scholarly journals Chaos in a one-dimensional integrable quantum system

2009 ◽  
Vol 373 (8-9) ◽  
pp. 826-831 ◽  
Author(s):  
Petr Šeba ◽  
Daniel Vašata
Keyword(s):  
Quantum System ◽  
One Dimensional ◽  
Integrable Quantum

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

scholarly journals Circuit Simulates One-Dimensional Quantum System

Physics ◽  
2018 ◽  
Vol 11 ◽  
Author(s):  
Emanuele Dalla Torre ◽  
Eran Sela
Keyword(s):  
Quantum System ◽  
One Dimensional

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.

BACKSCATTERING AND THE DECAY OF TRANSMITTANCE IN A COHERENTLY ABSORBING OR AMPLIFYING ORDERED CHAIN

1996 ◽  
Vol 10 (03n05) ◽  
pp. 125-132 ◽  
Author(s):  
ASOK K. SEN
Keyword(s):  
Quantum System ◽  
Electronic Properties ◽  
Recent Work ◽  
Active Medium ◽  
Open Quantum System ◽  
Tight Binding ◽  
One Dimensional ◽  
A Value ◽  
Closed Quantum System ◽  
Coherent Amplification

We study electronic properties of a one-dimensional, semi-infinite ordered chain in the presence of either absorption or amplification at each site (the site potentials having imaginary positive or negative parts) within a single-band, tight binding Hamiltonian. The spectrum in either case for an isolated (closed) quantum system becomes broader compared to the regular Bloch case. For an infinitely long ordered chain (open quantum system), the reflectance saturates to a value greater (lesser) than unity in the amplifying (absorbing) case and the transmittance decays to zero in either case. Thus, in contrast to a recent work of Pradhan and Kumar [Phys. Rev.B50, 9644 (1994)], it is not necessary to have any “synergy between wave confinement” due to any disorder or interaction induced confining mechanism on the transmitted wave and “coherent amplification by the active medium” to achieve an amplification in the reflectance.

scholarly journals A REMARK ON ONE-DIMENSIONAL MANY-BODY PROBLEMS WITH POINT INTERACTIONS

2000 ◽  
Vol 14 (07) ◽  
pp. 721-727 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
LUDWIK DABROWSKI ◽  
SHAO-MING FEI
Keyword(s):  
Singular Point ◽  
Bound States ◽  
Quantum Mechanical ◽  
Contact Interactions ◽  
Many Body ◽  
Point Interactions ◽  
One Dimensional ◽  
Integrable Quantum ◽  
Scattering Matrices ◽  
Many Body Systems

The integrability of one-dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) δ-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.

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