Heriot-Watt Mathematics Report Series
HWM06-22, 24 Apr 2006
Fast energy transfer mediated by multi-quanta bound states in a nonlinear quantum lattice
C Falvo, V Pouthier and J C Eilbeck
Abstract
By using a Generalized Hubbard model for bosons, the energy transfer
in a nonlinear quantum lattice is studied, with special emphasis on
the interplay between local and nonlocal nonlinearity. For a
strong local nonlinearity, it is shown that the creation of $v$
quanta on one site excites a soliton band formed by bound states
involving $v$ quanta trapped on the same site. The energy is first
localized on the excited site over a significant timescale and then
slowly delocalizes along the lattice. As when increasing the
nonlocal nonlinearity, a faster dynamics occurs and the energy
propagates more rapidly along the lattice. Nevertheless, the larger
is the number of quanta, the slower is the dynamics. However, it is
shown that when the nonlocal nonlinearity reaches a critical value,
the lattice suddenly supports a very fast energy propagation whose
dynamics is almost independent on the number of quanta. The energy
is transfered by specific bound states formed by the superimposition
of states involving $v-p$ quanta trapped on one site and $p$ quanta
trapped on the nearest neighbour sites, with $p=0,..,v-1$. These
bound states behave as independent quanta and they exhibit a
dynamics which is insensitive to the nonlinearity and controlled by the single quantum hopping constant.
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