Within a hydrodynamic framework, the authors describe the out-of-equilibrium dynamics of noninteracting one-dimensional fermionic systems, featuring localized gain and loss of particles at the center of the system. They discuss quenches from equilibrium and nonequilibrium homogeneous initial states as well as from inhomogeneous ones. The results demonstrate the existence of a Zeno effect for large loss rates and the emergence of exotic nonequilibrium steady states with a stepwise uniform density profile that is discontinuous in correspondence with the localized loss.
Within a hydrodynamic framework, the authors describe the out-of-equilibrium dynamics of noninteracting one-dimensional fermionic systems, featuring localized gain and loss of particles at the center of the system. They discuss quenches from equilibrium and nonequilibrium homogeneous initial states as well as from inhomogeneous ones. The results demonstrate the existence of a Zeno effect for large loss rates and the emergence of exotic nonequilibrium steady states with a stepwise uniform density profile that is discontinuous in correspondence with the localized loss.
We address the effects of dissipative defects giving rise to a localized particle loss, in one-dimensional noninteracting lattice fermionic gases confined within a region of size $\ensuremath{\ell}$. We consider homogeneous systems within hard walls and inhomogeneous systems where the particles are trapped by space-dependent external potentials, such as harmonic traps. We model the dissipative particle-decay mechanism by Lindblad master equations governing the time evolution of the density matrix. The resulting quantum dynamics is analyzed in protocols starting from the ground state of the Hamiltonian for N0 particles, then evolving under the effect of one dissipative particle-loss defect, for example, at the center of the system. We study the interplay between time, size $\ensuremath{\ell}$, and the number N0 of initial particles, considering two different situations: (i) fixed number N0 of initial particles; and (ii) fixed ratio ${N}_{0}/\ensuremath{\ell}$, corresponding to the thermodynamic limit of the initial equilibrium state. We show that the quantum evolutions of the particle number and density develop various intermediate and asymptotic dynamic regimes, and nontrivial large-time states when the dissipative mechanism acts at the center of the system.
Abstract We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.
We consider a quantum quench in a noninteracting fermionic one-dimensional field theory. The system of size L is initially prepared into two halves L $([\ensuremath{-}L/2,0])$ and R([0,L/2]), each of them thermalized at two different temperatures TL and TR, respectively. At a given time, the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system $(L\ensuremath{\rightarrow}\ensuremath{\infty})$, we show that the time evolution of the particle and energy densities is well described via a hydrodynamic approach which allows us to evaluate the correspondent stationary currents. We show, in such a case, that the two-point correlation functions are deduced, at large times, from a simple nonequilibrium steady state. Otherwise, whenever the boundary conditions are retained (in a properly defined thermodynamic limit), any current is suppressed at large times, and the stationary state is described by a generalized Gibbs ensemble, which is diagonal and depends only on the post-quench mode occupation.
Abstract We study the out-of-equilibrium dynamics of noninteracting fermions in one dimension and in continuum space, in the presence of a delta impurity potential at the origin whose strength g is varied at time t = 0. The system is prepared in its ground state with g = g 0 = +∞, with two different densities and Fermi wave-vectors k L and k R on the two half-spaces x > 0 and x < 0 respectively. It then evolves for t > 0 as an isolated system, with a finite impurity strength g . We compute exactly the time dependent density and current. For a fixed position x and in the large time limit t → ∞, the system reaches a non-equilibrium stationary state (NESS). We obtain analytically the correlation kernel, density, particle current, and energy current in the NESS, and characterize their relaxation, which is algebraic in time. In particular, in the NESS, we show that, away from the impurity, the particle density displays oscillations which are the non-equilibrium analog of the Friedel oscillations. In the regime of ‘rays’, x / t = ξ fixed with x , t → ∞, we compute the same quantities and observe the emergence of two light cones, associated to the Fermi velocities k L and k R in the initial state. Interestingly, we find non trivial quantum correlations between two opposite rays with velocities ξ and − ξ which we compute explicitly. We extend to a continuum setting and to a correlated initial state the analytical methods developed in a recent work of Ljubotina, Sotiriadis and Prosen, in the context of a discrete fermionic chain with an impurity. We also generalize our results to an initial state at finite temperature, recovering, via explicit calculations, some predictions of conformal field theory in the low energy limit.
I investigated the quench dynamics of inhomogeneous quantum spin chains. Here quench means the sudden change of an external parameter. The system is initially in its ground state. After the change of the parameter the ground state is not an eigenstate of the new Hamiltonian and a non-trivial dynamics starts. The dynamics is investigated with free fermion techniques. Various types of inhomogeneities were considered, homogeneous system with local defect, quasi-periodic systems and a disordered model. The results are qualitatively described by a special quasi-classical theory.
Recent experimental advances on ultracold atomic gases and trapped ions have made it possible to simulate exactly solvable quantum systems of interacting particles. In particular, the feasibility of making rapid changes, so-called quantum quenches, to such set-ups has allowed experimentalists to probe non-equilibrium phenomena in closed interacting quantum systems. This, in turn, has spurred a considerable theoretical interest in quantum many-body systems out of equilibrium. In this thesis, we study non-equilibrium properties of quantum many-body systems in the framework of exactly solvable quantum field theory in one spatial dimension. Specific systems include interacting fermions described by the Luttinger model and effective descriptions of spin chains using conformal field theory (CFT). Special emphasis is placed on heat and charge transport, studied from the point of view of quench dynamics, and, in particular, the effects of breaking conformal symmetries on transport properties. Examples include the Luttinger model with non-local interactions, breaking Lorentz and scale invariance, and inhomogeneous CFT, which generalizes standard CFT in that the usual propagation velocity v is replaced by a function v(x) that depends smoothly on the position x, breaking translation invariance. The quench dynamics studied here is for quantum quenches between, in general, different smooth inhomogeneous systems. An example of this is the so-called smooth-profile protocol, in which the initial state is defined by, e.g., smooth inhomogeneous profiles of inverse temperature and chemical potential, and the time evolution is governed by a homogeneous Hamiltonian. Using this protocol, we compute exact analytical results for the full time evolution of the systems mentioned above. In particular, we derive finite-time results that are universal in the sense that the same relations between the non-equilibrium dynamics and the initial profiles hold for any unitary CFT. These results also make clear that heat and charge transport in standard CFT are purely ballistic. Finally, we propose and study an inhomogeneous CFT model with v(x) given by a random function. We argue that this model naturally emerges as an effective description of one-dimensional quantum many-body systems with certain static random impurities. Using tools from wave propagation in random media, we show that such impurities lead to normal and anomalous diffusive contributions to heat transport on top of the ballistic one known from standard CFT.