Related papers: On the spectral gap of the Kac walk and other bina…
Reducing the complexity of large systems described as complex networks is key to understand them and a crucial issue is to know which properties of the initial system are preserved in the reduced one. Here we use random walks to design a…
The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical…
We give bounds in total variation distance for random walks associated to pure central states on free orthogonal quantum groups. As a consequence, we prove that the analogue of the uniform plane Kac walk on this quantum group has a cut-off…
We analyze a class of coupled quantum systems whose dynamics can be understood via two uncoupled, lower-dimensional quantum settings with auxiliary interactions. The general reduction scheme, based on algebraic properties of the potential…
Caputo, Ligget, and Richthammer proved Aldous' spectral gap conjecture, which asserts that the spectral gaps of a random walk and an interchange process on the common weighted graph are equal. In this paper, we will prove an analogue of…
Motivated by the $1/N_c$ expansion, we study a simple model in which the pi-K scattering amplitude is the sum of a current-algebra contact term and resonance pole exchanges. This phenomenological model is crossing symmetric and, when a…
Quantum walks in general graphs, or more specifically scattering on graphs, encompass enough complexity to perform universal quantum computation. Any given quantum circuit can be broken down into single- and two-qubit gates, which can then…
The effect of Coulomb and short-range interactions on the spectral properties of two-dimensional disordered systems with two spinless fermions is investigated by numerical scaling techniques. The size independent universality of the…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
In this brief paper we present some results on creating and manipulating spectral gaps for a (regular) quantum graph by inserting appropriate internal structures into its vertices. Complete proofs and extensions of the results are planned…
Computational spectrometers are at the forefront of spectroscopy, promising portable, on-chip, or in-situ spectrum analysis through the integration of advanced computational techniques into optical systems. However, existing computational…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented…
The tacnode process is a universal behavior arising in nonintersecting particle systems and tiling problems. For Dyson Brownian bridges, the tacnode process describes the grazing collision of two packets of walkers. We consider such a Dyson…
We consider the operator associated to a random walk on finite volume surfaces with hyperbolic cusps. We study the spectral gap (upper and lower bound) associated to this operator and deduce some rate of convergence of the iterated kernel…
Quantum interference and entanglement are in the core of quantum computations. The fast spread of information in the quantum circuit helps to mitigate the circuit depth. Although the information scrambling in the closed systems has been…
We prove a uniform spectral gap for complex transfer operators near the critical line associated to overlapping $C^2$ iterated function systems on the real line satisfying a Uniform Non-Integrability (UNI) condition. Our work extends that…