Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation
Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation
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作为广义克莱默方程解的渐进性的量子力学
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发表时间：
2010
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通讯作者：
E. Beniaminov
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作者：
E. Beniaminov
我们考虑相空间中给定波函数的扩散散射过程。在这个过程中，热扩散只考虑沿着动量方向。我们写下描述这种情况的修改后的克拉默斯方程。在这个模型中，通常的量子描述出现作为这个过程的渐近性，对于每单位质量粒子的介质电阻的大值。它表明，在这种情况下，该过程通过几个阶段。在第一个短阶段，波函数进入一个“稳定”值。在第二个长阶段，波函数根据薛定谔方程在“定态”的子空间中变化。此外，该过程的耗散会导致退相干，并且任何状态的叠加都会变成汉密尔顿算符的本征态之一。在最后阶段，由于介质的热影响和汉密尔顿算符本征态之间的随机跃迁，热平衡的混合态（吉布斯态）出现。此外，还表明，如果单位质量粒子的介质阻力很小，则在所考虑的模型中，概率分布密度ρ =| ϕ| 2满足经典统计力学中的标准刘维尔方程。C
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this model, the usual quantum description arises as asymptotics of this process for large values of resistance of the medium per unit of mass of particle. It is shown that in this case the process passes several stages. During the first short stage, the wave function goes to one of "stationary" values. At the second long stage, the wave function varies in the subspace of "stationary" states according to the Schrodinger equation. Further, dissipation of the process leads to decoherence, and any superposition of states goes to one of eigenstates of the Hamilton operator. At the last stage, the mixed state of heat equilibrium (the Gibbs state) arises due to the heat influence of the medium and the random transitions among the eigenstates of the Hamilton operator. Besides that, it is shown that, on the contrary, if the resistance of the medium per unit of mass of particle is small, then in the considered model, the density of distribution of probability ρ = |ϕ| 2 satisfies the standard Liouville equation, as in classical statistical mechanics. c