López-Saldívar Julio A, Man'ko Margarita A, Man'ko Vladimir I
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, Ciudad de México 04510, Mexico.
Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow 141700, Russia.
Entropy (Basel). 2021 Oct 31;23(11):1445. doi: 10.3390/e23111445.
The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum systems are proposed to define a temperature scale for this type of states. This proposal is then confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. The use of these properties as measures for the temperature of quantum systems is mentioned.
我们得到了由二次哈密顿量描述的单模和双模量子系统热吉布斯态的维格纳（Wigner）表示和断层扫描表示。这是通过使用上述态的协方差矩阵来实现的。我们提出用量子系统维格纳函数的面积和断层扫描图的宽度来定义这类态的温度标度。然后，这一建议在一般一维情形以及两个耦合谐振子系统中得到了证实。文中提到了利用这些性质作为量子系统温度的度量。
