论文标题
具有永久性偶极矩的非交换性狄拉克振荡器的热力学特性
Thermodynamic properties of the noncommutative Dirac oscillator with a permanent electric dipole moment
论文作者
论文摘要
在本文中，我们研究了在与热浴的电磁场存在下，具有永久性电偶极矩的非交通性狄拉克振荡器的热力学性质。使用规范合奏，我们通过\ textit {euler-maclaurin}公式在高温方向上确定相对论和非派别案例的性质。特别是，主要特性是：Helmholtz自由能，熵，平均能量和热容量。接下来，我们通过2D图分析属性的行为与温度的函数。结果，我们注意到，Helmholtz自由能随温度和$ω_θ$降低，并随$ω$，$ \tildeΩ$，$ω_η$增加而增加，其中$ω$是振荡器的频率，$ \tildeΩ$是cyclotron频率的类型，$ω_θ$和$ω$和$ω_____之uncult and不合转。关于熵，我们注意到温度和$ω_θ$的升高，以及$ω$，$ \tildeΩ$，$ω_η$的减少。现在，关于平均能量，我们注意到，这种特性随温度线性增加，而相对论情况的值是非派别案例的两倍。作为此的直接结果，相对论案例的热容量的价值也是非依赖性案例的两倍，并且两者都是常数，因此满足了\ textit {dulong-petit}定律。最后，我们还指出，电场不会以任何方式影响属性。
In this paper, we investigate the thermodynamic properties of the noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field in contact with a heat bath. Using the canonical ensemble, we determine the properties for both relativistic and nonrelativistic cases through the \textit{Euler-MacLaurin} formula in the high temperatures regime. In particular, the main properties are: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. Next, we analyze via 2D graphs the behavior of the properties as a function of temperature. As a result, we note that the Helmholtz free energy decreases with the temperature and $ω_θ$, and increases with $ω$, $\Tildeω$, $ω_η$, where $ω$ is the frequency of the oscillator, $\Tildeω$ is a type of cyclotron frequency, and $ω_θ$ and $ω_η$ are the noncommutative frequencies of position and momentum. With respect to entropy, we note an increase with the temperature and $ω_θ$, and a decrease with $ω$, $\Tildeω$, $ω_η$. Now, with respect to mean energy, we note that such property increases linearly with the temperature, and their values for the relativistic case are twice that of the nonrelativistic case. As a direct consequence of this, the value of the heat capacity for the relativistic case is also twice that of the nonrelativistic case, and both are constants, thus satisfying the \textit{Dulong-Petit} law. Lastly, we also note that the electric field does not influence the properties in any way.
