Related papers: The simplest 2D quantum walk detects chaoticity

Billiards are flat cavities where a particle is free to move between elastic collisions with the boundary. In chaos theory these systems are simple prototypes, their conservative dynamics of a billiard may vary from regular to chaotic,…

Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…

We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum…

The staggered quantum walk is a type of discrete-time quantum walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered…

Motion in bounded domains represents a paradigm in several settings: from billiard dynamics, to random walks in a finite lattice, with applications to relevant physical, ecological and biological problems. A remarkable universal property,…

Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of…

We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…

Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and…

We study numerically the scaling properties of scars in stadium billiard. Using the semiclassical criterion, we have searched systematically the scars of the same type through a very wide range, from ground state to as high as the 1…

We experimentally studied evolution of quasi-eigenmodes as classical dynamics undergoing a transition from being regular to chaotic in open quantum billiards. In a deformation-variable microcavity we traced all high-Q cavity modes in a wide…

Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…

We report on the experimental study of the spectral properties of quantum systems consisting of two quantum billiards (QBs), one with chaotic, the other one with integrable classical dynamics, that are coupled to each other via an opening…

We study a spin-1/2-particle moving on a one dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the…

We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots, comparing behavior in actual chaotic billiards with analytic results previously…

The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence…

In numerically solving the Helmholtz equation inside a connected plane domain with Dirichlet boundary conditions (the problem of the quantum billiard) one surprisingly faces enormous difficulties if the domain has a problematic geometry…

The dynamics of chaotic billiards is significantly influenced by coexisting regions of regular motion. Here we investigate the prevalence of a different fundamental structure, which is formed by marginally unstable periodic orbits and…

We perform a detailed study of the chaotic component in mixed-type Hamiltonian systems on the example of a family of billiards [introduced by Robnik in J. Phys. A: Math. Gen. 16, 3971 (1983)]. The phase space is divided into a grid of cells…

Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…

We report on the theoretical analysis of bosonic and fermionic non-interacting systems in a discrete two-particle quantum walk affected by different kinds of disorder. We considered up to 100-step QWs with a spatial, temporal and…