一维ϕ^(4)平均场中单粒子系统的热力学行为研究

Thermodynamic Behavior of Single Particle System in One⁃Dimensional ϕ^(4) Mean Field

本文利用亥姆霍兹定理对一维ϕ^(4)平均场中单粒子系统的热力学行为进行研究,分析了粒子的运动特征和系统的能量与温度、熵等物理量之间的依赖关系,并对系统发生的热力学行为进行讨论。结果表明:作为一个简单的动力学体系,一维ϕ^(4)单粒子系统同样存在宏观体系所具有的热力学量,且在满足热力学关系的基础上呈现出了小体系特有的相变、负热容、负压缩率等反常热力学行为。这些独特的现象来源于在临界能量处体系能量微小的增加所引起的相轨道空间的突变。该模型中负热容的产生机理,可用于解释Na,Ar,Cu等原子团簇中出现的负热容现象。

Helmholtz’s theorem was used to study the thermodynamic behavior of a single particle system in a one-dimensional ϕ^(4) mean field.It analyzed the motion characteristics of particles and the dependence between the energy of the system and physical quantities such as temperature and entropy,and analyzed the changes that occur in the system.Thermodynamic behavior of the system was discussed.The results show that:as a simple dynamic system,the one-dimensional ϕ^(4) single-particle system also has the thermo-dynamic quantities of the macroscopic system,and on the basis of satisfying the thermodynamic relations,it shows the unique phase transition,negative heat capacity,and negative compression ratio such an abnor-mal thermodynamic behavior of the small system.These unique phenomena originate from the sudden change in the phase orbital space caused by a small increase in the system energy at the critical energy.The mechanism of negative heat capacity in this model can be used to explain the negative heat capacity phenomenon in atomic clusters such as Na,Ar,and Cu etc.