29,900 research outputs found
Principal Solutions Revisited
The main objective of this paper is to identify principal solutions
associated with Sturm-Liouville operators on arbitrary open intervals , as introduced by Leighton and Morse in the scalar
context in 1936 and by Hartman in the matrix-valued situation in 1957, with
Weyl-Titchmarsh solutions, as long as the underlying Sturm-Liouville
differential expression is nonoscillatory (resp., disconjugate or bounded from
below near an endpoint) and in the limit point case at the endpoint in
question. In addition, we derive an explicit formula for Weyl-Titchmarsh
functions in this case (the latter appears to be new in the matrix-valued
context).Comment: 27 pages, expanded Sect. 2, added reference
Coherent phenomena in semiconductors
A review of coherent phenomena in photoexcited semiconductors is presented.
In particular, two classes of phenomena are considered: On the one hand the
role played by optically-induced phase coherence in the ultrafast spectroscopy
of semiconductors; On the other hand the Coulomb-induced effects on the
coherent optical response of low-dimensional structures.
All the phenomena discussed in the paper are analyzed in terms of a
theoretical framework based on the density-matrix formalism. Due to its
generality, this quantum-kinetic approach allows a realistic description of
coherent as well as incoherent, i.e. phase-breaking, processes, thus providing
quantitative information on the coupled ---coherent vs. incoherent--- carrier
dynamics in photoexcited semiconductors.
The primary goal of the paper is to discuss the concept of quantum-mechanical
phase coherence as well as its relevance and implications on semiconductor
physics and technology. In particular, we will discuss the dominant role played
by optically induced phase coherence on the process of carrier photogeneration
and relaxation in bulk systems. We will then review typical field-induced
coherent phenomena in semiconductor superlattices such as Bloch oscillations
and Wannier-Stark localization. Finally, we will discuss the dominant role
played by Coulomb correlation on the linear and non-linear optical spectra of
realistic quantum-wire structures.Comment: Topical review in Semiconductor Science and Technology (in press)
(Some of the figures are not available in electronic form
Time Averaged Quantum Dynamics and the Validity of the Effective Hamiltonian Model
We develop a technique for finding the dynamical evolution in time of an
averaged density matrix. The result is an equation of evolution that includes
an Effective Hamiltonian, as well as decoherence terms in Lindblad form.
Applying the general equation to harmonic Hamiltonians, we confirm a previous
formula for the Effective Hamiltonian together with a new decoherence term
which should in general be included, and whose vanishing provides the criteria
for validity of the Effective Hamiltonian approach. Finally, we apply the
theory to examples of the AC Stark Shift and Three- Level Raman Transitions,
recovering a new decoherence effect in the latter.Comment: 7 pages, 2 figure
Hamevol1.0: a C++ code for differential equations based on Runge-Kutta algorithm. An application to matter enhanced neutrino oscillation
We present a C++ implementation of a fifth order semi-implicit Runge-Kutta
algorithm for solving Ordinary Differential Equations. This algorithm can be
used for studying many different problems and in particular it can be applied
for computing the evolution of any system whose Hamiltonian is known. We
consider in particular the problem of calculating the neutrino oscillation
probabilities in presence of matter interactions. The time performance and the
accuracy of this implementation is competitive with respect to the other
analytical and numerical techniques used in literature. The algorithm design
and the salient features of the code are presented and discussed and some
explicit examples of code application are given.Comment: 18 pages, Late
Patterns on liquid surfaces: cnoidal waves, compactons and scaling
Localized patterns and nonlinear oscillation formation on the bounded free
surface of an ideal incompressible liquid are analytically investigated .
Cnoidal modes, solitons and compactons, as traveling non-axially symmetric
shapes are discused. A finite-difference differential generalized Korteweg-de
Vries equation is shown to describe the three-dimensional motion of the fluid
surface and the limit of long and shallow channels one reobtains the well known
KdV equation. A tentative expansion formula for the representation of the
general solution of a nonlinear equation, for given initial condition is
introduced on a graphical-algebraic basis. The model is useful in multilayer
fluid dynamics, cluster formation, and nuclear physics since, up to an overall
scale, these systems display liquid free surface behavior.Comment: 14 pages RevTex, 5 figures in p
Second Josephson excitations beyond mean field as a toy model for thermal pressure: exact quantum dynamics and the quantum phase model
A simple four-mode Bose-Hubbard model with intrinsic time scale separation
can be considered as a paradigm for mesoscopic quantum systems in thermal
contact. In our previous work we showed that in addition to coherent particle
exchange, a novel slow collective excitation can be identified by a series of
Holstein-Primakoff transformations. This resonant energy exchange mode is not
predicted by linear Bogoliubov theory, and its frequency is sensitive to
interactions among Bogoliubov quasi-particles; it may be referred to as a
second Josephson oscillation, in analogy to the second sound mode of liquid
Helium II. In this paper we will explore this system beyond the
Gross-Pitaevskii mean field regime. We directly compare the classical mean
field dynamics to the exact full quantum many-particle dynamics and show good
agreement over a large range of the system parameters. The second Josephson
frequency becomes imaginary for stronger interactions, however, indicating
dynamical instability of the symmetric state. By means of a generalized quantum
phase model for the full four-mode system, we then show that, in this regime,
high-energy Bogoliubov quasiparticles tend to accumulate in one pair of sites,
while the actual particles preferentially occupy the opposite pair. We
interpret this as a simple model for thermal pressure
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