1,557 research outputs found
Semiclassical Coherent States propagator
In this work, we derived a semiclassical approximation for the matrix
elements of a quantum propagator in coherent states (CS) basis that avoids
complex trajectories, it only involves real ones. For that propose, we used
the, symplectically invariant, semiclassical Weyl propagator obtained by
performing a stationary phase approximation (SPA) for the path integral in the
Weyl representation. After what, for the transformation to CS representation
SPA is avoided, instead a quadratic expansion of the complex exponent is used.
This procedure also allows to express the semiclassical CS propagator uniquely
in terms of the classical evolution of the initial point, without the need of
any root search typical of Van Vleck Gutzwiller based propagators. For the case
of chaotic Hamiltonian systems, the explicit time dependence of the CS
propagator has been obtained. The comparison with a
\textquotedbl{}realistic\textquotedbl{} chaotic system that derives from a
quadratic Hamiltonian, the cat map, reveals that the expression here derived is
exact up to quadratic Hamiltonian systems.Comment: 13 pages, 2 figure. Accepted for publication in PR
The effect of short ray trajectories on the scattering statistics of wave chaotic systems
In many situations, the statistical properties of wave systems with chaotic
classical limits are well-described by random matrix theory. However,
applications of random matrix theory to scattering problems require
introduction of system specific information into the statistical model, such as
the introduction of the average scattering matrix in the Poisson kernel. Here
it is shown that the average impedance matrix, which also characterizes the
system-specific properties, can be expressed in terms of classical trajectories
that travel between ports and thus can be calculated semiclassically.
Theoretical results are compared with numerical solutions for a model
wave-chaotic system
Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport
We investigate the effect of different edge types on the statistical
properties of both the energy spectrum of closed graphene billiards and the
conductance of open graphene cavities in the semiclassical limit. To this end,
we use the semiclassical Green's function for ballistic graphene flakes that we
have derived in Reference 1. First we study the spectral two point correlation
function, or more precisely its Fourier transform the spectral form factor,
starting from the graphene version of Gutzwiller's trace formula for the
oscillating part of the density of states. We calculate the two leading order
contributions to the spectral form factor, paying particular attention to the
influence of the edge characteristics of the system. Then we consider transport
properties of open graphene cavities. We derive generic analytical expressions
for the classical conductance, the weak localization correction, the size of
the universal conductance fluctuations and the shot noise power of a ballistic
graphene cavity. Again we focus on the effects of the edge structure. For both,
the conductance and the spectral form factor, we find that edge induced
pseudospin interference affects the results significantly. In particular
intervalley coupling mediated through scattering from armchair edges is the key
mechanism that governs the coherent quantum interference effects in ballistic
graphene cavities
Hubbard physics in the symmetric half-filled periodic Anderson-Hubbard model
Two very different methods -- exact diagonalization on finite chains and a
variational method -- are used to study the possibility of a metal-insulator
transition in the symmetric half-filled periodic Anderson-Hubbard model. With
this aim we calculate the density of doubly occupied sites as a function of
various parameters. In the absence of on-site Coulomb interaction ()
between electrons, the two methods yield similar results. The double
occupancy of levels remains always finite just as in the one-dimensional
Hubbard model. Exact diagonalization on finite chains gives the same result for
finite , while the Gutzwiller method leads to a Brinkman-Rice transition
at a critical value (), which depends on and .Comment: 10 pages, 5 figure
Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories
Electronic transport through chaotic quantum dots exhibits universal, system
independent, properties, consistent with random matrix theory. The quantum
transport can also be rooted, via the semiclassical approximation, in sums over
the classical scattering trajectories. Correlations between such trajectories
can be organized diagrammatically and have been shown to yield universal
answers for some observables. Here, we develop the general combinatorial
treatment of the semiclassical diagrams, through a connection to factorizations
