Eigenvalue Problem of Metastability in Macrosystem
Eigenvalue Problem of Metastability in Macrosystem
复制标题
宏观系统亚稳定性的特征值问题
DOI：
10.1143/ptp.56.786
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发表时间：
1976
影响因子：
--
通讯作者：
Hideyuki Kidachi
中科院分区：
文献类型：
--
作者：
H. Tomita;A. Itō;Hideyuki Kidachi
利用详细平衡条件将随机主方程转化为自伴形式。通过这种变换，福克-普朗克方程在形式上等价于薛定谔方程，其中系统尺寸参数的倒数对应于普朗克常数。例如，亚稳态的衰变过程可以看作是量子力学中多阱势的本征值问题。衰减率对应于几乎与基态简并的第一激发本征值，即，真正的平衡状态。计算包括对系统尺寸和外场的依赖性。接近平衡分布的过程类似于量子力学中波函数的穿透或隧穿。
Stochastic master equation is transformed into a self-adjoint form by using the detailed balance condition. A Fokker-Planck equation becomes formally equivalent to a Schrodinger equation by this transformation, where the inverse of a system-size parameter corresponds to Planck's constant. For example, the decay process of a metastable state can be considered as an eigenvalue problem of multi-well potential in quantum mechanics. The decay rate corresponds to the first excited eigenvalue which almost degenerates with that of the ground state, i.e., the true equilibrium state. Calculations include the dependence on the system-size and external field. The process of approach to equilibrium distribution is analogous to the penetration or tunneling of wave-function in quantum mechanics.