27 research outputs found
Boundary conditions for the states with resonant tunnelling across the -potential
The one-dimensional Schr\"odinger equation with the point potential in the
form of the derivative of Dirac's delta function, with
being a coupling constant, is investigated. This equation is known to
require an extension to the space of wave functions discontinuous at
the origin under the two-sided (at ) boundary conditions given through
the transfer matrix where . However, the recent studies, where a resonant
non-zero transmission across this potential has been established to occur on
discrete sets in the -space, contradict
to these boundary conditions used widely by many authors. The present
communication aims at solving this discrepancy using a more general form of
boundary conditions.Comment: Submitted Phys. Lett. A. Essentially revised and extended version, 1
figure added. 12 page
Two-dimensional dynamics of a free molecular chain with a secondary structure
A simple two-dimensional Í‘2DÍ’ model of an isolated (free) molecular chain with primary and secondary structures has been suggested and investigated both analytically and numerically. This model can be considered as the simplest generalization of the well-known Fermi-Pasta-Ulam model of an anharmonic chain in order to include transverse degrees of freedom of the chain molecules. Both the structures are provided by the first-and second-neighbor intermolecular bonds, respectively, resulting in a regular zig-zag (''2D helix'') chain on a plane. The set of two coupled nonlinear field equations with respect to the longitudinal and transverse displacements of the chain molecules has been derived. Two types of stable Í‘nontopologicalÍ’ soliton solutions which describe either Í‘iÍ’ a supersonic solitary wave of longitudinal stretching accompanied by transverse slendering or, as in the 1D model, Í‘iiÍ’ supersonic pulses of longitudinal compression propagating together with localized transverse thickening (bulge) have been found. Some peculiar stability properties of these two-component soliton solutions have been discovered by using numerical techniques developed in this paper. Í“S1063-651XÍ‘96Í’10809-6
Discrete kink dynamics in hydrogen-bonded chains I: The one-component model
We study topological solitary waves (kinks and antikinks) in a nonlinear
one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse
type. This chain is used to describe the collective proton dynamics in
quasi-one-dimensional networks of hydrogen bonds, where the on-site potential
plays role of the proton potential in the hydrogen bond. The system supports a
rich variety of stationary kink solutions with different symmetry properties.
We study the stability and bifurcation structure of all these stationary kink
states. An exactly solvable model with a piecewise ``parabola-constant''
approximation of the double-Morse potential is suggested and studied
analytically. The dependence of the Peierls-Nabarro potential on the system
parameters is studied. Discrete travelling-wave solutions of a narrow permanent
profile are shown to exist, depending on the anharmonicity of the Morse
potential and the cooperativity of the hydrogen bond (the coupling constant of
the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure
Soliton ratchets
The mechanism underlying the soliton ratchet, both in absence and in presence
of noise, is investigated. We show the existence of an asymmetric internal mode
on the soliton profile which couples, trough the damping in the system, to the
soliton translational mode. Effective soliton transport is achieved when the
internal mode and the external force are phase locked. We use as working model
a generalized double sine-Gordon equation. The phenomenon is expected to be
valid for generic soliton systems.Comment: 4 pages, 4 figure
Stability of mode-locked kinks in the ac driven and damped sine-Gordon lattice
Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice
that is driven by the oscillating force is studied. The investigation is
focused mostly on the properties of the mode-locked states in the {\it
overband} case, when the driving frequency lies above the linear band. With the
help of Floquet theory it is demonstrated that the destabilizing of the
mode-locked state happens either through the Hopf bifurcation or through the
tangential bifurcation. It is also observed that in the overband case the
standing mode-locked kink state maintains its stability for the bias amplitudes
that are by the order of magnitude larger than the amplitudes in the
low-frequency case.Comment: To appear in Springer Series on Wave Phenomena, special volume
devoted to the LENCOS'12 conference; 6 figure
Directed motion of domain walls in biaxial ferromagnets under the influence of periodic external magnetic fields
Directed motion of domain walls (DWs) in a classical biaxial ferromagnet
placed under the influence of periodic unbiased external magnetic fields is
investigated. Using the symmetry approach developed in this article the
necessary conditions for the directed DW motion are found. This motion turns
out to be possible if the magnetic field is applied along the most easy axis.
The symmetry approach prohibits the directed DW motion if the magnetic field is
applied along any of the hard axes. With the help of the soliton perturbation
theory and numerical simulations, the average DW velocity as a function of
different system parameters such as damping constant, amplitude, and frequency
of the external field, is computed.Comment: Added references, corrected typos, extended introductio
Soliton ratchets induced by ac forces with harmonic mixing
The ratchet dynamics of a kink (topological soliton) of a dissipative
sine-Gordon equation in the presence of ac forces with harmonic mixing (at
least bi-harmonic) of zero mean is studied. The dependence of the kink mean
velocity on system parameters is investigated numerically and the results are
compared with a perturbation analysis based on a point particle representation
of the soliton. We find that first order perturbative calculations lead to
incomplete descriptions, due to the important role played by the soliton-phonon
interaction in establishing the phenomenon. The role played by the temporal
symmetry of the system in establishing soliton ratchets is also emphasized. In
particular, we show the existence of an asymmetric internal mode on the kink
profile which couples to the kink translational mode through the damping in the
system. Effective soliton transport is achieved when the internal mode and the
external force get phase locked. We find that for kinks driven by bi-harmonic
drivers consisting of the superposition of a fundamental driver with its first
odd harmonic, the transport arises only due to this {\it internal mode}
mechanism, while for bi-harmonic drivers with even harmonic superposition, also
a point-particle contribution to the drift velocity is present. The phenomenon
is robust enough to survive the presence of thermal noise in the system and can
lead to several interesting physical applications.Comment: 9 pages, 13 figure