1,805 research outputs found
Disorder and interference: localization phenomena
The specific problem we address in these lectures is the problem of transport
and localization in disordered systems, when interference is present, as
characteristic for waves, with a focus on realizations with ultracold atoms.Comment: Notes of a lecture delivered at the Les Houches School of Physics on
"Ultracold gases and quantum information" 2009 in Singapore. v3: corrected
mistakes, improved script for numerics, Chapter 9 in "Les Houches 2009 -
Session XCI: Ultracold Gases and Quantum Information" edited by C. Miniatura
et al. (Oxford University Press, 2011
Multiple scattering of light by atoms with internal degeneracy
An analytical microscopic theory for the resonant multiple scattering of
light by cold atoms with arbitrary internal degeneracy is presented. It permits
to calculate the average amplitude and the average intensity for one-photon
states of the full transverse electromagnetic field in a dilute medium of
unpolarized atoms. Special emphasis is laid upon an analysis in terms of
irreducible representations of the rotation group. It allows to sum explicitly
the ladder and maximally crossed diagrams, giving the average intensity in the
Boltzmann approximation and the interference corrections responsible for weak
localization and coherent backscattering. The exact decomposition into field
modes shows that the atomic internal degeneracy contributes to the
depolarization of the average intensity and suppresses the interference
corrections. Static as well as dynamic quantities like the transport velocity,
diffusion constants and relaxation times for all field modes and all atomic
transitions are derived.Comment: Corrected minor errors. Slightly extended version of the article
appeared in prin
Keldysh action for disordered superconductors
Keldysh representation of the functional integral for the interacting
electron system with disorder is used to derive microscopically an effective
action for dirty superconductors. In the most general case this action is a
functional of the 8 x 8 matrix Q(t,t') which depends on two time variables, and
on the fluctuating order parameter field and electric potential. We show that
this approach reproduces, without the use of the replica trick, the well-known
result for the Coulomb-induced renormalization of the electron-electron
coupling constant in the Cooper channel. Turning to the new results, we
calculate the effects of the Coulomb interaction upon: i) the subgap Andreev
conductance between superconductor and 2D dirty normal metal, and ii) the
Josephson proximity coupling between superconductive islands via such a metal.
These quantities are shown to be strongly suppressed by the Coulomb interaction
at sufficiently low temperatures due to both zero-bias anomaly in the density
of states and disorder-enhanced repulsion in the Cooper channel.Comment: RevTeX; 39 pages + 10 EPS figure
Diffusion of Monochromatic Classical Waves
We study the diffusion of monochromatic classical waves in a disordered
acoustic medium by scattering theory. In order to avoid artifacts associated
with mathematical point scatterers, we model the randomness by small but finite
insertions. We derive expressions for the configuration-averaged energy flux,
energy density, and intensity for one, two and three dimensional (1D, 2D and
3D) systems with an embedded monochromatic source using the ladder
approximation to the Bethe-Salpeter equation. We study the transition from
ballistic to diffusive wave propagation and obtain results for the
frequency-dependence of the medium properties such as mean free path and
diffusion coefficient as a function of the scattering parameters. We discover
characteristic differences of the diffusion in 2D as compared to the
conventional 3D case, such as an explicit dependence of the energy flux on the
mean free path and quite different expressions for the effective transport
velocity.Comment: 11 pages, 2 figure
Fading Gravity and Self-Inflation
We study the cosmology of a toy modified theory of gravity in which gravity
shuts off at short distances, as in the fat graviton scenario of Sundrum. In
the weak-field limit, the theory is perturbatively local, ghost-free and
unitary, although likely suffers from non-perturbative instabilities. We derive
novel self-inflationary solutions from the vacuum equations of the theory,
without invoking scalar fields or other forms of stress energy. The modified
perturbation equation expressed in terms of the Newtonian potential closely
resembles its counterpart for inflaton fluctuations. The resulting scalar
spectrum is therefore slightly red, akin to the simplest scalar-driven
inflationary models. A key difference, however, is that the gravitational wave
spectrum is generically not scale invariant. In particular the tensor spectrum
can have a blue tilt, a distinguishing feature from standard inflation.Comment: 35 pages, 4 figures. v3: version to appear in Phys. Rev.
Many-body quantum chaos: Analytic connection to random matrix theory
A key goal of quantum chaos is to establish a relationship between widely
observed universal spectral fluctuations of clean quantum systems and random
matrix theory (RMT). For single particle systems with fully chaotic classical
counterparts, the problem has been partly solved by Berry (1985) within the
so-called diagonal approximation of semiclassical periodic-orbit sums.
Derivation of the full RMT spectral form factor from semiclassics has
been completed only much later in a tour de force by Mueller et al (2004). In
recent years, the questions of long-time dynamics at high energies, for which
the full many-body energy spectrum becomes relevant, are coming at the
forefront even for simple many-body quantum systems, such as locally
interacting spin chains. Such systems display two universal types of behaviour
which are termed as `many-body localized phase' and `ergodic phase'. In the
ergodic phase, the spectral fluctuations are excellently described by RMT, even
for very simple interactions and in the absence of any external source of
disorder. Here we provide the first theoretical explanation for these
observations. We compute explicitly in the leading two orders in and
show its agreement with RMT for non-integrable, time-reversal invariant
many-body systems without classical counterparts, a generic example of which
are Ising spin 1/2 models in a periodically kicking transverse field.Comment: 10 pages in RevTex with 4 figures and a few diagrams; v3: version
accepted by PR
Semiclassical two-step model for strong-field ionization
We present a semiclassical two-step model for strong-field ionization that
accounts for path interferences of tunnel-ionized electrons in the ionic
potential beyond perturbation theory. Within the framework of a classical
trajectory Monte-Carlo representation of the phase-space dynamics, the model
employs the semiclassical approximation to the phase of the full quantum
propagator in the exit channel. By comparison with the exact numerical solution
of the time-dependent Schr\"odinger equation for strong-field ionization of
hydrogen, we show that for suitable choices of the momentum distribution after
the first tunneling step, the model yields good quantitative agreement with the
full quantum simulation. The two-dimensional photoelectron momentum
distributions, the energy spectra, and the angular distributions are found to
be in good agreement with the corresponding quantum results. Specifically, the
model quantitatively reproduces the fan-like interference patterns in the
low-energy part of the two-dimensional momentum distributions as well as the
modulations in the photoelectron angular distributions.Comment: 31 pages, 7 figure
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