1f2 law in one-dimensional quantum transport: an example of weak chaos in quantum systems

1995 ◽  
Vol 5 (7) ◽  
pp. 1077-1083
Author(s):  
T. Haga ◽  
Y. Takane ◽  
K. Nakamura
Keyword(s):  
Quantum Transport ◽  
Quantum Systems ◽  
One Dimensional

scholarly journals Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder

2019 ◽  
Vol 3 (4) ◽  
pp. 47 ◽  
Author(s):  
Renat T. Sibatov ◽  
HongGuang Sun
Keyword(s):  
Quantum Transport ◽  
Stable Distribution ◽  
Quantum Wires ◽  
Quantum Systems ◽  
Spatial Distributions ◽  
Wire Length ◽  
One Dimensional ◽  
Fractional Equations ◽  
Weak Scattering ◽  
Conductance Distribution

New aspects of electron transport in quantum wires with Lévy-type disorder are described. We study the weak scattering and the incoherent sequential tunneling in one-dimensional quantum systems characterized by a tempered Lévy stable distribution of spacing between scatterers or tunneling barriers. The generalized Dorokhov–Mello–Pereyra–Kumar equation contains the tempered fractional derivative on wire length. The solution describes the evolution from the anomalous conductance distribution to the Dorokhov function for a long wire. For sequential tunneling, average values and relative fluctuations of conductance and resistance are calculated for different parameters of spatial distributions. A tempered Lévy stable distribution of spacing between barriers leads to a transition in conductance scaling.

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.

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