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Modern Physics Letters B

NEW APPROACH TO DERIVING THE THERMO-MINIMUM UNCERTAINTY STATES AND ITS WIGNER FUNCTION

Hong‐Chun Yuan, Xue-xiang Xu, Hong-Yi Fan

Published Sep 17, 2010• 1 citation
Publisher

Abstract

Based on our previous study [Mod. Phys. Lett. A18 (2003) 677] in which minimum uncertainty states for thermo-field dynamics were proposed, we use a new approach to derive the thermo-minimum uncertainty states via the relation of two-variable Hermite polynomial. In addition, the compact expression for its corresponding Wigner function is obtained analytically by using the Weyl-ordered invariance under the similar transformations, which seems a new result.

DOI
10.1142/s0217984910024936

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Based on our previous study [Mod. Phys. Lett. A18 (2003) 677] in which minimum uncertainty states for thermo-field dynamics were proposed, we use a new approach to derive the thermo-minimum uncertainty states via the relation of two-variable Hermite polynomial. In addition, the compact expression for its corresponding Wigner function is obtained analytically by using the Weyl-ordered invariance under the similar transformations, which seems a new result.
With the correspondence between operator ordering rules and probability distribution functions, moments can be calculated in many ways. We show here the independence of minimum uncertainty relations on the choice of Hermitian ordering rule. Generalized Wigner functions were expressed in terms of ordering real-valued function ϴ(x) for x ϵ R satisfying ϴ(0)=1. Uncertainties of position and momentum are obtained for a Gaussian state. Results confirm that the minimum uncertainty relation holds even when the Hermitian ordering rule is modified.