相关论文: Coassociative grammar, periodic orbits and quantum…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph,…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
In this paper we consider an excited random walk on $\mathbb{Z}$ in identically piled periodic environment. This is a discrete time process on $\mathbb{Z}$ defined by parameters $(p_1,\dots p_M) \in [0,1]^M$ for some positive integer $M$,…
We study a natural construction of a general class of inhomogeneous quantum walks (namely walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on…
Quantum walks have emerged as a transformative paradigm in quantum information processing and can be applied to various graph problems. This study explores discrete-time quantum walks on simplicial complexes, a higher-order generalization…
In this paper, we determine periodicity of quantum walks defined by mixed paths and mixed cycles. By the spectral mapping theorem of quantum walks, consideration of periodicity is reduced to eigenvalue analysis of $\eta$-Hermitian adjacency…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…
We propose a phenomenon of discrete-time quantum walks on graphs called the pulsation, which is a generalization of a phenomenon in the quantum searches. This phenomenon is discussed on a composite graph formed by two connected graphs…
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
We present an explicit formula for the characteristic polynomial of the transition matrix of the discrete-time quantum walk on a graph via the second weighted zeta function. As applications, we obtain new proofs for the results on spectra…
The "loop equations" of random matrix theory are a hierarchy of equations born of attempts to obtain explicit formulae for generating functions of map enumeration problems. These equations, originating in the physics of 2-dimensional…
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…