Related papers: Structure and eigenvalues of heat-bath Markov chai…

Based on generalization and extension of previous work [Phys. Rev. Lett. {\bf 112}, 067201 (2014)] to multiple independent markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak…

The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for…

We consider integrable quantum spin chains with competing interactions. We apply the quantum transfer matrix approach to these spin chains. This allowed us to derive a set of non-linear integral equations for the thermodynamics of these…

We present a recurrence-transience classification for discrete-time Markov chains on manifolds with negative curvature. Our classification depends only on geometric quantities associated to the increments of the chain, defined via the…

We solve the long-standing central spin problem for a general set of inhomogeneous bath couplings and a large class of initial bath states. We compute the time evolution of the coherence of a central spin coupled to a spin bath by resumming…

We study the mixing time of systematic scan Markov chains on finite spin systems. It is known that, in a single site setting, the mixing time of systematic scan can be bounded in terms of the influences sites have on each other. We…

We show that two, non interacting, infinitely long spin chains can become globally entangled at the mesoscopic level of their fluctuation operators through a purely noisy microscopic mechanism induced by the presence of a common heat bath.…

We investigate spin and heat currents in the non-equilibrium steady state of inhomogeneous $XX$-spin chains, which act as interfaces between two bosonic heat baths. Using special functions that diagonalize the single-particle Hamiltonian,…

We define the spectral gap of a Markov chain on a finite state space as the second-smallest singular value of the generator of the chain, generalizing the usual definition of spectral gap for reversible chains. We then define the relaxation…

We consider thermodynamic properties, e.g. specific heat, magnetic susceptibility, of alternating Heisenberg spin chains. Due to a hidden Ising symmetry these chains can be decomposed into a set of finite chain fragments. The problem of…

Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…

We investigate the thermal responses of a harmonic oscillator chain coupled at its boundaries to heat baths held at different temperatures. This setup sustains a steady energy flux, continuously dissipating heat into both reservoirs. By…

We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An…

Describing the thermodynamic properties of quantum systems far from equilibrium is challenging, in particular when the system is strongly coupled to its environment, or when memory effects cannot be neglected. Here, we address such regimes…

We consider continuous-space, discrete-time Markov chains on $\mathbb{R}^d$, that admit a finite number $N$ of metastable states. Our main motivation for investigating these processes is to analyse random Poincar\'e maps, which describe…

We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. We relate them by showing that the mixing time of the lazy chain is equivalent…

In this article, we derive the stochastic master equations corresponding to the statistical model of a heat bath. These stochastic differential equations are obtained as continuous time limits of discrete models of quantum repeated…

Single-chain magnets are molecular spin chains displaying slow relaxation of the magnetisation on a macroscopic time scale. To this similarity with single-molecule magnets they own their name. In this chapter the distinctive features of…

We investigate the effective temperature of a harmonic chain whose two ends are coupled to two baths at different temperatures. We propose to take the weighted average temperature as the effective temperature of the system. The weight…

In order to better understand the minimal ingredients for thermal rectification, we perform a detailed investigation of a simple spin chain, namely, the open XX model with a Lindblad dynamics involving global dissipators. We use a…