322 research outputs found
Statistical fluctuations of the parametric derivative of the transmission and reflection coefficients in absorbing chaotic cavities
Motivated by recent theoretical and experimental works, we study the
statistical fluctuations of the parametric derivative of the transmission T and
reflection R coefficients in ballistic chaotic cavities in the presence of
absorption. Analytical results for the variance of the parametric derivative of
T and R, with and without time-reversal symmetry, are obtained for both
asymmetric and left-right symmetric cavities. These results are valid for
arbitrary number of channels, in completely agreement with the one channel case
in the absence of absorption studied in the literature.Comment: Modified version as accepted in PR
Composite fermion wave functions as conformal field theory correlators
It is known that a subset of fractional quantum Hall wave functions has been
expressed as conformal field theory (CFT) correlators, notably the Laughlin
wave function at filling factor ( odd) and its quasiholes, and the
Pfaffian wave function at and its quasiholes. We develop a general
scheme for constructing composite-fermion (CF) wave functions from conformal
field theory. Quasiparticles at are created by inserting anyonic
vertex operators, , that replace a subset of the electron
operators in the correlator. The one-quasiparticle wave function is identical
to the corresponding CF wave function, and the two-quasiparticle wave function
has correct fractional charge and statistics and is numerically almost
identical to the corresponding CF wave function. We further show how to exactly
represent the CF wavefunctions in the Jain series as the CFT
correlators of a new type of fermionic vertex operators, ,
constructed from free compactified bosons; these operators provide the CFT
representation of composite fermions carrying flux quanta in the CF Landau level. We also construct the corresponding quasiparticle- and
quasihole operators and argue that they have the expected fractional charge and
statistics. For filling fractions 2/5 and 3/7 we show that the chiral CFTs that
describe the bulk wave functions are identical to those given by Wen's general
classification of quantum Hall states in terms of -matrices and - and
-vectors, and we propose that to be generally true. Our results suggest a
general procedure for constructing quasiparticle wave functions for other
fractional Hall states, as well as for constructing ground states at filling
fractions not contained in the principal Jain series.Comment: 26 pages, 3 figure
Random Matrix Theory Analysis of Cross Correlations in Financial Markets
We confirm universal behaviors such as eigenvalue distribution and spacings
predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the
daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been
reported for New York Stock Exchange in previous studies. It is shown that the
random part of the eigenvalue distribution of the cross correlation matrix is
stable even when deterministic correlations are present. Some deviations in the
small eigenvalue statistics outside the bounds of the universality class of RMT
are not completely explained with the deterministic correlations as proposed in
previous studies. We study the effect of randomness on deterministic
correlations and find that randomness causes a repulsion between deterministic
eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of
``level repulsion'' in RMT and explains some deviations from the previous
studies observed in the market data. We also study correlated groups of issues
in these markets and propose a refined method to identify correlated groups
based on RMT. Some characteristic differences between properties of Tokyo Stock
Exchange and New York Stock Exchange are found.Comment: RevTex, 17 pages, 8 figure
Statistical wave scattering through classically chaotic cavities in the presence of surface absorption
We propose a model to describe the statistical properties of wave scattering
through a classically chaotic cavity in the presence of surface absorption.
Experimentally, surface absorption could be realized by attaching an "absorbing
patch" to the inner wall of the cavity. In our model, the cavity is connected
to the outside by a waveguide with N open modes (or channels), while an
experimental patch is simulated by an "absorbing mirror" attached to the inside
wall of the cavity; the mirror, consisting of a waveguide that supports Na
channels, with absorption inside and a perfectly reflecting wall at its end, is
described by a subunitary scattering matrix Sa. The number of channels Na, as a
measure of the geometric cross section of the mirror, and the lack of unitarity
of Sa as a measure of absorption, are under our control: these parameters have
an important physical significance for real experiments. The absorption
strength in the cavity is quantified by the trace of the lack of unitarity. The
statistical distribution of the resulting S matrix for N=1 open channel and
only one absorbing channel, Na =1, is solved analytically for the orthogonal
and unitary universality classes, and the results are compared with those
arising from numerical simulations. The relation with other models existing in
the literature, in some of which absorption has a volumetric character, is also
studied.Comment: 6 pages, 3 figures, submitted to Phys. Rev.
