arXiv:1903.05002

Quantum Walk and Quantum Billiards. Towards a better understanding of Quantum Chaos

César Alonso-Lobo, Manuel Martínez–Quesada

Published Mar 12, 2019• 0 citations

Abstract

Quantum billiards have been simulated so far in many ways, but in this work a new aproximation is considerated. This study is based on the quantum billiard already obtained by others authors via a tensor product of two 1-D quantum walks . Chaotic and non chaotic billiards are tested.

DOI: 10.48550/arxiv.1903.05002

Related papers

Quantum Chaos

H.‐J. Stöckmann

This book introduces the quantum mechanics of classically chaotic systems, or quantum chaos for short. The author's philosophy has been to keep the discussion simple and to illustrate theory, wherever possible, with experimental or numerical examples. The microwave billiard experiments, initiated by the author and his group, play a major role in this respect. Topics covered include the various types of billiard experiment, random matrix theory, systems with periodic time dependences, the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectral level dynamics, where an external parameter takes the role of time, scattering theory distributions and fluctuation, properties of scattering matrix elements, semiclassical quantum mechanics, periodic orbit theory, and the Gutzwiller trace formula. This book will be of great value to anyone working in quantum chaos.

Cambridge University Press eBooksOct 13, 1999959 citations

Quantum anomaly and effective field description of a quantum chaotic billiard(6) Approaches from mathematical science and quantum information, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

Nobuhiko Taniguchi

この論文は国立情報学研究所の電子図書館事業により電子化されました。

物性研究Jun 20, 20050 citations

Chaos on the Quantum Scale Simulations of atomic-scale billiards reveal chaotic phenomena that expand theory and applications, especially in nanotechnology

Mason Alexander Porter, Richard L. Liboff

During the 20th century, two new ways of describing physical sys tems emerged to thwart scientists' hopes of ever completely predicting nature's behavior. First, the theory of quantum mechanics uncovered ram pant uncertainty at the tiniest scales of matter?in the canonical example, an electron's precise position and momen tum cannot simultaneously be known at any particular moment. The second body of thought is what we now call chaos theory. Some phenomena, it turns out, depend intimately on a sys tem's initial conditions, so that an im perceptible change in the beginning value of a variable can make the out come of a process impossible to pre dict. Chaos appears in examples as dis tinct as the frequency of drips from a faucet and the motion of planets. Given the unpredictability that char acterizes both chaos and quantum me chanics, one might well wonder what would happen if these phenomena were merged. Utter chaos, perhaps? Probably not; in fact we have tools for approaching the modeling of quantum chaos, or chaotic behavior on the quan tum scale. Early attempts to under stand this exotic realm have produced results that are both mathematically and scientifically important. Having

Jan 1, 20160 citations

Quantum versus chaos : questions emerging from mesoscopic cosmos

勝弘中村

Preface. 1. Genesis of Chaos and Breakdown of Quantization of Adiabatic Invariants. 2. Semiclassical Quantization of Chaos: Trace Formula. 3. Pseudo-Chaos Without Classical Counterpart in 1-Dimensional Quantum Transport. 4. Chaos and Quantum Transport in Open Magnetic Billiards: From Stadium to Sinai Billiards. 5. Chaotic Scattering on Hyperbolic Billiards: Success of Semiclassical Theory. 6. Nonadiabaticity-Induced Quantum Chaos. 7. Level Dynamics and Statistical Mechanics. 8. Towards Time-Discrete Quantum Mechanics. 9. Conclusions and Prospects. Index.

Kluwer Academic Publishers eBooksJan 1, 19971 citation

Minimal models for chaotic quantum dynamics in spatially extended many-body systems

J. T. Chalker

I will give an overview of recent work on minimal models for quantum chaos in spatially extended many-body quantum systems, describing simple, solvable models. The detailed study of generic quantum systems - ones without exact or approximate conservation laws - goes back at least as far as investigations of highly-excited states in nuclei in the 1950s. It saw revivals in the 1980s with work on systems such as quantum billiards, that have only a few degrees of freedom, and also in the context of mesoscopic conductors. It is attracting renewed current interest with a focus on many-body systems that are spatially extended. Part of the motivation for this comes from experiments on cold atom systems, and part comes from development on the theoretical understanding of eigenstates of many-body systems. The study of dynamics in spatially many-body systems introduces new questions that do not arise in finite systems such as quantum billiards, or in extended single-particle systems, such as mesoscopic conductors. The questions concern the dynamics of quantum information and the approach to equilibrium. I will discuss how these can be answered in the context of minimal models. References: A. Chan, A. De Luca, and J. T. Chalker, Phys. Rev. Lett. 121, 060601 (2018) and Phys. Rev. X 8, 041019 (2018)

StatPhys 27 Main ConferenceMay 15, 20190 citations

Non-Linear Geometric Chaos, Based on Quantum Simulation of Chaos Dynamics

Jincheng Zhang

This paper investigates the application of quantum simulation to the study of non-linear geometric chaos. Traditional chaos theory methods often struggle with the complexities of intricate geometric systems, limiting the ability to accurately model and control their behavior. Quantum simulation offers a novel approach by providing a fundamentally different method for representing and analyzing chaotic dynamics. We propose a new algorithm utilizing quantum simulations to emulate the formation and evolution of complex geometric structures, with the goal of optimizing control strategies through the analysis of simulated chaos. This work demonstrates the potential of quantum simulation to enhance our understanding and control of non-linear geometric chaos.

Sep 7, 20260 citations