Related papers: Quantum walks assisted by particle number fluctuat…
In this paper, we consider the quantum walk on $\mathbb{Z}$ with attachment of one-length path periodically. This small modification to $\mathbb{Z}$ provides localization of the quantum walk. The eigenspace causing this localization is…
We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy…
Quantum walks are at present an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior.…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motion and create offspring at constant rate. Particles of type…
Quantum walks on the line with a single particle possess a classical analog. Involving more walkers opens up the possibility to study collective quantum effects, such as many particle correlations. In this context, entangled initial states…
We introduce the concept of a quantum walk with two particles and study it for the case of a discrete time walk on a line. A quantum walk with more than one particle may contain entanglement, thus offering a resource unavailable in the…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation…
We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes…
We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in…
For a supercritical catalytic branching random walk on Z^d (d is positive integer) with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. Namely, we divide by t the position coordinates…
We investigate Anderson transitions for a system of two particles moving in a three-dimensional disordered lattice and subject to on-site (Hubbard) interactions of strength U. The two-body problem is exactly mapped into an effective…
We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous time quantum walks in a one-dimensional ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is…
Usually one finds that dissipation tends to make a quantum system more classical in nature. In this paper we study the effect of momentum dissipation on a quantum system. The momentum of the particle is coupled bilinearly to the momenta of…
Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically…
We investigate the effect of disorder on the transfer of quantum states across a one-dimensional lattice with varying levels of control resources. We find that the application of properly designed control signals, even when applied only to…
We investigate continuous-time quantum walks of two indistinguishable particles [bosons, fermions or hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are well consistent with…
We consider two particles hopping on a chain with a contact interaction between them. At strong interaction, there is a molecular bound state separated by a direct gap from a continuous band of atomic states. Introducing weak disorder in…
We consider pairs of non-interacting quantum particles transmitted through a disordered medium, with emphasis on the role of their quantum statistics. It is shown that particle-number correlations measured in transmission are strikingly…