Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field

We study nonequilibrium dynamics of the quantum Ising chain at zero temperature when the transverse field is varied stochastically. In the equivalent fermion representation, the equation of motion of Majorana operators is derived in the form of a one-dimensional, continuous-time quantum random walk with stochastic, time-dependent transition amplitudes. This type of external noise gives rise to decoherence in the associated quantum walk and the semiclassical wave-packet generally has a diffusive behavior. As a consequence, in the quantum Ising chain, the average entanglement entropy grows in time as $t^{1/2}$ and the logarithmic average magnetization decays in the same form. In the case of a dichotomous noise, when the transverse-field is changed in discrete time-steps, $\tau$, there can be excitation modes, for which coherence is maintained, provided their energy satisfies $\epsilon_k \tau\approx n\pi$ with a positive integer $n$. If the dispersion of $\epsilon_k$ is quadratic, the long-time behavior of the entanglement entropy and the logarithmic magnetization is dominated by these ballistically traveling coherent modes and both will have a $t^{3/4}$ time-dependence.Comment: 12 pages, 10 figure

Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields

In transverse-field Ising models, disorder in the couplings gives rise to a drastic reduction of the critical energy gap and, accordingly, to an unfavorable, slower-than-algebraic scaling of the density of defects produced when the system is driven through its quantum critical point. By applying Kibble-Zurek theory and numerical calculations, we demonstrate in the one-dimensional model that the scaling of defect density with annealing time can be made algebraic by balancing the coupling disorder with suitably chosen inhomogeneous driving fields. Depending on the tail of the coupling distribution at zero, balancing can be either perfect, leading to the well-known inverse-square law of the homogeneous system, or partial, still resulting in an algebraic decrease but with a smaller, non-universal exponent. We also study defect production during an environment-temperature quench of the open variant of the model in which the system is slowly cooled down to its quantum critical point. According to our scaling and numerical results, balanced disorder leads again to an algebraic temporal decrease of the defect density.Comment: 11 pages, 6 figure

Anomalous diffusion in disordered multi-channel systems

We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong disorder renormalization group method and Monte Carlo simulations are used. Generally, we observe anomalous diffusion, where the average distance travelled by the particle, []_{av}, has a power-law time-dependence []_{av} ~ t^{\mu_K(v)}, with a diffusion exponent 0 \le \mu_K(v) \le 1. In the presence of left-right symmetry of the distribution of random rates, the recurrent point of the multi-channel system is independent of K, and the diffusion exponent is found to increase with K and decrease with v. In the absence of this symmetry, the recurrent point may be shifted with K and the current can be reversed by varying the lane change rate v.Comment: 16 pages, 7 figure

Scaling behavior of the contact process in networks with long-range connections

We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that are characterized by different shortest-path dimensions and random-walk dimensions. We provide numerical evidence that an absorbing phase transition occurs at some finite value of the infection rate and the corresponding dynamical critical exponents depend on the underlying network. Furthermore, the time-dependent quantities exhibit log-periodic oscillations in agreement with the discrete scale invariance of the networks. In case of spreading from an initial active seed, the critical exponents are found to depend on the location of the initial seed and break the hyper-scaling law of the directed percolation universality class due to the inhomogeneity of the networks. However, if the cluster spreading quantities are averaged over initial sites the hyper-scaling law is restored.Comment: 9 pages, 10 figure

Correlation amplitude and entanglement entropy in random spin chains

Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1/2 chain focusing on the long-length and ground-state behavior of the average time-independent spin-spin correlation function C(l)=\upsilon l^{-\eta}. In addition to the well-known universal (disorder-independent) power-law exponent \eta=2, we find interesting universal features displayed by the prefactor \upsilon=\upsilon_o/3, if l is odd, and \upsilon=\upsilon_e/3, otherwise. Although \upsilon_o and \upsilon_e are nonuniversal (disorder dependent) and distinct in magnitude, the combination \upsilon_o + \upsilon_e = -1/4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.Comment: v1: 16 pages, 15 figures; v2: 17 pages, improved discussions and statistics, references added, published versio

Random walks in a random environment on a strip: a renormalization group approach

We present a real space renormalization group scheme for the problem of random walks in a random environment on a strip, which includes one-dimensional random walk in random environment with bounded non-nearest-neighbor jumps. We show that the model renormalizes to an effective one-dimensional random walk problem with nearest-neighbor jumps and conclude that Sinai scaling is valid in the recurrent case, while in the sub-linear transient phase, the displacement grows as a power of the time.Comment: 9 page

The antiepileptic potential of nucleosides

Despite newly developed antiepileptic drugs to suppress epileptic symptoms, approximately one third of patients remain drug refractory. Consequently, there is an urgent need to develop more effective therapeutic approaches to treat epilepsy. A great deal of evidence suggests that endogenous nucleosides, such as adenosine (Ado), guanosine (Guo), inosine (Ino) and uridine (Urd), participate in the regulation of pathomechanisms of epilepsy. Adenosine and its analogues, together with non-adenosine (non-Ado) nucleosides (e.g., Guo, Ino and Urd), have shown antiseizure activity. Adenosine kinase (ADK) inhibitors, Ado uptake inhibitors and Ado-releasing implants also have beneficial effects on epileptic seizures. These results suggest that nucleosides and their analogues, in addition to other modulators of the nucleoside system, could provide a new opportunity for the treatment of different types of epilepsies. Therefore, the aim of this review article is to summarize our present knowledge about the nucleoside system as a promising target in the treatment of epilepsy

Partially asymmetric exclusion models with quenched disorder

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated distance traveled by the particles, x, scales with the time, t, as x ~ t^{1/z}, with a dynamical exponent z > 0. Using extreme value statistics and an asymptotically exact strong disorder renormalization group method we analytically calculate, z_{pt}, for particlewise (pt) disorder, which is argued to be related to the dynamical exponent for sitewise (st) disorder as z_{st}=z_{pt}/2. In the symmetric situation with zero mean drift the particle diffusion is ultra-slow, logarithmic in time.Comment: 4 pages, 3 figure

Asymmetric simple exclusion process in one-dimensional chains with long-range links

We study the boundary-driven asymmetric simple exclusion process (ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting $pL$ different pairs of sites selected randomly where $L$ and $p$ denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at rate $\alpha$ and out of a chain at the other boundary at rate $\beta$, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low density, high density, and maximal current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases; an empty phase with $\rho = 0$, a jammed phase with $\rho = 1$, and a shock phase with $0<\rho<1$ where $\rho$ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the non-equilibrium phase transition is explained by an analytic theory based on a mean-field approximation and an annealed approximation.Comment: revised version (16 pages and 6 eps figures