643 research outputs found
Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions
Eigenvalues and eigenfunctions of Mathieu's equation are found in the short
wavelength limit using a uniform approximation (method of comparison with a
`known' equation having the same classical turning point structure) applied in
Fourier space. The uniform approximation used here relies upon the fact that by
passing into Fourier space the Mathieu equation can be mapped onto the simpler
problem of a double well potential. The resulting eigenfunctions (Bloch waves),
which are uniformly valid for all angles, are then used to describe the
semiclassical scattering of waves by potentials varying sinusoidally in one
direction. In such situations, for instance in the diffraction of atoms by
gratings made of light, it is common to make the Raman-Nath approximation which
ignores the motion of the atoms inside the grating. When using the
eigenfunctions no such approximation is made so that the dynamical diffraction
regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important
references to existing work on uniform approximations, such as Olver's method
applied to the modified Mathieu equation. It is emphasised that the paper
presented here pertains to Fourier space uniform approximation
Reflectionless Potentials and PT Symmetry
Large families of Hamiltonians that are non-Hermitian in the conventional
sense have been found to have all eigenvalues real, a fact attributed to an
unbroken PT symmetry. The corresponding quantum theories possess an
unconventional scalar product. The eigenvalues are determined by differential
equations with boundary conditions imposed in wedges in the complex plane. For
a special class of such systems, it is possible to impose the PT-symmetric
boundary conditions on the real axis, which lies on the edges of the wedges.
The PT-symmetric spectrum can then be obtained by imposing the more transparent
requirement that the potential be reflectionless.Comment: 4 Page
Classical and Quantum Chaos in a quantum dot in time-periodic magnetic fields
We investigate the classical and quantum dynamics of an electron confined to
a circular quantum dot in the presence of homogeneous magnetic
fields. The classical motion shows a transition to chaotic behavior depending
on the ratio of field magnitudes and the cyclotron
frequency in units of the drive frequency. We determine a
phase boundary between regular and chaotic classical behavior in the
vs plane. In the quantum regime we evaluate the quasi-energy
spectrum of the time-evolution operator. We show that the nearest neighbor
quasi-energy eigenvalues show a transition from level clustering to level
repulsion as one moves from the regular to chaotic regime in the
plane. The statistic confirms this
transition. In the chaotic regime, the eigenfunction statistics coincides with
the Porter-Thomas prediction. Finally, we explicitly establish the phase space
correspondence between the classical and quantum solutions via the Husimi phase
space distributions of the model. Possible experimentally feasible conditions
to see these effects are discussed.Comment: 26 pages and 17 PstScript figures, two large ones can be obtained
from the Author
Laudatores Temporis Acti, or Why Cosmology is Alive and Well - A Reply to Disney
A recent criticism of cosmological methodology and achievements by Disney
(2000) is assessed. Some historical and epistemological fallacies in the said
article have been highlighted. It is shown that---both empirically and
epistemologically---modern cosmology lies on sounder foundations than it is
portrayed. A brief historical account demonstrates that this form of
unsatisfaction with cosmology has had a long tradition, and rather meagre
results in the course of the XX century.Comment: 11 pages, no figures; a criticism of astro-ph/0009020; Gen. Rel.
Grav., accepted for publicatio
Factorial cumulants reveal interactions in counting statistics
Full counting statistics concerns the stochastic transport of electrons in
mesoscopic structures. Recently it has been shown that the charge transport
statistics for non-interacting electrons in a two-terminal system is always
generalized binomial: it can be decomposed into independent single-particle
events and the zeros of the generating function are real and negative. Here we
investigate how the zeros of the generating function move into the complex
plane due to interactions and demonstrate that the positions of the zeros can
be detected using high-order factorial cumulants. As an illustrative example we
consider electron transport through a Coulomb blockade quantum dot for which we
show that the interactions on the quantum dot are clearly visible in the
high-order factorial cumulants. Our findings are important for understanding
the influence of interactions on counting statistics and the characterization
in terms of zeros of the generating function provides us with a simple
interpretation of recent experiments, where high-order statistics have been
measured.Comment: 12 pages, 7 figures, Editors' Suggestion in Phys. Rev.
