Eigenvalue Problem of Metastability in Macrosystem

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Abstract
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 Schrödinger 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.

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