We study the steady state of a finite XX chain coupled at its boundaries to quantum reservoirs made of free spins that interact one after the other with the chain. The two-point correlations are calculated exactly and it is shown that the steady state is completely characterized by the magnetization profile and the associated current. Except at the boundary sites, the magnetization is given by the average of the reservoirs' magnetizations. The steady state current, proportional to the difference in the reservoirs' magnetizations, shows a non-monotonous behavior with respect to the system-reservoir coupling strength, with an optimal current state for a finite value of the coupling. Moreover, we show that the steady state can be described by a generalized Gibbs state.Understanding non-equilibrium behavior of quantum systems on the basis of general principles is one of the more challenging prospects of statistical physics. In particular, the complete characterization of the so-called Quantum Non-Equilibrium Steady-States (QNESS), i. e. stationary current full quantum states, is of primer and central focus since they are possible candidates for playing a role similar to Gibbs states in constructing a nonequilibrium statistical mechanics [1,2,3,4,5,6,7,8].To elucidate the general guiding principles for a nonequilibrium statistical mechanics, exactly solvable models play a central role. Among many models, the XX quantum chain is one of the simplest non-trivial manybody system. Its N -sites Hamiltonian is given bywhere the σs are the usual Pauli matrices, J is the exchange coupling and h a transverse (possibly external) magnetic field. Due to the fact that its dynamics can be described in an explicit way, the one-dimensional XX model has been extensively studied in various nonequilibrium contexts [9]. On the experimental side, the most promising perspectives for these studies come from the ultra-cold atoms community since the XX model (1) Antal et al.[13] studied the ground state of the Ising and XX chain Hamiltonian with the addition of a magnetization or energy current J via a Lagrange multiplier. The ground state of the effective Hamiltonian H S − λJ was interpreted as a non-equilibrium stationary current full state. Such an effective Hamiltonian was supposed to capture locally the essential features of a finite chain coupled at its boundary sites to quantum reservoirs. Soon after, Ogata [14], Aschbacher and Pillet [15] considered the anisotropic XY steady state induced by the unitary dynamics, U (t) = e −itHS , starting with an initial state in which the left and right halves are set at inverse temperature β L and β R . They showed that the QNESS can be effectively described by a generalized Gibbs state ∼ e −βHS +δY whereβ = (β L +β R )/2 is the average inverse temperature, δ = (β L − β R )/2 is a driving force coupled to a long-range operator Y commuting with H S . The operator Y is given by Y = ∞ l=1 µ l Y l where Y l are currents operators associated to lth sites conserved quantities and where the coefficients ...

Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play important roles in controlling noise in gene expression and phenotypic variation. A quantitative understanding of the impact of these factors requires analysis of the corresponding stochastic models. However, for stochastic models of gene expression with feedback and bursting, exact analytical results for protein distributions have not been obtained so far. Here, we analyze a model of gene expression with bursting and feedback regulation and obtain exact results for the corresponding protein steady-state distribution. The results obtained provide new insights into the role of bursting and feedback in noise regulation and optimization. Furthermore, for a specific choice of parameters, the system studied maps on to a two-state biochemical switch driven by a bursty input noise source. The analytical results derived provide quantitative insights into diverse cellular processes involving noise in gene expression and biochemical switching.

Abstract. We study zero-temperature XX chains and transverse Ising chains and join an initially separate finite piece on one or on both sides to an infinite remainder. In both critical and non-critical systems we find a typical increase of the entanglement entropy after the quench, followed by a slow decay towards the value of the homogeneous chain. In the critical case, the predictions of conformal field theory are verified for the first phase of the evolution, while at late times a step structure can be observed.

Abstract. We present the results obtained on the magnetisation relaxation properties of an XX quantum chain in a transverse magnetic field. We first consider an initial thermal kink-like state where half of the chain is initially thermalized at a very high temperature T b while the remaining half, called the system, is put at a lower temperature T s . From this initial state, we derive analytically the Green function associated to the dynamical behaviour of the transverse magnetisation. Depending on the strength of the magnetic field and on the temperature of the system, different regimes are obtained for the magnetic relaxation. In particular, with an initial dropletlike state, that is a cold subsystem of finite size in contact at both ends with an infinite temperature environnement, we derive analytically the behaviour of the timedependent system magnetisation.