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理论物理通讯：英文版

Pseudo-Classical Partition Function of Spin One-Half Derived by Coherent State Method

许业军, 范洪义

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

用 bosonic 协调州的表示和我们为量 Hamiltonian H = ia 发现公式的尖动量的 Schwinger bosonic 操作员实现 ? iijU ? 为苏(2 ) 旋转 U 的 jlal，这样，我们进一步指定尖速度，在此是泡利不相容原理矩阵。不过是的旋转量看得见没有古典通讯，我们可以仍然作为 3 个 Euler 角度描绘的僵硬身体旋转模仿它，并且计算它的伪 classical 旋转一个一半的旋转分区功能。

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用 bosonic 协调州的表示和我们为量 Hamiltonian H = ia 发现公式的尖动量的 Schwinger bosonic 操作员实现 ? iijU ? 为苏(2 ) 旋转 U 的 jlal，这样，我们进一步指定尖速度，在此是泡利不相容原理矩阵。不过是的旋转量看得见没有古典通讯，我们可以仍然作为 3 个 Euler 角度描绘的僵硬身体旋转模仿它，并且计算它的伪 classical 旋转一个一半的旋转分区功能。
Using the bosonic coherent state representation and the Schwinger bosonic operator realization of angular momentum we find the formula for the quantum Hamiltonian H = ia † i ij U † jl al for SU(2) rotation U , in this way we further specify the angular velocity , where is the Pauli matrix. Though the spin as a quantum observable has no classical correspondence, we may still mimic it as a rigid body rotation characterized by 3 Euler angles, and calculate its Pseudo-classical rotational partition function of spin one-half.
The path integral single spin partition function in the basis of boson coherent states, for a general normal ordered two-mode Schwinger boson Hamiltonian, has been computed. Within the initial phase of the calculational process, by a specific approach, the Schwinger boson constraint by means of the projection operator has been implemented.\nAfter, the case of the Zeeman Hamiltonian has been taken on. Using the expression for the partition function obtained for the general case, the appropriate single spin partition function has been produced. Additionally, partition functions have been computed for a few specific spin quantum numbers and then compared with those calculated by the straightforward means, which brought about great confidence in the projection operator implementation; both results match perfectly. \nFinally, the Heisenberg Model has been tackled, and the appropriate expressions for the partition functions have been computed. Their validity has not been verified for any specific cases, but the Zeeman Hamiltonian case dealt with earlier appears to be a strong indicator that these are indeed the correct expressions. \nMany open questions remain, however, for future research to address. All in all, it has been discovered that using the projection operator as a means to enforce the Schwinger boson constraint, veritably works for a Zeeman Hamiltonian problem for specific spin quantum numbers.
In this work, we study the thermodynamics of a hybrid system based on the Da Providencia–Schütte Hamiltonian. The model consists of bosons, i.e., photons in a cavity, interacting with an ensemble of spins through a pseudo-Hermitian Hamiltonian. We compute the exact partition function of the system, and from it, we derive the statistical properties of the system. Finally, we evaluate the work that can be extracted from the system by performing an Otto cycle and discuss the advantages of the proposed pseudo-Hermitian interaction.