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Modern Physics Letters A

THERMO MINIMUM UNCERTAINTY STATE FOR FERMIONIC TFD THEORY

Xuefen Xu, Hong-Yi Fan

Published Nov 15, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217732307022955

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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.
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.
By making use of thermo-field dynamics(TFD),higher-order fluctuations and higher-order squeezing of quadrature components for coherent states and squeezed states with thermal noise have been studied.The higher-order fluctuations of the phase for these thermalized states have been investigated using the concept of measured phase operators.Thus the dependence of the lower-and higher-order fluctuations and squeezing on temperature in these states at finite temperature can be seen.It is significant to discuss the effect of temperature on the fluctuations and squeezing,since the states of real field are always at finite temperatures.