Paramagnetic-diamagnetic interplay in quantum dots for non-zero temperatures
In the usual Fock-and Darwin-formalism with parabolic potential characterized
by the confining energy \eps_o := \hbar\omega_o= 3.37 meV, but including
explicitly also the Zeeman coupling between spin and magnetic field, we study
the combined orbital and spin magnetic properties of quantum dots in a
two-dimensional electron gas with parameters for GaAs, for N =1 and N >> 1
electrons on the dot.
For N=1 the magnetization M(T,B) consists of a paramagnetic spin contribution
and a diamagnetic orbital contribution, which dominate in a non-trivial way at
low temperature and fields rsp. high temperature and fields.
For N >> 1, where orbital and spin effects are intrinsically coupled in a
subtle way and cannot be separated, we find in a simplified Hartree
approximation that at N=m^2, i.e. at a half-filled last shell, M(T,B,N) is
parallel (antiparallel) to the magnetic field, if temperatures and fields are
low enough (high enough), whereas for N\ne m^2 the magnetization oscillates
with B and N as a T-dependent periodic function of the variable
x:=\sqrt{N}eB/(2m^*c\omega_o), with T-independent period \Delta x =1 (where m^*
:= 0.067 m_o is the small effective mass of GaAs, while m_o is the electron
mass). Correspondingly, by an adiabatic demagnetization process, which should
only be fast enough with respect to the slow transient time of the magnetic
properties of the dot, the temperature of the dot diminishes rsp. increases
with decreasing magnetic field, and in some cases we obtain quite pronounced
effects.Comment: LaTeX, 28 pages; including three .eps-figures; final version accepted
by J. Phys. CM, with minimal changes w.r.to v
Exciton correlations in coupled quantum wells and their luminescence blue shift
In this paper we present a study of an exciton system where electrons and
holes are confined in double quantum well structures. The dominating
interaction between excitons in such systems is a dipole - dipole repulsion. We
show that the tail of this interaction leads to a strong correlation between
excitons and substantially affects the behavior of the system. Making use of
qualitative arguments and estimates we develop a picture of the exciton -
exciton correlations in the whole region of temperature and concentration where
excitons exist. It appears that at low concentration degeneracy of the excitons
is accompanied with strong multi-particle correlation so that the system cannot
be considered as a gas. At high concentration the repulsion suppresses the
quantum degeneracy down to temperatures that could be much lower than in a Bose
gas with contact interaction. We calculate the blue shift of the exciton
luminescence line which is a sensitive tool to observe the exciton - exciton
correlations.Comment: 27 pages in PDF and DVI format, 8 figure
The two-fluid model with superfluid entropy
The two-fluid model of liquid helium is generalized to the case that the
superfluid fraction has a small entropy content. We present theoretical
arguments in favour of such a small superfluid entropy. In the generalized
two-fluid model various sound modes of HeII are investigated. In a
superleak carrying a persistent current the superfluid entropy leads to a new
sound mode which we call sixth sound. The relation between the sixth sound and
the superfluid entropy is discussed in detail.Comment: 22 pages, latex, published in Nuovo Cimento 16 D (1994) 37
Novel Sets of Coupling Expansion Parameters for low-energy pQCD
In quantum theory, physical amplitudes are usually presented in the form of
Feynman perturbation series in powers of coupling constant \al . However, it
is known that these amplitudes are not regular functions at
For QCD, we propose new sets of expansion parameters {\bf w}_k(\as) that
reflect singularity at \as=0 and should be used instead of powers \as^k.
Their explicit form is motivated by the so called Analytic Perturbation Theory.
These parameters reveal saturation in a strong coupling case at the level
\as^{eff}(\as\gg1)={\bf w}_1(\as\gg 1) \sim 0.5 . They can be used for
quanitative analysis of divers low-energy amplitudes.
We argue that this new picture with non-power sets of perturbation expansion
parameters, as well as the saturation feature, is of a rather general nature.Comment: 8 pages, 1 figure, submitted to Part. Nucl. Phys. Let
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