20 research outputs found
A quantum evaporation effect
A small momentum transfer to a particle interacting with a steep potential
barrier gives rise to a quantum evaporation effect which increases the
transmission appreciably. This effect results from the unexpectedly large
population of quantum states with energies above the height of the barrier. Its
characteristic properties are studied and an example of physical system in
which it may be observed is given.Comment: 7 pages + 3 figure
Running coupling constants of the Luttinger liquid
Two running coupling constants of the Luttinger liquid are computed in the
fermion-fermion and fermion-antifermion channels. Nontrivial scaling laws are
found together with Landau poles. The apparent contradiction with the expected
vanishing of the beta functions is explained.Comment: Final version, to appear in Phys. Lett.
Statistics of quantum transmission in one dimension with broad disorder
We study the statistics of quantum transmission through a one-dimensional
disordered system modelled by a sequence of independent scattering units. Each
unit is characterized by its length and by its action, which is proportional to
the logarithm of the transmission probability through this unit. Unit actions
and lengths are independent random variables, with a common distribution that
is either narrow or broad. This investigation is motivated by results on
disordered systems with non-stationary random potentials whose fluctuations
grow with distance.
In the statistical ensemble at fixed total sample length four phases can be
distinguished, according to the values of the indices characterizing the
distribution of the unit actions and lengths. The sample action, which is
proportional to the logarithm of the conductance across the sample, is found to
obey a fluctuating scaling law, and therefore to be non-self-averaging, in
three of the four phases. According to the values of the two above mentioned
indices, the sample action may typically grow less rapidly than linearly with
the sample length (underlocalization), more rapidly than linearly
(superlocalization), or linearly but with non-trivial sample-to-sample
fluctuations (fluctuating localization).Comment: 26 pages, 4 figures, 1 tabl
Conductance of 1D quantum wires with anomalous electron-wavefunction localization
We study the statistics of the conductance through one-dimensional
disordered systems where electron wavefunctions decay spatially as for , being a constant. In
contrast to the conventional Anderson localization where and the conductance statistics is determined by a single
parameter: the mean free path, here we show that when the wave function is
anomalously localized () the full statistics of the conductance is
determined by the average and the power . Our theoretical
predictions are verified numerically by using a random hopping tight-binding
model at zero energy, where due to the presence of chiral symmetry in the
lattice there exists anomalous localization; this case corresponds to the
particular value . To test our theory for other values of
, we introduce a statistical model for the random hopping in the tight
binding Hamiltonian.Comment: 6 pages, 8 figures. Few changes in the presentation and references
updated. Published in PRB, Phys. Rev. B 85, 235450 (2012
Quantum Chaotic Scattering in Microwave Resonators
In a frequency range where a microwave resonator simulates a chaotic quantum
billiard, we have measured moduli and phases of reflection and transmission
amplitudes in the regimes of both isolated and of weakly overlapping resonances
and for resonators with and without time-reversal invariance. Statistical
measures for S-matrix fluctuations were determined from the data and compared
with extant and/or newly derived theoretical results obtained from the
random-matrix approach to quantum chaotic scattering. The latter contained a
small number of fit parameters. The large data sets taken made it possible to
test the theoretical expressions with unprecedented accuracy. The theory is
confirmed by both, a goodness-of-fit-test and the agreement of predicted values
for those statistical measures that were not used for the fits, with the data
From one cell to the whole froth: a dynamical map
We investigate two and three-dimensional shell-structured-inflatable froths,
which can be constructed by a recursion procedure adding successive layers of
cells around a germ cell. We prove that any froth can be reduced into a system
of concentric shells. There is only a restricted set of local configurations
for which the recursive inflation transformation is not applicable. These
configurations are inclusions between successive layers and can be treated as
vertices and edges decorations of a shell-structure-inflatable skeleton. The
recursion procedure is described by a logistic map, which provides a natural
classification into Euclidean, hyperbolic and elliptic froths. Froths tiling
manifolds with different curvature can be classified simply by distinguishing
between those with a bounded or unbounded number of elements per shell, without
any a-priori knowledge on their curvature. A new result, associated with
maximal orientational entropy, is obtained on topological properties of natural
cellular systems. The topological characteristics of all experimentally known
tetrahedrally close-packed structures are retrieved.Comment: 20 Pages Tex, 11 Postscript figures, 1 Postscript tabl
Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices
The concept of Lyapunov exponent has long occupied a central place in the
theory of Anderson localisation; its interest in this particular context is
that it provides a reasonable measure of the localisation length. The Lyapunov
exponent also features prominently in the theory of products of random matrices
pioneered by Furstenberg. After a brief historical survey, we describe some
recent work that exploits the close connections between these topics. We review
the known solvable cases of disordered quantum mechanics involving random point
scatterers and discuss a new solvable case. Finally, we point out some
limitations of the Lyapunov exponent as a means of studying localisation
properties.Comment: LaTeX, 23 pages, 3 pdf figures ; review for a special issue on
"Lyapunov analysis" ; v2 : typo corrected in eq.(3) & minor change
Induced optical tunneling
It is shown that the transmission of light through an optical
barrier can be increased by varying momentarily the refractive
index in the front prism with the help of light pulses of short
duration and weak intensity. The observed phenomenon provides the
first experimental evidence of the existence of a tunnel effect
induced by the small motions of a potential barrier