We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m(0) for x<0 to m(0) for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Phi(x/t) and the profile develops a flat part (m=Phi=0) in the (x/t)1/2 while it expands with the maximum velocity c(0)=1 for m(0)-->0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.

We study the formation of localized shocks in one-dimensional driven diffusive systems with spacially homogeneous creation and annihilation of particles (Langmuir kinetics).We show how to obtain hydrodynamic equations which describe the density profile in systems with uncorrelated steady state as well as in those exhibiting correlations. As a special example of the latter case the Katz-Lebowitz-Spohn model is considered. The existence of a localized double density shock is demonstrated for the first time in one-dimensional driven diffusive systems. This corresponds to phase separation into regimes of three distinct densities, separated by localized domain walls. Our analytical approach is supported by Monte-Carlo simulations.

Abstract.We discuss the long-time limit of the integrated current distribution for the onedimensional zero-range process with open boundaries. We observe that the current fluctuations become site-dependent above some critical current and argue that this is a precursor of the condensation transition which occurs in such models. Our considerations for the totally asymmetric zero-range process are complemented by a Bethe ansatz treatment for the equivalent exclusion process.

We study zero-temperature quantum spin chains, which are characterized by a nonvanishing current. For the XX model starting from the initial state mid R:cdots, three dots, centered upward arrow upward arrow upward arrow downward arrow downward arrow downward arrowcdots, three dots, centered we derive an exact expression for the variance of the total spin current. We show that asymptotically the variance exhibits an anomalously slow logarithmic growth; we also extract the subleading constant term. We then argue that the logarithmic growth remains valid for the XXZ model in the critical region.

We consider the behaviour of current fluctuations in the one-dimensional partially asymmetric zero-range process with open boundaries. Significantly, we find that the distribution of large current fluctuations does not satisfy the Gallavotti-Cohen symmetry and that such a breakdown can generally occur in systems with unbounded state space. We also discuss the dependence of the asymptotic current distribution on the initial state of the system.

The ground-state correlations are investigated for an isotropic transverse XY chain which is constrained to carry either a current of magnetization (J M ) or a current of energy (J E ). We find that the effect of J M = 0 on the large-distance decay of correlations is twofold: i) oscillations are introduced and ii) the amplitude of the power law decay increases with increasing current. The effect of energy current is more complex. Generically, correlations in current carrying states are found to decay faster than in the J E = 0 states, contrary to expectations that correlations are increased by the presence of currents. However, increasing the current, one reaches a special line where the correlations become comparable to those of the J E = 0 states. On this line, the symmetry of the ground state is enhanced and the transverse magnetization vanishes. Further increase of the current destroys the extra symmetry but the transverse magnetization remains at the high-symmetry, zero value.

We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the totally asymmetric simple exclusion process (only pieces of size 1 break off a given cluster). We express the exact solution of master equation for the process in terms of a determinant which can be derived using the Bethe ansatz. From this determinant we compute the distribution of the current across an arbitrary bond which after appropriate scaling is given by the distribution of the largest eigenvalue of the Gaussian unitary ensemble of random matrices. This result confirms universality of the scaling form of the current distribution in the KPZ universality class and suggests that there is a link between integrable particle systems and random matrix ensembles.

We consider the fluctuations of generalized currents in stochastic Markovian dynamics. The large deviations of current fluctuations are shown to obey a Gallavotti-Cohen (GC) type symmetry in systems with a finite state space. However, this symmetry is not guaranteed to hold in systems with an infinite state space. A simple example of such a case is the zero-range process (ZRP). Here we discuss in more detail the already reported (Harris et al 2006 Europhys. Lett. 75 227) breakdown of the GC symmetry in the context of the ZRP with open boundaries and we give a physical interpretation of the phases that appear. Furthermore, the earlier analytical results for the single-site case are extended to cover multiple-site systems. We also use our exact results to test an efficient numerical algorithm of Giardinà et al (2006 Phys. Rev. Lett. 96 120603), which was developed to measure the current large deviation function directly. We find that this method breaks down in some phases which we associate with the gapless spectrum of an effective Hamiltonian.