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Modern Physics Letters A

NEW MINIMUM UNCERTAINTY STATES FOR THERMO FIELD DYNAMICS

Hong-Yi Fan

Published Mar 28, 2003• 4 citations
Publisher

Abstract

In Takahashi–Umezawa Thermo Field Dynamics theory every operator a acting on real field space is accompanied by its image ã acting on fictitious field space, we propose a new uncertainty relation which embodies the finite temperature effect and derive the corresponding minimum uncertainty state — a new thermolized two-variable Hermite polynomial state.

DOI
10.1142/s0217732303007965

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In Takahashi–Umezawa Thermo Field Dynamics theory every operator a acting on real field space is accompanied by its image ã acting on fictitious field space, we propose a new uncertainty relation which embodies the finite temperature effect and derive the corresponding minimum uncertainty state — a new thermolized two-variable Hermite polynomial state.
By analyzing the characters of Thermo Field Dynamics (TFD) that every annihilation operator f acting on real Hilbert space has an image [Formula: see text] acting on fictitious space we should choose [Formula: see text] and [Formula: see text], or their linear combination [Formula: see text], and [Formula: see text] for measuring Fermi field's fluctuation at finite temperature. As a consequence, the corresponding minimum uncertainty states are derived, which resembles the form of fermionic squeezed state. This work is the fermionic counterpart of Ref. 8 in which bosonic TFD's minimum uncertainty states are obtained.
According to the thermo field dynamics proposed by Takahashi–Umezawa, the Hamiltonian h = a†a - ã†ã and h|n, ñ〉 = 0 of the original optical field excitation state |n〉 and its tilde state |ñ〉 in the Hilbert space cannot embody the eigenvalue spectrum of h. To avoid the weakness, new thermo excitation states are successfully constructed by introducing appropriate thermo excitation operators. It is noted that they are entangled states. Applications of the new thermo excitation state in constructing new thermo squeezed state and phase state are also presented.
We discussed how much information is lost when a particle is in equilibrium with the thermal reservoir of temperature T = 1/beta. The universal temperature correction to the r.h.s. of U(X,P:psi) greater than or = 1 + ln(pi) is determined. For this purpose, it is convenient to employ the framework of thermo-field dynamics (TFD). This formulation of finite-temperature (T not = 0) quantum theory utilizes the doubled Hilbert space, the normal operator (A) acting on the objective space, and its corresponding tildian operator on the fictitious space. The physical probability density associated with the measurement of the normal operator, A, is given, and the information entropy at T not = 0 is defined. The results describe how the thermal disturbance effects in S sub X or S sub P (delta X or delta P) can be suppressed by squeezing with keeping U = S sub X + S sub P (delta X x delta P) its minimum value.