58 research outputs found
Quasiperiodic Envelope Solitons
We analyse nonlinear wave propagation and cascaded self-focusing due to
second-harmonic generation in Fibbonacci optical superlattices and introduce a
novel concept of nonlinear physics, the quasiperiodic soliton, which describes
spatially localized self-trapping of a quasiperiodic wave. We point out a link
between the quasiperiodic soliton and partially incoherent spatial solitary
waves recently generated experimentally.Comment: Submitted to PRL. 4 pages with 5 figure
Anderson localization in metamaterials and other complex media
We review some recent (mostly ours) results on the Anderson localization of
light and electron waves in complex disordered systems, including: (i)
left-handed metamaterials, (ii) magneto-active optical structures, (iii)
graphene superlattices, and (iv) nonlinear dielectric media. First, we
demonstrate that left-handed metamaterials can significantly suppress
localization of light and lead to an anomalously enhanced transmission. This
suppression is essential at the long-wavelength limit in the case of normal
incidence, at specific angles of oblique incidence (Brewster anomaly), and in
the vicinity of the zero-epsilon or zero-mu frequencies for dispersive
metamaterials. Remarkably, in disordered samples comprised of alternating
normal and left-handed metamaterials, the reciprocal Lyapunov exponent and
reciprocal transmittance increment can differ from each other. Second, we study
magneto-active multilayered structures, which exhibit nonreciprocal
localization of light depending on the direction of propagation and on the
polarization. At resonant frequencies or realizations, such nonreciprocity
results in effectively unidirectional transport of light. Third, we discuss the
analogy between the wave propagation through multilayered samples with
metamaterials and the charge transport in graphene, which enables a simple
physical explanation of unusual conductive properties of disordered graphene
superlatices. We predict disorder-induced resonances of the transmission
coefficient at oblique incidence of the Dirac quasiparticles. Finally, we
demonstrate that an interplay of nonlinearity and disorder in dielectric media
can lead to bistability of individual localized states excited inside the
medium at resonant frequencies. This results in nonreciprocity of the wave
transmission and unidirectional transport of light.Comment: 37 pages, 30 figures, Review pape
Nonreciprocal Anderson Localization in Magneto-Optical Random Structures
We study, both analytically and numerically, disorder-induced localization of
light in random layered structures with magnetooptical materials. The Anderson
localization in such structures demonstrates nonreciprocal features in the
averaged localization length and individual transmission resonances. We employ
short-wavelength approximation where the localization effects are strong, and
consider both the Faraday and Voigt magnetooptical geometries. In the Faraday
geometry, the transmission is strongly nonreciprocal for the circularly
polarized waves, whereas in the Voigt geometry, the nonreciprocity is much
weaker, and it may appear only for the individual transmission resonances of
the TM-polarized waves.Comment: 8 pages, 6 figure
Infrared Spectroscopy of Quantum Crossbars
Infrared (IR) spectroscopy can be used as an important and effective tool for
probing periodic networks of quantum wires or nanotubes (quantum crossbars,
QCB) at finite frequencies far from the Luttinger liquid fixed point. Plasmon
excitations in QCB may be involved in resonance diffraction of incident
electromagnetic waves and in optical absorption in the IR part of the spectrum.
Direct absorption of external electric field in QCB strongly depends on the
direction of the wave vector This results in two types of
dimensional crossover with varying angle of an incident wave or its frequency.
In the case of QCB interacting with semiconductor substrate, capacitive contact
between them does not destroy the Luttinger liquid character of the long wave
QCB excitations. However, the dielectric losses on a substrate surface are
significantly changed due to appearance of additional Landau damping. The
latter is initiated by diffraction processes on QCB superlattice and manifests
itself as strong but narrow absorption peaks lying below the damping region of
an isolated substrate.SubmiComment: Submitted to Phys. Rev.
