Role of electron-electron and electron-phonon interaction effect in the optical conductivity of VO2

We have investigated the charge dynamics of VO2 by optical reflectivity measurements. Optical conductivity clearly shows a metal-insulator transition. In the metallic phase, a broad Drude-like structure is observed. On the other hand, in the insulating phase, a broad peak structure around 1.3 eV is observed. It is found that this broad structure observed in the insulating phase shows a temperature dependence. We attribute this to the electron-phonon interaction as in the photoemission spectra.Comment: 6 pages, 8 figures, accepted for publication in Phys. Rev.

Dynamical transition for a particle in a squared Gaussian potential

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $\psi= \phi^2/2$ where $\phi$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.Comment: 18 pages, 4 figures .eps, JPA styl

Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices

We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the SOP and for their Cauchy transforms, given as expectation values of traces and determinants or their inverses, respectively. Our proof uses the fact that the joint probability distribution function for all combinations of real eigenvalues and complex conjugate eigenvalue pairs can be written as a product. Examples for the SOP are given in terms of Laguerre polynomials for the chiral ensemble (also called the non-Hermitian real Wishart-Laguerre ensemble), both without and with the insertion of characteristic polynomials. Such characteristic polynomials play the role of mass terms in applications to complex Dirac spectra in field theory. In addition, for the elliptic real Ginibre ensemble we recover the SOP of Forrester and Nagao in terms of Hermite polynomials

Statistical properties of random density matrices

Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analyzed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter--circle distribution characteristic of the Hilbert--Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.Comment: 8 revtex pages with one eps file included, ver. 2 - minor misprints correcte

The 3-SAT problem with large number of clauses in ∞\infty-replica symmetry breaking scheme

In this paper we analyze the structure of the UNSAT-phase of the overconstrained 3-SAT model by studying the low temperature phase of the associated disordered spin model. We derive the $\infty$ Replica Symmetry Broken equations for a general class of disordered spin models which includes the Sherrington - Kirkpatrick model, the Ising $p$-spin model as well as the overconstrained 3-SAT model as particular cases. We have numerically solved the $\infty$ Replica Symmetry Broken equations using a pseudo-spectral code down to and including zero temperature. We find that the UNSAT-phase of the overconstrained 3-SAT model is of the $\infty$-RSB kind: in order to get a stable solution the replica symmetry has to be broken in a continuous way, similarly to the SK model in external magnetic field.Comment: 19 pages, 7 figures; some section improved; iopart styl

Trace distance from the viewpoint of quantum operation techniques

In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states, there are an uncountably infinite number of maximizing quantum operations. Conversely, for any operation of the described type, there are an uncountably infinite number of those pairs of states that the maximum is reached by the operation. A behavior of the trace distance under considered operations is studied. Relations and distinctions between the trace distance and the sine distance are discussed.Comment: 26 pages, no figures. The bibliography is extended, explanatory improvement

Thermodynamic Properties and Phase Transitions in a Mean-Field Ising Spin Glass on Lattice Gas: the Random Blume-Emery-Griffiths-Capel Model

The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable Replica Symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and accompanied by a latent heat. In this last case coexistence of phases takes place. The thermodynamics is worked out in the Full Replica Symmetry Breaking scheme, and the relative Parisi equations are solved using a pseudo-spectral method down to zero temperature.Comment: 24 pages, 12 figure

Integrable theory of quantum transport in chaotic cavities

The problem of quantum transport in chaotic cavities with broken time-reversal symmetry is shown to be completely integrable in the universal limit. This observation is utilised to determine the cumulants and the distribution function of conductance for a cavity with ideal leads supporting an arbitrary number $n$ of propagating modes. Expressed in terms of solutions to the fifth Painlev\'e transcendent and/or the Toda lattice equation, the conductance distribution is further analysed in the large-$n$ limit that reveals long exponential tails in the otherwise Gaussian curve.Comment: 4 pages; final version to appear in Physical Review Letter

Hilbert--Schmidt volume of the set of mixed quantum states

We compute the volume of the convex N^2-1 dimensional set M_N of density matrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area of the boundary of this set is also found and its ratio to the volume provides an information about the complex structure of M_N. Similar investigations are also performed for the smaller set of all real density matrices. As an intermediate step we analyze volumes of the unitary and orthogonal groups and of the flag manifolds.Comment: 13 revtex pages, ver 3: minor improvement