TY - JOUR

T1 - The quantum discrete self-trapping equation in the Hartree approximation

AU - Wright, Ewan

AU - Eilbeck, J. C.

AU - Hays, M. H.

AU - Miller, P. D.

AU - Scott, A. C.

N1 - Funding Information:
We thank Lisa Bernstein for a careful reading of the manuscript and acknowledge support from the Joint Services Optical Program, from the SERC Nonlinear Systems Initiative and the EC under SCI-0229-C89-100079/JU l, and from the National Science Foundation under Grant No. DMS-9114503.

PY - 1993/11/15

Y1 - 1993/11/15

N2 - We show how the Hartree approximation (HA) can be used to study the quantum discrete self-trapping (QDST) equation, which - in turn - provides a model for the quantum description of several interesting nonlinear effects such as energy localization, soliton interactions, and chaos. The accuracy of the Hartree approximation is evaluated by comparing results with exact quantum mechanical calculations using the number state method. Since the Hartree method involves solving a classical DST equation, two classes of solutions are of particular interest: (i) Stationary solutions, which approximate certain energy eigenstates, and (ii) Time dependent solutions, which approximate the dynamics of wave packets of energy eigenstates. Both classes of solution are considered for systems with two and three degrees of freedom (the dimer and the trimer), and some comments are made on systems with an arbitrary number of freedoms.

AB - We show how the Hartree approximation (HA) can be used to study the quantum discrete self-trapping (QDST) equation, which - in turn - provides a model for the quantum description of several interesting nonlinear effects such as energy localization, soliton interactions, and chaos. The accuracy of the Hartree approximation is evaluated by comparing results with exact quantum mechanical calculations using the number state method. Since the Hartree method involves solving a classical DST equation, two classes of solutions are of particular interest: (i) Stationary solutions, which approximate certain energy eigenstates, and (ii) Time dependent solutions, which approximate the dynamics of wave packets of energy eigenstates. Both classes of solution are considered for systems with two and three degrees of freedom (the dimer and the trimer), and some comments are made on systems with an arbitrary number of freedoms.

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U2 - 10.1016/0167-2789(93)90178-4

DO - 10.1016/0167-2789(93)90178-4

M3 - Article

AN - SCOPUS:0002610806

VL - 69

SP - 18

EP - 32

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -