Parametric invariant Random Matrix Model and the emergence of multifractality

We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the non-perturbative crossover that has been discussed by Wigner 50 years ago. Of particular interest is the emergence of an additional crossover to multifractality.Comment: 7 pages, 6 figures, expanded versio

Scaling properties of delay times in one-dimensional random media

The scaling properties of the inverse moments of Wigner delay times are investigated in finite one-dimensional (1D) random media with one channel attached to the boundary of the sample. We find that they follow a simple scaling law which is independent of the microscopic details of the random potential. Our theoretical considerations are confirmed numerically for systems as diverse as 1D disordered wires and optical lattices to microwave waveguides with correlated scatterers.Comment: 5 pages, 4 figures Submitted to Physical Review B Revision 2: 1) Theoretical curve fits added to Figures 1-4. 2) Scaling parameter added to inset of Figure 2. 3) Minor text changes to reflect referee comments. 4) Some extra refereces were adde

Transport in a gravity dual with a varying gravitational coupling constant

We study asymptotically AdS Brans-Dicke (BD) backgrounds, where the Ricci tensor R is coupled to a scalar in the radial dimension, as effective models of metals with a varying coupling constant. We show that, for translationally invariant backgrounds, the regular part of the dc conductivity σ$_{Q}$ deviates from the universal result of Einstein-Maxwell-dilaton (EMD) models. However, the shear viscosity to entropy ratio saturates the Kovtun-Son-Starinets (KSS) bound. Similar results apply to more general f(R) gravity models. In four bulk dimensions we study momentum relaxation induced by gravitational and electromagnetic axion-dependent couplings. For sufficiently strong momentum dissipation induced by the former, a recently proposed bound on the dc conductivity σ is violated for any finite electromagnetic axion coupling. Interestingly, in more than four bulk dimensions, the dc conductivity for strong momentum relaxation decreases with temperature in the low temperature limit. In line with other gravity backgrounds with momentum relaxation, the shear viscosity to entropy ratio is always lower than the KSS bound. The numerical computation of the optical conductivity reveals a linear growth with the frequency in the limit of low temperature, low frequency and large momentum relaxation. We have also shown that the module and argument of the optical conductivity for intermediate frequencies are not consistent with cuprates' experimental results, even assuming several channel of momentum relaxation.A.M.G. acknowledges support from EPSRC, Grant No. EP/I004637/1. B.L. is supported by CAPES/COT Grant No. 11469/13-17. A.R.B. acknowledges support from the Department of Physics and the Theory of Condensed Matter group of the University of Cambridge as well as the Cambridge Philosophical Society

Scattering at the Anderson transition: Power--law banded random matrix model

We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal insulator transition. We focus on the scaling of Wigner delay times $\tau$ and resonance widths $\Gamma$. We found that the typical values of $\tau$ and $\Gamma$ (calculated as the geometric mean) scale with the system size $L$ as $\tau^{\tiny typ}\propto L^{D_1}$ and $\Gamma^{\tiny typ} \propto L^{-(2-D_2)}$, where $D_1$ is the information dimension and $D_2$ is the correlation dimension of eigenfunctions of the corresponding closed system.Comment: 6 pages, 8 figure

Mesoscopic mean-field theory for spin-boson chains in quantum optical systems

We present a theoretical description of a system of many spins strongly coupled to a bosonic chain. We rely on the use of a spin-wave theory describing the Gaussian fluctuations around the mean-field solution, and focus on spin-boson chains arising as a generalization of the Dicke Hamiltonian. Our model is motivated by experimental setups such as trapped ions, or atoms/qubits coupled to cavity arrays. This situation corresponds to the cooperative (E⊗β) Jahn-Teller distortion studied in solid-state physics. However, the ability to tune the parameters of the model in quantum optical setups opens up a variety of novel intriguing situations. The main focus of this paper is to review the spin-wave theoretical description of this problem as well as to test the validity of mean-field theory. Our main result is that deviations from mean-field effects are determined by the interplay between magnetic order and mesoscopic cooperativity effects, being the latter strongly size-dependent

A large sample analysis of European rivers on seasonal river flow correlation and its physical drivers

The geophysical and hydrological processes governing river flow formation exhibit persistence at several timescales, which may manifest itself with the presence of positive seasonal correlation of streamflow at several different time lags. We investigate here how persistence propagates along subsequent seasons and affects low and high flows. We define the high-flow season (HFS) and the low-flow season (LFS) as the 3-month and the 1-month periods which usually exhibit the higher and lower river flows, respectively. A dataset of 224 rivers from six European countries spanning more than 50 years of daily flow data is exploited. We compute the lagged seasonal correlation between selected river flow signatures, in HFS and LFS, and the average river flow in the antecedent months. Signatures are peak and average river flow for HFS and LFS, respectively. We investigate the links between seasonal streamflow correlation and various physiographic catchment characteristics and hydro-climatic properties. We find persistence to be more intense for LFS signatures than HFS. To exploit the seasonal correlation in the frequency estimation of high and low flows, we fit a bi-variate meta-Gaussian probability distribution to the selected flow signatures and average flow in the antecedent months in order to condition the distribution of high and low flows in the HFS and LFS, respectively, upon river flow observations in the previous months. The benefit of the suggested methodology is demonstrated by updating the frequency distribution of high and low flows one season in advance in a real-world case. Our findings suggest that there is a traceable physical basis for river memory which, in turn, can be statistically assimilated into high- and low-flow frequency estimation to reduce uncertainty and improve predictions for technical purposes

