409 research outputs found
Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum
We generalize the momentum average (MA) approximation to study the properties
of models with momentum-dependent electron-phonon coupling. As in the case of
the application of the original MA to the Holstein model, the results are
analytical, numerically trivial to evaluate, exact for both zero bandwidth and
for zero electron-phonon coupling, and are accurate everywhere in parameter
space. Comparison with available numerical data confirms this accuracy. We then
show that further improvements can be obtained based on variational
considerations, using the one-dimensional breathing-mode Hamiltonian as a
specific example. For example, by using this variational MA, we obtain ground
state energies within at most 0.3% error of the numerical data.Comment: 15 pages, 10 figure
Sub-nanosecond delay of light in (Cd,Zn)Te crystal
We study excitonic polariton relaxation and propagation in bulk CdZnTe using
time- resolved photoluminescence and time-of-flight techniques. Propagation of
picosecond optical pulses through 0.745 mm thick crystal results in time delays
up to 350 ps, depending on the photon energy. Optical pulses with 150 fs
duration become strongly stretched. The spectral dependence of group velocity
is consistent with the dispersion of the lower excitonic polariton branch. The
lifetimes of excitonic polariton in the upper and lower branches are 1.5 and 3
ns, respectively.Comment: 5 pages, 4 figure
A Variational Approach to Nonlocal Exciton-Phonon Coupling
In this paper we apply variational energy band theory to a form of the
Holstein Hamiltonian in which the influence of lattice vibrations (optical
phonons) on both local site energies (local coupling) and transfers of
electronic excitations between neighboring sites (nonlocal coupling) is taken
into account. A flexible spanning set of orthonormal eigenfunctions of the
joint exciton-phonon crystal momentum is used to arrive at a variational
estimate (bound) of the ground state energy for every value of the joint
crystal momentum, yielding a variational estimate of the lowest polaron energy
band across the entire Brillouin zone, as well as the complete set of polaron
Bloch functions associated with this band. The variation is implemented
numerically, avoiding restrictive assumptions that have limited the scope of
previous assaults on the same and similar problems. Polaron energy bands and
the structure of the associated Bloch states are studied at general points in
the three-dimensional parameter space of the model Hamiltonian (electronic
tunneling, local coupling, nonlocal coupling), though our principal emphasis
lay in under-studied area of nonlocal coupling and its interplay with
electronic tunneling; a phase diagram summarizing the latter is presented. The
common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure
On fractional Choquard equations
We investigate a class of nonlinear Schrodinger equations with a generalized
Choquard nonlinearity and fractional diffusion. We obtain regularity,
existence, nonexistence, symmetry as well as decays properties.Comment: revised version, 22 page
Fractal and chaotic solutions of the discrete nonlinear Schr\"odinger equation in classical and quantum systems
We discuss stationary solutions of the discrete nonlinear Schr\"odinger
equation (DNSE) with a potential of the type which is generically
applicable to several quantum spin, electron and classical lattice systems. We
show that there may arise chaotic spatial structures in the form of
incommensurate or irregular quantum states. As a first (typical) example we
consider a single electron which is strongly coupled with phonons on a
chain of atoms --- the (Rashba)--Holstein polaron model. In the adiabatic
approximation this system is conventionally described by the DNSE. Another
relevant example is that of superconducting states in layered superconductors
described by the same DNSE. Amongst many other applications the typical example
for a classical lattice is a system of coupled nonlinear oscillators. We
present the exact energy spectrum of this model in the strong coupling limit
and the corresponding wave function. Using this as a starting point we go on to
calculate the wave function for moderate coupling and find that the energy
eigenvalue of these structures of the wave function is in exquisite agreement
with the exact strong coupling result. This procedure allows us to obtain
(numerically) exact solutions of the DNSE directly. When applied to our typical
example we find that the wave function of an electron on a deformable lattice
(and other quantum or classical discrete systems) may exhibit incommensurate
and irregular structures. These states are analogous to the periodic,
quasiperiodic and chaotic structures found in classical chaotic dynamics
Analysis on reflection spectra in strained ZnO thin films
Thin films of laser molecular-beam epitaxy grown ZnO films were studied with
respect to their optical properties. 4-K reflectivity was used to analyze
various samples grown at different biaxial in-plane strain. The spectra show
two structures at 3.37 eV corresponding to the A-free exciton transition and at
3.38 eV corresponding to the B-free exciton transition. Theoretical
reflectivity spectra were calculated using the spatial dispersion model. Thus,
the transverse energies, the longitudinal transversal splitting (ELT,), the
oscillator strengths, and the damping parameters were determined for both the
A- and B-free excitons of ZnO. As a rough trend, the strain dependence of the
energy E_LT for the A-excitons is characterized by a negatively-peaking
behavior with a minimum around the zero strain, while ELT for the B-excitons is
an increasing function of the strain field values.Comment: 4 pages, 2 figures, 1 table, conference: ICMAT2005 (Singapore), to
appear in an issue of J. Cryst. Growt
Electron-phonon interaction via Pekar mechanism in nanostructures
We consider an electron-acoustic phonon coupling mechanism associated with
the dependence of crystal dielectric permittivity on the strain (the so-called
Pekar mechanism) in nanostructures characterized by strong confining electric
fields. The efficiency of Pekar coupling is a function of both the absolute
value and the spatial distribution of the electric field. It is demonstrated
that this mechanism exhibits a phonon wavevector dependence similar to that of
piezoelectricity and must be taken into account for electron transport
calculations in an extended field distribution. In particular, we analyze the
role of Pekar coupling in energy relaxation in silicon inversion layers.
Comparison with the recent experimental results is provided to illustrate its
potential significance
Coherent Propagation of Polaritons in Semiconductor Heterostructures: Nonlinear Pulse Transmission in Theory and Experiment
The influence of coherent optical nonlinearities on polariton propagation
effects is studied within a theory-experiment comparison. A novel approach that
combines a microscopic treatment of the boundary problem in a sample of finite
thickness with excitonic and biexcitonic nonlinearities is introduced.
Light-polarization dependent spectral changes are analyzed for single-pulse
transmission and pump-probe excitation
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