Related papers: On nonlinear scattering for quantum walks
We are concerned with random walks on $\mathbb{Z}^d$, $d\geq 3$, in an i.i.d. random environment with transition probabilities $\epsilon$-close to those of simple random walk. We assume that the environment is balanced in one fixed…
We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…
Quantum walks are not only algorithmic tools for quantum computation but also not trivial models which describe various physical processes. The paper compares one-dimensional version of the free particle Dirac equation with discrete time…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles…
We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such…
We consider the problem of large data scattering for the quintic nonlinear Schr\"odinger equation on $\R \times \T^2$. This equation is critical both at the level of energy and mass. Most notably, we exhibit a new type of profile (a "large…
We consider the problem of large data scattering for the quintic nonlinear Schr\"odinger equation on $\R \times \T^2$. This equation is critical both at the level of energy and mass. Most notably, we exhibit a new type of profile (a "large…
We attempt to analyze a one-dimensional space-inhomogeneous quantum walk (QW) with one defect at the origin, which has two different quantum coins in positive and negative parts. We call the QW "the two-phase QW", which we treated…
We analyse when and why unitarity violations might occur in quantum cosmology restricted to minisuperspace. To this end we discuss in detail backscattering transitions between expanding and contracting solutions of the Wheeler-DeWitt…
For a discrete two-state quantum walk (QW) on the half-line with a general condition at the boundary, we formulate and prove a weak limit theorem describing the terminal behavior of its transition probabilities. In this context,…
We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
We study the resonant scattering for discrete time quantum walks on graphs with some tails. In our arguments, we reduce the study of resonances to the perturbation of eigenvalues of a finite rank matrix associated with the internal graph.…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
In this paper, we claim that a common underlying structure--a skeleton structure--is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneous coin matrix. This skeleton structure is independent of the…