Chaotic Waveguide-Based Resonators for Microlasers

We propose the construction of highly directional emission microlasers using two-dimensional high-index semiconductor waveguides as {\it open} resonators. The prototype waveguide is formed by two collinear leads connected to a cavity of certain shape. The proposed lasing mechanism requires that the shape of the cavity yield mixed chaotic ray dynamics so as to have the appropiate (phase space) resonance islands. These islands allow, via Heisenberg's uncertainty principle, the appearance of quasi bound states (QBS) which, in turn, propitiate the lasing mechanism. The energy values of the QBS are found through the solution of the Helmholtz equation. We use classical ray dynamics to predict the direction and intensity of the lasing produced by such open resonators for typical values of the index of refraction.Comment: 5 pages, 5 figure

Numerical stability of a fixed point iterative method to determine patterns of turbulent flow in a rectangular cavity with different aspect ratios

2D isothermal viscous incompressible flows are presented from the Navier- Stokes equations in the Stream function-vorticity formulation and in the velocity-vorticity formulation. The simulation is made using a numerical method based on a fixed point it- erative process to solve the nonlinear elliptic system that results after time discretization. The iterative process leads us to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems from which efficient solvers exist regardless of the space discretiza- tion. The experiments take place on the lid driven cavity problem for Reynolds numbers up to Re = 10000 and different aspect ratios A (A=ratio of the height to the width) A = 1 and A /= 1 such aAs = 1/2, till A = 3. It appears that with velocity and vorticity variables is more difficult to solve this kind of flows, at least with a numerical procedure similar to the one applied in stream function and vorticity variables to solve an analogous nonlinear elliptic system. To obtain such flows is not an easy task, especially with the velocity-vorticity formulation. We report here results for moderate Reynolds numbers (Re 10000), although with them enough effectiveness is achieved to be able to vary the aspect ratio of the cavity A, which causes the flow to be more unstable. Con- tribution in this work is to consider rectangular cavities of drag, which can impact on isothermal turbulent flow patterns. Another contribution is to include a wide region of the Reynolds number as well as different aspect ratios where we tested stability of the numerical scheme

Laboratory Characterization and Astrophysical Detection of Vibrationally Excited States of Vinyl Cyanide in Orion-KL

New laboratory data of CH$_2$CHCN (vinyl cyanide) in its ground and vibrationally excited states at the microwave to THz domain allow searching for these excited state transitions in the Orion-KL line survey. Frequency-modulated spectrometers combined into a single broadband 50-1900 GHz spectrum provided measurements of CH$_2$CHCN covering a spectral range of 18-1893 GHz, whose assignments was confirmed by Stark modulation spectra in the 18-40 GHz region and by ab-initio anharmonic force field calculations. For analyzing the emission lines of CH$_2$CHCN species detected in Orion-KL we used the excitation and radiative transfer code (MADEX) at LTE conditions. The rotational transitions of the ground state of this molecule emerge from four cloud components of hot core nature which trace the physical and chemical conditions of high mass star forming regions in the Orion-KL Nebula. The total column density of CH$_2$CHCN in the ground state is (3.0$\pm$0.9)x10$^{15}$ cm$^{-2}$. We report on the first interstellar detection of transitions in the v10=1/(v11=1,v15=1) dyad in space, and in the v11=2 and v11=3 states in Orion-KL. The lowest energy vibrationally excited states of vinyl cyanide such as v11=1 (at 328.5 K), v15=1 (at 478.6 K), v11=2 (at 657.8 K), the v10=1/(v11=1,v15=1) dyad (at 806.4/809.9 K), and v11=3 (at 987.9 K) are populated under warm and dense conditions, so they probe the hottest parts of the Orion-KL source. Column density and rotational and vibrational temperatures for CH$_2$CHCN in their ground and excited states, as well as for the isotopologues, have been constrained by means of a sample of more than 1000 lines in this survey. Moreover, we present the detection of methyl isocyanide (CH$_3$NC) for the first time in Orion-KL and a tentative detection of vinyl isocyanide (CH$_2$CHNC) and give column density ratios between the cyanide and isocyanide isomers.Comment: 46 pages, 22 figures, 14 tables, 9 online table

Universal insulating-to-metallic crossover in tight-binding random geometric graphs

Within the scattering matrix approach to electronic transport, the scattering and transport properties of tight-binding random graphs are analyzed. In particular, we compute the scattering matrix elements, the transmission, the channel-to-channel transmission distributions (including the total transmission distribution), the shot noise power, and the elastic enhancement factor. Two graph models are considered: random geometric graphs and bipartite random geometric graphs. The results show an insulating to a metallic crossover in the scattering and transport properties by increasing the average degree of the graphs from small to large values. Also, the scattering and transport properties are shown to be invariant under a scaling parameter depending on the average degree and the graph size. Furthermore, for large connectivity and in the perfect coupling regime, the scattering and transport properties of both graph models are well described by the random matrix theory predictions of electronic transport, except for bipartite graphs in particular scattering setups.Comment: 13 pages, 16 figure