82 research outputs found
Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian
The spectrum of a one-dimensional pseudospin-one Hamiltonian with a
three-component potential is studied for two configurations: (i) all the
potential components are constants over the whole coordinate space and (ii) the
profile of some components is of a rectangular form. In case (i), it is
illustrated how the structure of three (lower, middle and upper) bands depends
on the configuration of potential strengths including the appearance of flat
bands at some special values of these strengths. In case (ii), the set of two
equations for finding bound states is derived. The spectrum of bound-state
energies is shown to depend crucially on the configuration of potential
strengths. Each of these configurations is specified by a single strength
parameter . The bound-state energies are calculated as functions of the
strength and a one-point approach is developed realizing correspondent
point interactions. For different potential configurations, the energy
dependence on the strength is described in detail, including its one-point
approximation. From a whole variety of bound-state spectra, four characteristic
types are singled out.Comment: To appear in Journal of Physics A: Mathematical and Theoretical. 11
figure
Almost compact moving breathers with fine-tuned discrete time quantum walks
Discrete time quantum walks are unitary maps defined on the Hilbert space of
coupled two-level systems. We study the dynamics of excitations in a nonlinear
discrete time quantum walk, whose fine-tuned linear counterpart has a flat band
structure. The linear counterpart is, therefore, lacking transport, with exact
solutions being compactly localized. A solitary entity of the nonlinear walk
moving at velocity would therefore not suffer from resonances with small
amplitude plane waves with identical phase velocity, due to the absence of the
latter. That solitary excitation would also have to be localized stronger than
exponential, due to the absence of a linear dispersion. We report on the
existence of a set of stationary and moving breathers with almost compact
superexponential spatial tails. At the limit of the largest velocity the
moving breather turns into a completely compact bullet.Comment: 8 pages, 8 figure
Bound states of a one-dimensional Dirac equation with multiple delta-potentials
Two approaches are developed for the study of the bound states of a
one-dimensional Dirac equation with the potential consisting of
-function centers. One of these uses the Green's function method. This
method is applicable to a finite number of -point centers, reducing
the bound state problem to finding the energy eigenvalues from the determinant
of a matrix. The second approach starts with the matrix for a
single delta-center that connects the two-sided boundary conditions for this
center. This connection matrix is obtained from the squeezing limit of a
piecewise constant approximation of the delta-function. Having then the
connection matrices for each center, the transmission matrix for the whole
system is obtained by multiplying the one-center connection matrices and the
free transfer matrices between neighbor centers. An equation for bound state
energies is derived in terms of the elements of the total transfer matrix.
Within both the approaches, the transcendental equations for bound state
energies are derived, the solutions to which depend on the strength of
delta-centers and the distance between them, and this dependence is illustrated
by numerical calculations. The bound state energies for the potentials composed
of one, two, and three delta-centers () are computed explicitly.
The principle of strength additivity is analyzed in the limits as the
delta-centers merge at a single point or diverge to infinity.Comment: 4 figure
Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response
We consider low-dimensional dynamical systems exposed to a heat bath and to
additional ac fields. The presence of these ac fields may lead to a breaking of
certain spatial or temporal symmetries which in turn cause nonzero averages of
relevant observables. Nonlinear (non)adiabatic response is employed to explain
the effect. We consider a case of a particle in a periodic potential as an
example and discuss the relevant symmetry breakings and the mechanisms of
rectification of the current in such a system.Comment: 11 pages, 10 figure
Ratchet-like dynamics of fluxons in annular Josephson junctions driven by bi-harmonic microwave fields
Experimental observation of the unidirectional motion of a topological
soliton driven by a bi-harmonic ac force of zero mean is reported. The
observation is made by measuring the current-voltage characteristics for a
fluxon trapped in an annular Josephson junction that was placed into a
microwave field. The measured dependence of the fluxon mean velocity (rectified
voltage) at zero dc bias versus the phase shift between the first and second
harmonic of the driving force is in qualitative agreement with theoretical
expectations.Comment: 6 figure
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
Non Local Electron-Phonon Correlations in a Dispersive Holstein Model
Due to the dispersion of optical phonons, long range electron-phonon
correlations renormalize downwards the coupling strength in the Holstein model.
We evaluate the size of this effect both in a linear chain and in a square
lattice for a time averaged {\it e-ph} potential, where the time variable is
introduced according to the Matsubara formalism. Mapping the Holstein
Hamiltonian onto the time scale we derive the perturbing source current which
appears to be non time retarded. This property permits to disentangle phonon
and electron coordinates in the general path integral for an electron coupled
to dispersive phonons. While the phonon paths can be integrated out
analytically, the electron path integrations have to be done numerically. The
equilibrium thermodynamic properties of the model are thus obtained as a
function of the electron hopping value and of the phonon spectrum parameters.
We derive the {\it e-ph} corrections to the phonon free energy and show that
its temperature derivatives do not depend on the {\it e-ph} effective coupling
hence, the Holstein phonon heat capacity is strictly harmonic. A significant
upturn in the low temperature total heat capacity over ratio is attributed
to the electron hopping which largely contributes to the action.Comment: Phys.Rev.B (2005
Discrete breathers in an one-dimensional array of magnetic dots
The dynamics of the one-dimensional array of magnetic particles (dots) with the easy-plane anisotropy is
investigated. The particles interact with each other via the magnetic dipole interaction and the whole system is
governed by the set of Landau–Lifshitz equations. The spatially localized and time-periodic solutions known as
discrete breathers (or intrinsic localized modes) are identified. These solutions have no analogue in the continuum
limit and consist of the core where the magnetization vectors precess around the hard axis and the tails
where the magnetization vectors oscillate around the equilibrium position
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