772 research outputs found
AC-driven quantum spins: resonant enhancement of transverse DC magnetization
We consider s=1/2 spins in the presence of a constant magnetic field in
z-direction and an AC magnetic field in the x-z plane. A nonzero DC
magnetization component in y direction is a result of broken symmetries. A
pairwise interaction between two spins is shown to resonantly increase the
induced magnetization by one order of magnitude. We discuss the mechanism of
this enhancement, which is due to additional avoided crossings in the level
structure of the system.Comment: 7 pages, 7 figure
Slow Relaxation and Phase Space Properties of a Conservative System with Many Degrees of Freedom
We study the one-dimensional discrete model. We compare two
equilibrium properties by use of molecular dynamics simulations: the Lyapunov
spectrum and the time dependence of local correlation functions. Both
properties imply the existence of a dynamical crossover of the system at the
same temperature. This correlation holds for two rather different regimes of
the system - the displacive and intermediate coupling regimes. Our results
imply a deep connection between slowing down of relaxations and phase space
properties of complex systems.Comment: 14 pages, LaTeX, 10 Figures available upon request (SF), Phys. Rev.
E, accepted for publicatio
On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices
We consider time-periodic nonlinear localized excitations (NLEs) on
one-dimensional translationally invariant Hamiltonian lattices with arbitrary
finite interaction range and arbitrary finite number of degrees of freedom per
unit cell. We analyse a mapping of the Fourier coefficients of the NLE
solution. NLEs correspond to homoclinic points in the phase space of this map.
Using dimensionality properties of separatrix manifolds of the mapping we show
the persistence of NLE solutions under perturbations of the system, provided
NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam
chains we rigorously prove the existence of NLE solutions.Comment: 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E,
in press
Dimension dependent energy thresholds for discrete breathers
Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. We study the existence of energy thresholds for discrete breathers,
i.e., the question whether, in a certain system, discrete breathers of
arbitrarily low energy exist, or a threshold has to be overcome in order to
excite a discrete breather. Breather energies are found to have a positive
lower bound if the lattice dimension d is greater than or equal to a certain
critical value d_c, whereas no energy threshold is observed for d<d_c. The
critical dimension d_c is system dependent and can be computed explicitly,
taking on values between zero and infinity. Three classes of Hamiltonian
systems are distinguished, being characterized by different mechanisms
effecting the existence (or non-existence) of an energy threshold.Comment: 20 pages, 5 figure
Energy thresholds for discrete breathers
Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. An important issue, not only from a theoretical point of view but
also for their experimental detection, are their energy properties. We
considerably enlarge the scenario of possible energy properties presented by
Flach, Kladko, and MacKay [Phys. Rev. Lett. 78, 1207 (1997)]. Breather energies
have a positive lower bound if the lattice dimension is greater than or equal
to a certain critical value d_c. We show that d_c can generically be greater
than two for a large class of Hamiltonian systems. Furthermore, examples are
provided for systems where discrete breathers exist but do not emerge from the
bifurcation of a band edge plane wave. Some of these systems support breathers
of arbitrarily low energy in any spatial dimension.Comment: 4 pages, 4 figure
Discrete breathers in classical spin lattices
Discrete breathers (nonlinear localised modes) have been shown to exist in
various nonlinear Hamiltonian lattice systems. In the present paper we study
the dynamics of classical spins interacting via Heisenberg exchange on spatial
-dimensional lattices (with and without the presence of single-ion
anisotropy). We show that discrete breathers exist for cases when the continuum
theory does not allow for their presence (easy-axis ferromagnets with
anisotropic exchange and easy-plane ferromagnets). We prove the existence of
localised excitations using the implicit function theorem and obtain necessary
conditions for their existence. The most interesting case is the easy-plane one
which yields excitations with locally tilted magnetisation. There is no
continuum analogue for such a solution and there exists an energy threshold for
it, which we have estimated analytically. We support our analytical results
with numerical high-precision computations, including also a stability analysis
for the excitations.Comment: 15 pages, 12 figure
Solitons in anharmonic chains with ultra-long-range interatomic interactions
We study the influence of long-range interatomic interactions on the
properties of supersonic pulse solitons in anharmonic chains. We show that in
the case of ultra-long-range (e.g., screened Coulomb) interactions three
different types of pulse solitons coexist in a certain velocity interval: one
type is unstable but the two others are stable. The high-energy stable soliton
is broad and can be described in the quasicontinuum approximation. But the
low-energy stable soliton consists of two components, short-range and
long-range ones, and can be considered as a bound state of these components.Comment: 4 pages (LaTeX), 5 figures (Postscript); submitted to Phys. Rev.
Asymptotic Dynamics of Breathers in Fermi-Pasta-Ulam Chains
We study the asymptotic dynamics of breathers in finite Fermi-Pasta-Ulam
chains at zero and non-zero temperatures. While such breathers are essentially
stationary and very long-lived at zero temperature, thermal fluctuations tend
to lead to breather motion and more rapid decay
Tunneling of quantum rotobreathers
We analyze the quantum properties of a system consisting of two nonlinearly
coupled pendula. This non-integrable system exhibits two different symmetries:
a permutational symmetry (permutation of the pendula) and another one related
to the reversal of the total momentum of the system. Each of these symmetries
is responsible for the existence of two kinds of quasi-degenerated states. At
sufficiently high energy, pairs of symmetry-related states glue together to
form quadruplets. We show that, starting from the anti-continuous limit,
particular quadruplets allow us to construct quantum states whose properties
are very similar to those of classical rotobreathers. By diagonalizing
numerically the quantum Hamiltonian, we investigate their properties and show
that such states are able to store the main part of the total energy on one of
the pendula. Contrary to the classical situation, the coupling between pendula
necessarily introduces a periodic exchange of energy between them with a
frequency which is proportional to the energy splitting between
quasi-degenerated states related to the permutation symmetry. This splitting
may remain very small as the coupling strength increases and is a decreasing
function of the pair energy. The energy may be therefore stored in one pendulum
during a time period very long as compared to the inverse of the internal
rotobreather frequency.Comment: 20 pages, 11 figures, REVTeX4 styl
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