becomes nonunique. This allows us to approximate the system dynamics by an analytical model based on a dichotomous process that explains the behavior of the average current both in the classical and in the quantum cases. Due to the nonuniqueness, the scaled cumulant generating function for the current at the vicinity of the critical point exhibits behavior reminiscent of the dynamical first-order phase transition. Unless the system parameters are fine-tuned to a single point in the parameter space, the corresponding current fluctuations are moderate in the quantum case and large in the classical case.
Absorption refrigerators transfer thermal energy from a cold reservoir to a hot reservoir using input energy from a third, so-called work reservoir. We examine the operation of quantum absorption refrigerators when coherences between eigenstates survive in the steady state limit. In our model, the working medium comprises a discrete, four-level system. Several studies on related setups have demonstrated the performance-enhancing potential of steady-state eigenbasis quantum coherences. By contrast, in our model such coherences generally quench the cooling current in the refrigerator, while minimally affecting the coefficient of performance (cooling efficiency). We rationalize the behavior of the four-level refrigerator by studying three-level model systems for energy transport and refrigeration. Our calculations further illuminate the shortcomings of secular quantum master equations and the necessity of employing dynamical equations of motion that retain couplings between population and coherences.
We study the fluctuation statistics of integrated currents in noisy quantum diffusive systems, focusing on the Quantum Symmetric Simple Exclusion and Inclusion Processes (QSSEP/QSSIP). These one-dimensional fermionic (QSSEP) and bosonic (QSSIP) models feature stochastic nearest-neighbor hopping driven by Brownian noise, together with boundary injection and removal processes. They provide solvable microscopic settings in which quantum coherence coexists with diffusion. Upon noise averaging, their dynamics reduce to those of the classical SSEP/SSIP. We show that the cumulant-generating function of the integrated current, at large scales, obeys a large deviation principle. To leading order in system size and for each noise realization, it converges to that of the corresponding classical process, establishing a classical typicality of current fluctuations in these noisy quantum systems. We further demonstrate a direct connection with Macroscopic Fluctuation Theory (MFT), showing that the large-scale equations satisfied by biased quantum densities coincide with the steady-state Hamilton equations of MFT, thereby providing a microscopic quantum justification of the MFT framework in these models. Finally, we identify the leading finite-size corrections to the current statistics. We show the existence of subleading contributions of purely quantum origin, which are absent in the corresponding classical setting, and provide their explicit expressions for the second and third current cumulants. These quantum corrections are amenable to direct experimental or numerical verification, provided sufficient control over the noise realizations can be achieved. Their presence points toward the necessity of a quantum extension of MFT.
The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a tradeoff relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines. Here, we examine the interplay of quantum system coherences and heat current fluctuations on the validity of the thermodynamics uncertainty relation in the quantum regime. To achieve the current statistics, we perform a full counting statistics simulation of the Redfield quantum master equation. We focus on steady-state quantum absorption refrigerators where nonzero coherence between eigenstates can either suppress or enhance the cooling power, compared with the incoherent limit. In either scenario, we find enhanced relative noise of the cooling power (standard deviation of the power over the mean) in the presence of system coherence, thereby corroborating the thermodynamic uncertainty relation. Our results indicate that fluctuations necessitate consideration when assessing the performance of quantum coherent thermal machines.
Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar--Parisi--Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114, 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.
Abstract The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system
The methods of nonequilibrium density-matrix and coarse-temporal conception are used to obtain the kinetic equation for the parameters ${\ensuremath{\gamma}}_{\mathit{n}\mathit{m}}$(t)=Sp[\ensuremath{\rho}^(t)\ensuremath{\Vert}n〉〈m\ensuremath{\Vert}] of a quantum-dynamic system (QDS) interacting with a thermal bath and external stochastic field. It is important that the stochastic field is taken exactly into consideration. For diagonal QDS parameters ${\ensuremath{\gamma}}_{\mathit{n}\mathit{n}}$(t) this equation is reduced to the generalized Pauli equation (GPE) with stochastic time-dependent coefficients wnm(t). Special attention is given to the procedure of averaging over stochastic processes. It is shown that after averaging over energy fluctuations affected by the stochastic field, in the first cumulant approximation in terms of stochastic processes wnm(t), the GPE is transformed to the Pauli equation for the QDS state population Pn(t)=〈${\ensuremath{\gamma}}_{\mathit{n}\mathit{n}}$(t)〉f. As an example, the relaxation behavior of a two-level system interacting with a dichotomous field (dichotomous Markovian process of kangaroo type) and a harmonic oscillator coupled with a thermal bath is considered. It is shown that the probability of relaxation transitions between energy levels may be changed by several orders of magnitude under the influence of the dichotomous field.