Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians

The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum systems are proposed to define a temperature scale for this type of states. This proposal is then confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. The use of these properties as measures for the temperature of quantum systems is mentioned.

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Effect of an Isotopic Impurity on the Heat Flow in One-Dimensional Coupled Harmonic Oscillators

Progress of Theoretical Physics Supplement ◽

10.1143/ptps.23.207 ◽

1962 ◽

Vol 23 ◽

pp. 207-222 ◽

Cited By ~ 6

Author(s):

Shohei Kashiwamura ◽

Ei Teramoto

Keyword(s):

Heat Flow ◽

Harmonic Oscillators ◽

One Dimensional ◽

Coupled Harmonic Oscillators

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The effect of the mass of the center spring in one‐dimensional coupled harmonic oscillators

American Journal of Physics ◽

10.1119/1.15735 ◽

1988 ◽

Vol 56 (12) ◽

pp. 1120-1123 ◽

Cited By ~ 5

Author(s):

David L. Wallach ◽

William Beatty ◽

Karl Beisler ◽

Peter Chronowski ◽

Matthew Holloway ◽

...

Keyword(s):

Harmonic Oscillators ◽

One Dimensional ◽

Coupled Harmonic Oscillators

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Heat flow in a harmonic chain due to an impulse disturbance

Dal'nevostochnyi Matematicheskii Zhurnal ◽

10.47910/femj202005 ◽

2020 ◽

Vol 20 (1) ◽

pp. 52-57

Author(s):

A.I. Gudimenko ◽

Keyword(s):

Initial Conditions ◽

Local Heat ◽

Harmonic Oscillators ◽

Heat Current ◽

Maxwell Distribution ◽

State Correlation ◽

One Dimensional ◽

Coupled Harmonic Oscillators ◽

Harmonic Chain ◽

Analytical Expressions

The heat motion in a one-dimensional semi-infinite chain of coupled harmonic oscillators is studied for the Maxwell distribution of initial velocities and zero initial displacements of the chain particles. It is believed that such initial conditions are achieved by an impulse heating of the sample. Exact analytical expressions for the state correlation functions, local temperature, and local heat current of the chain are obtained.

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Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2016.0433 ◽

2017 ◽

Vol 375 (2108) ◽

pp. 20160433 ◽

Cited By ~ 4

Author(s):

Thomas Veness ◽

Fabian H. L. Essler ◽

Matthew P. A. Fisher

Keyword(s):

Energy Density ◽

Hubbard Model ◽

Strong Coupling ◽

Strong Coupling Expansion ◽

Finite Energy ◽

Quantum Systems ◽

Entropy Density ◽

One Dimensional ◽

Temperature Window ◽

Thermal States

We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL behaviour in the sense of Grover & Fisher (2014 J. Stat. Mech. 2014 , P10010. ( doi:10.1088/1742-5468/2014/10/P10010 )). These states are atypical in the sense that their entropy density is smaller than that of thermal states at the same energy density. Furthermore, we show that thermal states in a particular temperature window exhibit a weaker form of the QDL property, in agreement with recent results obtained by strong-coupling expansion methods in Veness et al. (2016 ( http://arxiv.org/abs/1611.02075 )). This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

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