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Acta Sinica Quantum Optica

The Applications of Coherent State Representation on the Distribution Functions of the Quantum Phase Space

Shuai Wang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

By means of the coherent state representation and the IWOP technique,the density matrix of free thermal state can be written as normal product form.And then the Wigner function of free thermal state and the thermal coherent state are reproduced by using the wigner function in coherent state representation.It is found that it is easy to obtain the Wigner function of some quantum states by using the Wigner function defined in terms of the coherent state and the normal product form of operators.

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By means of the coherent state representation and the IWOP technique,the density matrix of free thermal state can be written as normal product form.And then the Wigner function of free thermal state and the thermal coherent state are reproduced by using the wigner function in coherent state representation.It is found that it is easy to obtain the Wigner function of some quantum states by using the Wigner function defined in terms of the coherent state and the normal product form of operators.
The relation between the Wigner cistribution function and the P-representation of the density matrix for describing a boson system is investigated. The coherent-state representation of the density matrix is introduced for a Bose particle system. Especially the P-representation of the density matrix describing an ideal boson system in thermal equilibrium is obtained. It can be seen that the distribution function of the complex eigenvalues of the destruction operator is non-negative in this particular case. The coherent-state representation of the Wigner function is then obtained. The coherent-state representation of the components in the decomposition of the Wigner function is also found. The London-Placzek formula can be derived by using one of these components.
We present a novel method for deriving some new quantum operator formulas by carrying out the integrations within a normal product symbol. The idea underlying this method is combining the properties of normal product and of coherent state together. For example, we can deduce operator ordering theorems, the Fujiwara formula, and some disentangling theorems simply and directly. By means of this method we also get the explicit operator form and coherent state form for the Wigner function with these new forms, the wigner function's eigenstate is found and its zero point value property is discussed. Furthermore some famous quantum unitary transformations and the transformed matrix element for functional obtained conveniently. integral may be also