Entanglement dynamics of electron-electron scattering in low-dimensional semiconductor systems

We perform the quantitative evaluation of the entanglement dynamics in scattering events between two insistinguishable electrons interacting via Coulomb potential in 1D and 2D semiconductor nanostructures. We apply a criterion based on the von Neumann entropy and the Schmidt decomposition of the global state vector suitable for systems of identical particles. From the timedependent numerical solution of the two-particle wavefunction of the scattering carriers we compute their entanglement evolution for different spin configurations: two electrons with the same spin, with different spin, singlet, and triplet spin state. The procedure allows to evaluate the mechanisms that govern entanglement creation and their connection with the characteristic physical parameters and initial conditions of the system. The cases in which the evolution of entanglement is similar to the one obtained for distinguishable particles are discussed.Comment: 22 pages, 7 figures, submitted to Physical Review

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

Dynamical fluctuations in an exactly solvable model of spin glasses

In this work we calculate the dynamical fluctuations at O(1/N) in the low temperature phase of the $p=2$ spherical spin glass model. We study the large-times asymptotic regimes and we find, in a short time-differences regime, a fluctuation dissipation relation for the four-point correlation functions. This relation can be extended to the out of equilibrium regimes introducing a function $X_{t}$ which, for large time $t$, we find scales as $t^{-1/2}$ as in the case of the two-point functions.Comment: Latex, 8 page

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 $\nu=1/m$ ($m$ odd) and its quasiholes, and the Pfaffian wave function at $\nu=1/2$ and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at $\nu=1/m$ are created by inserting anyonic vertex operators, $P_{\frac{1}{m}}(z)$, 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 $\nu = s/(2sp+1)$ as the CFT correlators of a new type of fermionic vertex operators, $V_{p,n}(z)$, constructed from $n$ free compactified bosons; these operators provide the CFT representation of composite fermions carrying $2p$ flux quanta in the $n^{\rm th}$ 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 $K$-matrices and $l$- and $t$-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

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.

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

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

Magneto-polarisability of mesoscopic rings

We calculate the average polarisability of two dimensional mesoscopic rings in the presence of an Aharonov-Bohm flux. The screening is taken into account self-consistently within a mean-field approximation. We investigate the effects of statistical ensemble, finite frequency and disorder. We emphasize geometrical effects which make the observation of field dependent polarisability much more favourable on rings than on disks or spheres of comparable radius. The ratio of the flux dependent to the flux independent part is estimated for typical GaAs rings.Comment: pages, Revtex, 1 eps figur

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

An improved synthesis of (2E,4Z)-6-(benzyloxy)-4-bromohexa-2,4-dien-1-ol

An improved synthesis of (2E,4Z)-6-(benzyloxy)-4-bromohexa-2,4-dien-1-ol has been devised. This new route increases the throughput and yield of the diene product by circumventing a low yielding preparation of boronic acid intermediate as well as removing the need to use multi-gram quantities of highly toxic thallium salts. In the process of developing this new route, a higher yielding preparation of ( E)-3-hydroxyprop-1-enylboronic acid was also achieved. (c) 2007 Elsevier Ltd. All rights reserved