Related papers: Current statistics in the q-boson zero range proce…
We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two…
Equilibrium and nonequilibrium states of matter can exhibit fundamentally different behavior. A key example is the Kardar-Parisi-Zhang universality class in two spatial dimensions (2D KPZ), where microscopic deviations from equilibrium give…
The stochastic $R$ matrix for $U_q(A^{(1)}_n)$ introduced recently gives rise to an integrable zero range process of $n$ classes of particles in one dimension. For $n=2$ we investigate how finitely many first class particles fixed as…
The order parameter cumulants of infinite matrix product ground states are evaluated across a quantum phase transition. A scheme using the Binder cumulant, finite-entanglement scaling and scaling functions to obtain the critical point and…
We elucidate the universal spatio-temporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion process. By…
This review article discusses limit distributions and variance bounds for particle current in several dynamical stochastic systems of particles on the one-dimensional integer lattice: independent particles, independent particles in a random…
We carry out a numerical study of the bi-partite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the anti-ferromagnetic XXZ model. The universal…
We solve a long-standing puzzle in Statistical Mechanics of disordered systems. By performing a high-statistics simulation of the D=3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we…
The universal scaling behavior is studied for nonequilibrium transport through a quantum dot. To describe the dot we use the standard Anderson impurity model and use the non-equilibrium non-crossing approximation in the limit of infinite…
The q-model is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the q-model in two dimensions. We show that close to a…
We study the quantum transition at $T=0$ in the spin-$\frac12$ Ising spin--glass in a transverse field in two dimensions. The world line path integral representation of this model corresponds to an effective classical system in (2+1)…
Thesis is devoted to the application of cumulant analysis in the estimation of impulse response functions for continuous time-invariant linear systems, including systems with inner noises. The main assumption of the work is the second-order…
We study the totally asymmetric exclusion process (TASEP) on a finite one-dimensional lattice with open boundaries, i.e., in contact with two reservoirs at different potentials. The total (time-integrated) current through the system is a…
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…
Recent theoretical studies have predicted the existence of caustics in many-body quantum dynamics, where they manifest as extended regions of enhanced probability density that obey temporal and spatial scaling relations. Focusing on the…
Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle…
We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with…
Recently a remarkable connection has been proposed between the fluctuating hydrodynamic equations of a one-dimensional fluid and the Kardar-Parizi-Zhang (KPZ) equation for interface growth. This connection has been used to relate…
We calculate the vacuum-to-vacuum correlator of two quark tensor currents with two massive quarks, retaining full momentum dependence. For the first time, we include perturbative corrections up to next-to-leading order. Our fully analytical…
We employ non-perturbative flow equations to compute the equation of state for two flavor QCD within an effective quark meson model. This yields the temperature and quark mass dependence of quantities like the chiral condensate or the pion…