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Authors
Gabriel T. Landi
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We study the waiting-time distributions (WTDs) of quantum chains coupled to two Lindblad baths at each end. Our focus is on free fermion chains, for which closed-form expressions can be derived, allowing one to study arbitrarily large chain sizes. In doing so, we also derive formulas for 2-point correlation functions involving non-Hermitian propagators.
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We study the dynamics of microscopic quantum correlations, viz., bipartite entanglement and quantum discord between nearest neighbor sites, in Ising spin chain with a periodically varying external magnetic field along the transverse direction. Quantum correlations exhibit periodic revivals with the driving cycles in the finite-size chain. The time of first revival is proportional to the system size and is inversely proportional to the maximum group velocity of Floquet quasi-particles. On the other hand, the local quantum correlations in the infinite chain may get saturated to non-zero values after a sufficiently large number of driving cycles. Moreover, we investigate the convergence of local density matrices, from which the quantum correlations under study originate, towards the final steady-state density matrices as a function of driving cycles. We find that the geometric distance, $d$, between the reduced density matrices of non-equilibrium state and steady-state obeys a power-law scaling of the form $d sim n^{-B}$, where $n$ is the number of driving cycles and $B$ is the scaling exponent. The steady-state quantum correlations are studied as a function of time period of the driving field and are marked by the presence of prominent peaks in frequency domain. The steady-state features can be further understood by probing band structures of Floquet Hamiltonian and purity of the bipartite state between nearest neighbor sites. Finally, we compare the steady-state values of the local quantum correlations with that of the canonical Gibbs ensemble and infer about their canonical ergodic properties. Moreover, we identify generic features in the ergodic properties depending upon the quantum phases of the initial state and the pathway of repeated driving that may be within the same quantum phase or across two different equilibrium phases.
The first law of thermodynamics states that the average total energy current between different reservoirs vanishes at large times. In this note we examine this fact at the level of the full statistics of two times measurement protocols also known as the Full Counting Statistics. Under very general conditions, we establish a tight form of the first law asserting that the fluctuations of the total energy current computed from the energy variation distribution are exponentially suppressed in the large time limit. We illustrate this general result using two examples: the Anderson impurity model and a 2D spin lattice model.
Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling them to different baths at their edges. This was possible because of the concurrent advances in the models used to represent these systems, the methods employed, and the analysis of the emerging phenomenology. Here we aim to give a comprehensive review of these three integrated research directions. We first provide an overarching view of the models of boundary driven open quantum systems, both in the weak and strong coupling regimes. This is followed by a review of state-of-the-art analytical and numerical methods, both exact, perturbative and approximate. Finally, we discuss the transport properties of some paradigmatic one-dimensional chains, with an emphasis on disordered and quasiperiodic systems, the emergence of rectification and negative differential conductance, and the role of phase transitions.
The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set $A$ of sites of the subsystem considered and the set $K$ of excited momentum modes. In this work we make use of a general duality principle establishing the invariance of the entanglement entropy under exchange of the sets $A$ and $K$ to tackle complex problems by studying their dual counterparts. The duality principle is also a key ingredient in the formulation of a novel conjecture for the asymptotic behavior of the entanglement entropy of a free fermion system in the general case in which both sets $A$ and $K$ consist of an arbitrary number of blocks. We have verified that this conjecture reproduces the numerical results with excellent precision for all the configurations analyzed. We have also applied the conjecture to deduce several asymptotic formulas for the mutual and $r$-partite information generalizing the known ones for the single block case.
Open quantum systems can exhibit complex states, which classification and quantification is still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intra-cavity photonic mode, is one of the examples. Unraveling the corresponding Markovian master equation into an ensemble of quantum trajectories and employing the recently proposed calculation of quantum Lyapunov exponents [I.I. Yusipov {it et al.}, Chaos {bf 29}, 063130 (2019)], we identify `chaotic and `regular regimes there. In particular, we show that chaotic regimes manifest an intermediate power-law asymptotics in the distribution of photon waiting times. This distribution can be retrieved by monitoring photon emission with a single-photon detector, so that chaotic and regular states can be discriminated without disturbing the intra-cavity dynamics.
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