of permutations. We show agreement between the semiclassical and random matrix
approaches to the moments of the transmission eigenvalues. The result is valid
for all moments to all orders of the expansion in inverse channel number for
all three main symmetry classes (with and without time reversal symmetry and
spin-orbit interaction) and extends to nonlinear statistics. This finally
explains the applicability of random matrix theory to chaotic quantum transport
in terms of the underlying dynamics as well as providing semiclassical access
to the probability density of the transmission eigenvalues.Comment: Refereed version. 5 pages, 4 figure
Periodic orbit quantization of a Hamiltonian map on the sphere
In a previous paper we introduced examples of Hamiltonian mappings with phase
space structures resembling circle packings. It was shown that a vast number of
periodic orbits can be found using special properties. We now use this
information to explore the semiclassical quantization of one of these maps.Comment: 23 pages, REVTEX
Exact analytic results for the Gutzwiller wave function with finite magnetization
We present analytic results for ground-state properties of Hubbard-type
models in terms of the Gutzwiller variational wave function with non-zero
values of the magnetization m. In dimension D=1 approximation-free evaluations
are made possible by appropriate canonical transformations and an analysis of
Umklapp processes. We calculate the double occupation and the momentum
distribution, as well as its discontinuity at the Fermi surface, for arbitrary
values of the interaction parameter g, density n, and magnetization m. These
quantities determine the expectation value of the one-dimensional Hubbard
Hamiltonian for any symmetric, monotonically increasing dispersion epsilon_k.
In particular for nearest-neighbor hopping and densities away from half filling
the Gutzwiller wave function is found to predict ferromagnetic behavior for
sufficiently large interaction U.Comment: REVTeX 4, 32 pages, 8 figure
Transport and Spectra in the Half-filled Hubbard Model: A Dynamical Mean Field Study
We study the issues of scaling and universality in spectral and transport
properties of the infinite dimensional particle--hole symmetric (half-filled)
Hubbard model within dynamical mean field theory. One of the simplest and
extensively used impurity solvers, namely the iterated perturbation theory
approach is reformulated to avoid problems such as analytic continuation of
Matsubara frequency quantities or calculating multi-dimensional integrals,
while taking full account of the very sharp structures in the Green's functions
that arise close to the Mott transitions and in the Mott insulator regime. We
demonstrate its viability for the half-filled Hubbard model. Previous known
results are reproduced within the present approach. The universal behavior of
the spectral functions in the Fermi liquid regime is emphasized, and adiabatic
continuity to the non-interacting limit is demonstrated. The dc resistivity in
the metallic regime is known to be a non-monotonic function of temperature with
a `coherence peak'. This feature is shown to be a universal feature occurring
at a temperature roughly equal to the low energy scale of the system. A
comparison to pressure dependent dc resistivity experiments on Selenium doped
NiS yields qualitatively good agreement. Resistivity hysteresis across the
Mott transition is shown to be described qualitatively within the present
framework. A direct comparison of the thermal hysteresis observed in VO
with our theoretical results yields a value of the hopping integral, which we
find to be in the range estimated through first-principle methods. Finally, a
systematic study of optical conductivity is carried out and the changes in
absorption as a result of varying interaction strength and temperature are
identified.Comment: 19 pages, 12 figure
Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay
The ensemble averaged power scattered in and out of lossless chaotic cavities
decays as a power law in time for large times. In the case of a pulse with a
finite duration, the power scattered from a single realization of a cavity
closely tracks the power law ensemble decay initially, but eventually
transitions to an exponential decay. In this paper, we explore the nature of
this transition in the case of coupling to a single port. We find that for a
given pulse shape, the properties of the transition are universal if time is
properly normalized. We define the crossover time to be the time at which the
deviations from the mean of the reflected power in individual realizations
become comparable to the mean reflected power. We demonstrate numerically that,
for randomly chosen cavity realizations and given pulse shapes, the probability
distribution function of reflected power depends only on time, normalized to
this crossover time.Comment: 23 pages, 5 figure
- …