Many-body aspects of approach to equilibrium
Many-body aspects of approach to equilibrium
复制标题
平衡方法的多体方面
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
M. Loss
中科院分区：
文献类型：
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作者：
E. Carlen;M. C. Carvalho;M. Loss
通常在玻尔兹曼方程的范围内研究运动理论和平衡方法。除了几个值得注意的例外，人们对这个方程的解和它从基本原理推导出来的情况所知不多。1956年Mark Kac引入了n个相互作用粒子的概率模型。速度分布由马尔可夫半群控制，其单粒子边缘的演化（在无限粒子极限下）由空间齐次玻尔兹曼方程的讽刺画控制。在与Eric Carlen和Maria Carvalho的联合工作中，我们计算了这个马尔可夫半群的发生器的间隙，并表明在Kac模型中接近平衡的最佳可能速率正是线性化玻尔兹曼方程所预测的速率。类似的，但不那么精确的结果也适用于麦克斯韦分子。
Kinetic theory and approach to equilibrium is usually studied in the realm of the Boltzmann equation. With a few notable exceptions not much is known about the solutions of this equation and about its derivation from fundamental principles. In 1956 Mark Kac introduced a probabilistic model ofN interacting particles. The velocity distribution is governed by a Markov semi group and the evolution of its single particle marginals is governed (in the infinite particle limit) by a caricature of the spatially homogeneous Boltzmann equation. In joint work with Eric Carlen and Maria Carvalho we compute the gap of the generator of this Markov semigroup and show that the best possible rate of approach to equilibrium in the Kac model is precisely the one predicted by the linearized Boltzmann equation. Similar, but less precise results hold for Maxwellian molecules.