1,347 research outputs found
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
Decohering localized waves
In the absence of confinement localization of waves takes place due to
randomness or nonlinearity and relies on their phase coherence. We
quantitatively probe the sensitivity of localized wave packets to random phase
fluctuations and confirm the necessity of phase coherence for localization.
Decoherence resulting from a dynamical random environment leads to diffusive
spreading and destroys linear and nonlinear localization. We find that maximal
spreading is achieved for optimal phase fluctuation characteristics which is a
consequence of the competition between diffusion due to decoherence and
ballistic transport within the mean free path distance.Comment: Updated affiliatio
Nonlinear localized flatband modes with spin-orbit coupling
We report the coexistence and properties of stable compact localized states
(CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flatband
network with spin-orbit coupling (SOC). The system can be implemented by means
of a binary Bose-Einstein condensate loaded in the corresponding optical
lattice. In the linear limit, the SOC opens a minigap between flat and
dispersive bands in the system's bandgap structure, and preserves the existence
of CLSs at the flatband frequency, simultaneously lowering their symmetry.
Adding onsite cubic nonlinearity, the CLSs persist and remain available in an
exact analytical form, with frequencies which are smoothly tuned into the
minigap. Inside of the minigap, the CLS and DS families are stable in narrow
areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and
DSs are stable too.Comment: 10 figures, Physical Review B, in pres
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
Acoustic breathers in two-dimensional lattices
The existence of breathers (time-periodic and spatially localized lattice
vibrations) is well established for i) systems without acoustic phonon branches
and ii) systems with acoustic phonons, but also with additional symmetries
preventing the occurence of strains (dc terms) in the breather solution. The
case of coexistence of strains and acoustic phonon branches is solved (for
simple models) only for one-dimensional lattices.
We calculate breather solutions for a two-dimensional lattice with one
acoustic phonon branch. We start from the easy-to-handle case of a system with
homogeneous (anharmonic) interaction potentials. We then easily continue the
zero-strain breather solution into the model sector with additional quadratic
and cubic potential terms with the help of a generalized Newton method. The
lattice size is . The breather continues to exist, but is dressed
with a strain field. In contrast to the ac breather components, which decay
exponentially in space, the strain field (which has dipole symmetry) should
decay like . On our rather small lattice we find an exponent
Comment on "Coherent Ratchets in Driven Bose-Einstein Condensates"
C. E. Creffield and F. Sols (Phys. Rev. Lett. 103, 200601 (2009)) recently
reported finite, directed time-averaged ratchet current, for a noninteracting
quantum particle in a periodic potential even when time-reversal symmetry
holds. As we explain in this Comment, this result is incorrect, that is,
time-reversal symmetry implies a vanishing current.Comment: revised versio
Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
We study the spreading of an initially localized wavepacket in two nonlinear
chains (discrete nonlinear Schroedinger and quartic Klein-Gordon) with
disorder. Previous studies suggest that there are many initial conditions such
that the second moment of the norm and energy density distributions diverge as
a function of time. We find that the participation number of a wavepacket does
not diverge simultaneously. We prove this result analytically for
norm-conserving models and strong enough nonlinearity. After long times the
dynamical state consists of a distribution of nondecaying yet interacting
normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this
result holds for any initially localized wavepacket, a limit profile for the
norm/energy distribution with infinite second moment should exist in all cases
which rules out the possibility of slow energy diffusion (subdiffusion). This
limit profile could be a quasiperiodic solution (KAM torus)
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