Marginal States in Mean Field Glasses
We study mean field systems whose free energy landscape is dominated by
marginally stable states. We review and develop various techniques to describe
such states, elucidating their physical meaning and the interrelation between
them. In particular, we give a physical interpretation of the two-group replica
symmetry breaking scheme and confirm it by establishing the relation to the
cavity method and to the counting of solutions of the Thouless-Anderson-Palmer
equations. We show how these methods all incorporate the presence of a soft
mode in the free energy landscape and interpret the occurring order parameter
functions in terms of correlations between the soft mode and the local
magnetizations. The general formalism is applied to the prototypical case of
the Sherrington-Kirkpatrick-model where we re-examine the physical properties
of marginal states under a new perspective.Comment: 27 pages, 8 figure
Solitons and Quasielectrons in the Quantum Hall Matrix Model
We show how to incorporate fractionally charged quasielectrons in the finite
quantum Hall matrix model.The quasielectrons emerge as combinations of BPS
solitons and quasiholes in a finite matrix version of the noncommutative
theory coupled to a noncommutative Chern-Simons gauge field. We also
discuss how to properly define the charge density in the classical matrix
model, and calculate density profiles for droplets, quasiholes and
quasielectrons.Comment: 15 pages, 9 figure
Hidden Breit-Wigner distribution and other properties of random matrices with preferential basis
We study statistical properties of a class of band random matrices which
naturally appears in systems of interacting particles. The local spectral
density is shown to follow the Breit-Wigner distribution in both localized and
delocalized regimes with width independent on the band/system size. We analyse
the implications of this distribution to the inverse participation ratio, level
spacing statistics and the problem of two interacting particles in a random
potential.Comment: 4 pages, 4 postscript figures appended, new version with minor
change
Diagonal-unitary 2-designs and their implementations by quantum circuits
We study efficient generations of random diagonal-unitary matrices, an
ensemble of unitary matrices diagonal in a given basis with randomly
distributed phases for their eigenvalues. Despite the simple algebraic
structure, they cannot be achieved by quantum circuits composed of a few-qubit
diagonal gates. We introduce diagonal-unitary -designs and present two
quantum circuits that implement diagonal-unitary -designs with the
computational basis in -qubit systems. One is composed of single-qubit
diagonal gates and controlled-phase gates with randomized phases, which
achieves an exact diagonal-unitary -design after applying the gates on all
pairs of qubits. The number of required gates is . If the
controlled-Z gates are used instead of the controlled-phase gates, the circuit
cannot achieve an exact -design, but achieves an -approximate
-design by applying gates on randomly selected pairs of qubits. Due to the
random choice of pairs, the circuit obtains extra randomness and the required
number of gates is at most . We also provide an
application of the circuits, a protocol of generating an exact -design of
random states by combining the circuits with a simple classical procedure
requiring random classical bits.Comment: Revised, 22 pages + Appendix, 3 figures; major revision from v2;
presentation is improved in v4; v5 is a published versio
Dynamical TAP approach to mean field glassy systems
The Thouless, Anderson, Palmer (TAP) approach to thermodynamics of mean field
spin-glasses is generalised to dynamics. A method to compute the dynamical TAP
equations is developed and applied to the p-spin spherical model. In this
context we show to what extent the dynamics can be represented as an evolution
in the free energy landscape. In particular the relationship between the
long-time dynamics and the local properties of the free energy landscape shows
up explicitly within this approach. Conversely, by an instantaneous normal
modes analysis we show that the local properties of the energy landscape seen
by the system during its dynamical evolution do not change qualitatively at the
dynamical transition.Comment: final version, 21 pages, 1 eps figur
Vibrational spectrum of topologically disordered systems
The topological nature of the disorder of glasses and supercooled liquids
strongly affects their high-frequency dynamics. In order to understand its main
features, we analytically studied a simple topologically disordered model,
where the particles oscillate around randomly distributed centers, interacting
through a generic pair potential. We present results of a resummation of the
perturbative expansion in the inverse particle density for the dynamic
structure factor and density of states. This gives accurate results for the
range of densities found in real systems.Comment: Completely rewritten version, accepted in Physical Review Letter
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