https://doi.org/10.1140/epjst/e2015-50326-1
Regular Article
Localization and coherent states in a quantum DNLS trimer
1 Facultad de Química, Departamento de Matemáticas, Universidad Nacional Autónoma de México, 04510 México D. F., México
2 Depto. Matemáticas y Mecánica, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, 01000 México D.F., México
a e-mail: panos@mym.iimas.unam.mx
Received: 14 December 2015
Revised: 17 May 2016
Published online: 22 November 2016
We compare quantum states obtained from the integration of exact and approximate evolution equations for a quantized discrete nonlinear Schrödinger system (DNLS) with three lattice sites (trimer). The initial conditions are Glauber coherent states, and their projections to subspaces with a definite number of particles, and we are especially interested in coherent states that correspond to classical states that are in the neighborhood of breather solutions of the classical system. The breathers are well defined periodic orbits of the classical DNLS that we heuristically view as examples of spatially localized solutions. The two evolution equations give converging results in the subspaces with an increasing number of particles. This is no longer the case for normalized projections of Glauber states, where we see that the distance between the quantum states obtained by the exact and approximate equations shows recurrence phenomena that depend on the number of quanta and on the dynamical properties of the classical trajectory.
© EDP Sciences, Springer-Verlag, 2016
