Dynamics of One-Dimensional Quantum Systems

2009 ◽  
Author(s):  
Yoshio Kuramoto ◽  
Yusuke Kato
Keyword(s):  
Quantum Systems ◽  
One Dimensional

scholarly journals Probing the edge between integrability and quantum chaos in interacting few-atom systems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 486
Author(s):  
Thomás Fogarty ◽  
Miguel Ángel García-March ◽  
Lea F. Santos ◽  
Nathan L. Harshman
Keyword(s):  
Quantum Chaos ◽  
Cold Atoms ◽  
Quantum Systems ◽  
Particle Interactions ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
The Core ◽  
Emergence Of Chaos ◽  
Number Of Particles

Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

scholarly journals Transport in one-dimensional integrable quantum systems

2020 ◽  
Author(s):  
Jesko Sirker
Keyword(s):  
Transport Properties ◽  
Spin Chain ◽  
Linear Response ◽  
Summer School ◽  
Condensed Matter ◽  
Quantum Systems ◽  
Integrable Models ◽  
One Dimensional ◽  
Integrable Quantum ◽  
Linear Response Regime

These notes are based on a series of three lectures given at the Les Houches summer school on ’Integrability in Atomic and Condensed Matter Physics’ in August 2018. They provide an introduction into the unusual transport properties of integrable models in the linear response regime focussing, in particular, on the spin-1/21/2 XXZ spin chain.

scholarly journals Interaction instability of localization in quasiperiodic systems

2018 ◽  
Vol 115 (18) ◽  
pp. 4595-4600 ◽  
Author(s):  
Marko Žnidarič ◽  
Marko Ljubotina
Keyword(s):  
Transport Properties ◽  
Quantum Systems ◽  
Theoretical Physics ◽  
Solvable Models ◽  
Many Body ◽  
Small Perturbations ◽  
One Dimensional ◽  
Quasiperiodic Potential ◽  
Quasiperiodic Systems ◽  
Small Interactions

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

Hypervirial perturbative treatment of one-dimensional quantum systems

1982 ◽  
Vol 72 (2) ◽  
pp. 246-260 ◽  
Author(s):  
G. A. Arteca ◽  
F. M. Fernández ◽  
E. A. Castro
Keyword(s):  
Quantum Systems ◽  
One Dimensional ◽  
Perturbative Treatment

scholarly journals Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium

2009 ◽  
Vol 80 (3) ◽  
Author(s):  
Giuliano Benenti ◽  
Giulio Casati ◽  
Tomaž Prosen ◽  
Davide Rossini ◽  
Marko Žnidarič
Keyword(s):  
Spin Transport ◽  
Quantum Systems ◽  
Strongly Correlated ◽  
One Dimensional ◽  
Far From Equilibrium
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