Quantum Theory of Soliton in a Periodic Exponential Lattice

In this paper we advance a new approximation scheme for the dynamics of an N particle system, which is based on the expansion of the Heisenberg equations of motion in powers of h/ in the coherent state representation. The time evolution of the physical observables is generated classically by a Hamiltonian Hs, which is derived from the original Hamiltonian by adding 2N2 virtual particles to the system. These virtual particles are related to the dispersion of the quantum mechanical wave function, and reflect the (time dependent) sensitivity of the instantaneous positions and momenta xi, pi to the variation of the initial conditions. The approximate equations of motion preserve the commutation relations between the coordinates and the momenta and the total (quantum) energy. The present approximation may be adequate for the study of the dynamics of coupled anharmonic oscillators in the quasiperiodic regime.

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Quantum Theory of Soliton in a Periodic Exponential Lattice

Abstract: The quantum energy of one soliton state in the periodic exponential lattice is calcu· lated by the WKB (semi-classical) approximation method. And problems to clarify the notion of the quantum theory of solitons are briefly discussed.

Cited by 7 publications

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Solitons in Chemical Physics

Solitons in Chemical Physics

The quantum mechanical toda lattice

A semiclassical approximation to quantum dynamics

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