标题： 理想玻色子粒子-反粒子系统在有限温度下 显示英文标题

标题： Ideal Boson Particle-Antiparticle System at Finite Temperatures

摘要： 在标量场模型的框架下，研究了由粒子和反粒子组成的理想玻色子系统在有限温度下的热力学性质。假设存在粒子-反粒子对的产生；然而，系统同时受到精确电荷（同位旋）守恒的约束。为了实现这一约束，我们首先在大系综中考虑该系统，然后通过勒让德变换转换到正则系综。此过程提供了一种形式上一致的方案，将化学势在微观层面上纳入正则系综框架。为了强制电荷（同位旋，N_I）的精确守恒，我们进一步在扩展的正则系综中分析系统的热力学性质，在该系综中，化学势成为温度和守恒电荷的热力学函数。结果显示，当温度降低时，系统在临界温度T_c处经历二阶相变，形成玻色-爱因斯坦凝聚态，但仅当守恒电荷为有限值，N_I=const \ne 0时成立。在粒子-反粒子系统中，凝聚态仅在粒子数密度占主导的组分中形成，这决定了过剩电荷。我们证明，T=0时基态的对称性破缺来源于与玻色-爱因斯坦凝聚态形成相关的第一阶相变。尽管该转变涉及对称性破缺，但在严格的场论意义上并非自发的，而是由外部注入粒子所引发的。简要讨论了高能核碰撞中产生的π介子玻色-爱因斯坦凝聚的潜在实验信号。 显示英文摘要

摘要： The thermodynamic properties of an ideal bosonic system composed of particles and antiparticles at finite temperatures are examined within the framework of a scalar field model. It is assumed that particle-antiparticle pair creation occurs; however, the system is simultaneously subject to exact charge (isospin) conservation. To implement this constraint, we first consider the system within the Grand Canonical Ensemble and then transform to the Canonical Ensemble using a Legendre transformation. This procedure provides a formally consistent scheme for incorporating the chemical potential at the microscopic level into the Canonical Ensemble framework. To enforce exact conservation of charge (isospin, N_I), we further analyze the thermodynamic properties of the system within the extended Canonical Ensemble, in which the chemical potential becomes a thermodynamic function of the temperature and conserved charge. It is shown that as the temperature decreases, the system undergoes a second-order phase transition to a Bose-Einstein condensate at the critical temperature T_c, but only when the conserved charge is finite, N_I=const \ne 0. In a particle-antiparticle system, the condensate forms exclusively in the component with the dominant particle number density, which determines the excess charge. We demonstrate that the symmetry breaking of the ground state at T=0 results from a first-order phase transition associated with the formation of a Bose-Einstein condensate. Although the transition involves symmetry breaking, it is not spontaneous in the strict field-theoretic sense, but is instead induced by the external injection of particles. Potential experimental signals of Bose-Einstein condensation of pions produced in high-energy nuclear collisions are briefly discussed.