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Theoretical and Mathematical Physics

Eigenfunctions of quadratic Hamiltonians in the Wigner representation

�. A. Akhundova, V. V. Dodonov, Vladimir I. Man’ko

Published Sep 1, 1984• 10 citations
Publisher
DOI
10.1007/bf01017893

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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.