论文标题
量子统计中的广义吉布斯集合的量子分析对密度运算符的推导
Derivation of the density operator with quantum analysis for the generalized Gibbs ensemble in quantum statistics
论文作者
论文摘要
当存在保守量时，我们得出了通用熵和广义期望值的密度运算符方程，并具有量子分析。当采用常规期望值时，简化了派生方程。当托盘关系，$ [\hatρ，\ hat {h}] $和$ [\hatρ，\ hat {q}^{[a]} $时，也可以简化派生方程式，是密度运算符$ \hatρ$的功能，是$ \ hat {h hat { 数量。在常规期望值的情况下，我们得出了Von Neumann熵，Tsallis熵和Rényi熵的密度运算符。在伴游平均值（归一化$ q $ - 期望值）的情况下，我们还得出了Tsallis熵和Rényi熵的密度运算符，当时密度运算符与汉密尔顿和保守数量的通勤。我们发现，在常规期望值的情况下，即使保守数量不通勤，也将密度运算符的论点简单地扩展到了广义吉布斯集团的论点。该论点的简单扩展也显示在护送平均值的情况下，当密度运算符$ \hatρ$与Hamiltonian $ \ hat {h} $和保守的数量$ \ hat {q}^{[a a]} $：这些发现表明，在某些系统中，密度运算符的参数仅扩展到广义Gibbs集合的参数。
We derived the equation of the density operator for generalized entropy and generalized expectation value with quantum analysis when conserved quantities exist. The derived equation is simplified when the conventional expectation value is employed. The derived equation is also simplified when the commutation relations, $[\hatρ, \hat{H}]$ and $[\hatρ, \hat{Q}^{[a]}]$, are the functions of the density operator $\hatρ$, where $\hat{H}$ is the Hamiltonian, and $\hat{Q}^{[a]}$ is the conserved quantity. We derived the density operators for the von Neumann entropy, the Tsallis entropy, and the Rényi entropy in the case of the conventional expectation value. We also derived the density operators for the Tsallis entropy and the Rényi entropy in the case of the escort average (the normalized $q$-expectation value), when the density operator commutes with the Hamiltonian and the conserved quantities. We found that the argument of the density operator for the canonical ensemble is simply extended to the argument for the generalized Gibbs ensemble in the case of the conventional expectation value, even when conserved quantities do not commute. The simple extension of the argument is also shown in the case of the escort average, when the density operator $\hatρ$ commutes with the Hamiltonian $\hat{H}$ and the conserved quantity $\hat{Q}^{[a]}$: $[\hatρ, \hat{H}] = [\hatρ, \hat{Q}^{[a]}]=0$. These findings imply that the argument of the density operator for the canonical ensemble is simply extended to the argument for the generalized Gibbs ensemble in some systems.
