Related papers: Geometrical aspects of quantum walks on random two…
Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function…
We report transport mobility measurements for clean, two-dimensional (2D) electron systems confined to GaAs quantum wells (QWs), grown via molecular beam epitaxy, in two families of structures, a standard, symmetrically-doped GaAs set of…
Expanding media are typical in many different fields, e.g. in Biology and Cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties. Here, we focus on such…
We consider a discrete random walk (RW) in n dimensions . The RW is adapted with a geometric absorption process: at any discrete time there is a constant probability that absorption occurs in the current state. To model the RW with…
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are…
Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the…
Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…
Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…
Localization phenomena of quantum walks makes the propagation dynamics of a walker strikingly different from that corresponding to classical random walks. In this paper, we study the localization phenomena of four-state discrete-time…
Quantum random walks (QRWs) can be used to perform both quantum simulations and quantum algorithms. In order to exploit this potential, quantum walks on different types of graphs must be physically implemented. To this end we design, model…
Random walks are a fundamental tool for analyzing realistic complex networked systems and implementing randomized algorithms to solve diverse problems such as searching and sampling. For many real applications, their actual effect and…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
Quantum walks on networks are a paradigmatic model in quantum information theory. Quantum-walk algorithms have been developed for various applications, including spatial-search problems, element-distinctness problems, and node centrality…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Continuous-time random walk (CTRW) is a model of anomalous sub-diffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, $\psi(\tau) \tau^{-(1+\alpha)}$, leads to…
This paper is devoted to the study of continuous-time processes known as continuous-time open quantum walks (CTOQWs). A CTOQW represents the evolution of a quantum particle constrained to move on a discrete graph, but also has internal…
Quantum transport is strongly influenced by interference with phase relations that depend sensitively on the scattering medium. Since even small changes in the geometry of the medium can turn constructive interference to destructive, a…
Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…