Related papers: Dynamical Localization of Quantum Walks in Random …
In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and…
Quantization and asymptotic behaviour of a variant of discrete random walk on integers are investigated. This variant, the $\epsilon_{V^{k}}$ walk, has the novel feature that it uses many identical quantum coins keeping at the same time…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
We study the fate of dynamical localization of two quantum kicked rotors with contact interaction. This interaction mimics experimental realizations with ultracold atomic gases. Dynamical localization for a single rotor takes place in…
We propose a scheme to implement the one-dimensional coined quantum walk with electrons transported through a two-dimensional network of spintronic semiconductor quantum rings. The coin degree of freedom is represented by the spin of the…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
Quantum walk (QW) in presence of lattice disorders leads to a multitude of interesting phenomena, such as Anderson localization. While QW has been realized in various optical and atomic systems, its implementation with superconducting…
A connection between the asymptotic behavior of the open quantum walk and the spectrum of a generalized quantum coins is studied. For the case of simultaneously diagonalizable transition operators an exact expression for probability…
We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random…
In discrete-time quantum walk (DTQW) the walker's coin space entangles with the position space after the very first step of the evolution. This phenomenon may be exploited to obtain the value of the coin parameter $\theta$ by performing…
We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value…
This article establishes a proof of dynamical localization for a random scattering zipper model. The scattering zipper operator is the product of two unitary by blocks operators, multiplicatively perturbed on the left and right by random…
The classical walking behaviors of a single atom in an amplitude-modulated standing wave lattice beyond the internal dynamics are investigated. Based on a simple effective model, we identify a diversity of dynamic regimes of atomic motion…
One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum…
The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range…
We explore the free boson unitary dynamics subject to repeated random forced measurement. The input state is chosen as a Fock state in real space with the particle number conserved in the entire dynamics. We show that each boson is…
It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most of them are described by Gaussian distributions. We operate…
In the framework of quantum open systems, that is, simple quantum systems coupled to quantum baths, our aim is to characterize those actions of the quantum environment which give rise to dynamics dictated by classical noises. First, we…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
A thermodynamic theory is developed to describe the behavior of the entanglement between the coin and position degrees of freedom of the quantum walk on the line. This theory shows that, in spite of the unitary evolution, a steady state is…