Related papers: Hydrodynamic limit of quantum random walks
We study the random walk on dynamical percolation of $\mathbb{Z}^d$ (resp., the two-dimensional triangular lattice $\mathcal{T}$), where each edge (resp., each site) can be either open or closed, refreshing its status at rate $\mu\in…
We use a hydrodynamic model to describe the relaxation of optically injected currents in quantum wells on a picosecond time scale, numerically solving the continuity and velocity evolution equations with the Hermite-Gaussian functions…
We study a model, introduced initially by Gates and Westcott to describe crystal growth evolution, which belongs to the Anisotropic KPZ universality class. It can be thought of as a $(2+1)$-dimensional generalisation of the well known…
We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we…
We define a random walk adic transformation associated to an aperiodic random walk on $G=\mathbb{Z}^{k}\times\mathbb{R}^{D-k}$ driven by a $\beta$-transformation and study its ergodic properties. In particular, this transformation is…
We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties and concentration inequalities for the environment as seen…
In previous work by Avena and den Hollander, a model of a one-dimensional random walk in a dynamic random environment was proposed where the random environment is resampled from a given law along a growing sequence of deterministic times.…
We give bounds in total variation distance for random walks associated to pure central states on free orthogonal quantum groups. As a consequence, we prove that the analogue of the uniform plane Kac walk on this quantum group has a cut-off…
We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…
Fix a strictly positive measure $W$ on the $d$-dimensional torus $\bb T^d$. For an integer $N\ge 1$, denote by $W^N_x$, $x=(x_1, ..., x_d)$, $0\le x_i <N$, the $W$-measure of the cube $[x/N, (x+\mb 1)/N)$, where $\mb 1$ is the vector with…
We study dynamic random conductance models on $\mathbb{Z}^2$ in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove under a second moment assumption that two conditionally…
We define a random walk of a particle in $\mathbb{R}^3$ where the space is rotating. The particle is not glued to the space and will collide with it at random times, resulting in changes in its velocity and direction. After many collisions,…
We derive the hydrodynamic limit of the Kawasaki dynamics for the one-dimensional conservative system of unbounded real-valued spins with arbitrary strong, quadratic and finite-range interactions. This extends prior results for…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
In this paper, we study run-and-tumble particles moving on two copies of the discrete torus (referred to as layers), where the switching rate between layers depends on a mean-field interaction among the particles. We derive the hydrodynamic…
An easy-plane spin winding in a quantum spin chain can be treated as a transport quantity, which propagates along the chain but has a finite lifetime due to phase slips. In a hydrodynamic formulation for the winding dynamics, the quantum…
We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size and shape. In addition, particles may interact magnetically. Free energy of such systems is a random variable because it depends on the choice…
We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is…
We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.
We argue that flows of the quantum electronic liquid in the Fractional Quantum Hall state are comprehensively described by the hydrodynamics of vortices in the quantum incompressible rotating liquid. We obtain the quantum hydrodynamics of…