Umklapp-Assisted Electron Transport Oscillations in Metal Superlattices
We consider a superlattice of parallel metal tunnel junctions with a
spatially non-homogeneous probability for electrons to tunnel. In such
structures tunneling can be accompanied by electron scattering that conserves
energy but not momentum. In the special case of a tunneling probability that
varies periodically with period in the longitudinal direction, i.e.,
perpendicular to the junctions, electron tunneling is accompanied by "umklapp"
scattering, where the longitudinal momentum changes by a multiple of . We
predict that as a result a sequence of metal-insulator transitions can be
induced by an external electric- or magnetic field as the field strength is
increased.Comment: 5 pages, 3 figure
Electronic excitations and correlations in quantum bars
The spectrum of boson fields and two-point correlators are analyzed in a quantum bar system (a superlattice formed by two crossed interacting arrays of quantum wires), with a short-range interwire interaction. The standard bosonization procedure is shown to be valid, within the two-wave approximation. The system behaves as a sliding Luttinger liquid in the vicinity of the Γ point, but its spectral and correlation characteristics have either 1D or 2D nature depending on the direction of the wave vector in the rest of the Brillouin zone. Due to the interwire interaction, unperturbed states propagating along the two arrays of wires are always mixed, and the transverse components of the correlation functions do not vanish. This mixing is especially strong around the diagonals of the Brillouin zone, where the transverse correlators have the same order of magnitude as the longitudinal ones
Quantum dynamics in canonical and micro-canonical ensembles. Part I. Anderson localization of electrons
The new numerical approach for consideration of quantum dynamics and
calculations of the average values of quantum operators and time correlation
functions in the Wigner representation of quantum statistical mechanics has
been developed. The time correlation functions have been presented in the form
of the integral of the Weyl's symbol of considered operators and the Fourier
transform of the product of matrix elements of the dynamic propagators. For the
last function the integral Wigner- Liouville's type equation has been derived.
The numerical procedure for solving this equation combining both molecular
dynamics and Monte Carlo methods has been developed. For electrons in
disordered systems of scatterers the numerical results have been obtained for
series of the average values of the quantum operators including position and
momentum dispersions, average energy, energy distribution function as well as
for the frequency dependencies of tensor of electron conductivity and
permittivity according to quantum Kubo formula. Zero or very small value of
static conductivity have been considered as the manifestation of Anderson
localization of electrons in 1D case. Independent evidence of Anderson
localization comes from the behaviour of the calculated time dependence of
position dispersion.Comment: 8 pages, 10 figure
Soliton pinning by long-range order in aperiodic systems
We investigate propagation of a kink soliton along inhomogeneous chains with
two different constituents, arranged either periodically, aperiodically, or
randomly. For the discrete sine-Gordon equation and the Fibonacci and
Thue-Morse chains taken as examples, we have found that the phenomenology of
aperiodic systems is very peculiar: On the one hand, they exhibit soliton
pinning as in the random chain, although the depinning forces are clearly
smaller. In addition, solitons are seen to propagate differently in the
aperiodic chains than on periodic chains with large unit cells, given by
approximations to the full aperiodic sequence. We show that most of these
phenomena can be understood by means of simple collective coordinate arguments,
with the exception of long range order effects. In the conclusion we comment on
the interesting implications that our work could bring about in the field of
solitons in molecular (e.g., DNA) chains.Comment: 4 pages, REVTeX 3.0 + epsf, 3 figures in accompanying PostScript file
(Submitted to Phys Rev E Rapid Comm
Short--range impurity in the vicinity of a saddle point and the levitation of the 2D delocalized states in a magnetic field
The effect of a short--range impurity on the transmission through a
saddle--point potential for an electron, moving in a strong magnetic field, is
studied. It is demonstrated that for a random position of an impurity and
random sign of its potential the impurity--induced mixing of the Landau levels
diminishes {\em on average} the transmission coefficient. This results in an
upward shift (levitation) of the energy position of the delocalized state in a
smooth potential. The magnitude of the shift is estimated. It increases with
decreasing magnetic field as .Comment: LaTeX, 20 page
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