Related papers: Feynman checkers: the probability of direction rev…

Although the laws of classical physics are deterministic, thermodynamics gives rise to an arrow of time through irreversible processes. In quantum mechanics the unitary nature of the time evolution makes it intrinsically reversible, however…

We consider a generalized version of a directionally reinforced random walk, which was originally introduced by Mauldin, Monticino, and von Weizs\"{a}cker in \cite{drw}. Our main result is a stable limit theorem for the position of the…

Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…

Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…

We discretize the Weyl equation for a massless, spin-1/2 particle on a time-diagonal, hypercubic spacetime lattice with null faces. The amplitude for a step of right-handed chirality is proportional to the spin projection operator in the…

We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…

We study a model of multi-excited random walk on a regular tree which generalizes the models of the once excited random walk and the digging random walk introduced by Volkov (2003). We show the existence of a phase transition of the…

We analyze the properties of a two and three dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [1]. In that model, particles are dynamically confined on the brane due to…

We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula (2.5). Using this representation, we derive a relation between the spectral decomposition of the Markov additive…

In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the…

A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the…

The paper by A.N. Kolmogorov 1934 "Random Moves", hereinafter ANK34, uses a Fokker-Planck-type equation for a 6-dimensional vector with a total rather than a partial derivative with respect to time, and with a Laplacian in the space of…

In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an…

We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…

The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement…

We investigate the evolution of a discrete-time one-dimensional quantum walk driven by a position-dependent coin. The rotation angle which depends upon the position of a quantum particle parameterizes the coin operator. For different values…

We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters allowing for the engineered realization of distinct topological phases. The option to directly monitor…

We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…

In this paper we study a substantial generalization of the model of excited random walk introduced in [Electron. Commun. Probab. 8 (2003) 86-92] by Benjamini and Wilson. We consider a discrete-time stochastic process $(X_n,n=0,1,2,...)$…

We propose a variation of the quantum walk on a circle in phase space by conjoining the Hadamard coin flip with simultaneous displacement of the walker's location in phase space and show that this generalization is a proper quantum walk…