Wigner function of the thermo number states

Based on thermo field dynamics （TFD） and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature （named thermo number states）. The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.

Quantum fluctuation in excited states of mesoscopic LC circuits at finite temperature

We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.

Thermal vacuum state for the two-coupled-oscillator model at finite temperature: Derivation and application

Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann-Feynman theorem and the entroy variation in the context of the TVS.

QGP中的热胶子质量和J/ψ,ψ′的分解

用热场动力学方法，计算了有限温度和有限密度下胶子的有效质量和屏蔽质量，并得到了Ｊ／ψ。