Brownian Motion Model of Quantization Ambiguity and Universality in Chaotic Systems

We examine spectral equilibration of quantum chaotic spectra to universal statistics, in the context of the Brownian motion model. Two competing time scales, proportional and inversely proportional to the classical relaxation time, jointly govern the equilibration process. Multiplicity of quantum systems having the same semiclassical limit is not sufficient to obtain equilibration of any spectral modes in two-dimensional systems, while in three-dimensional systems equilibration for some spectral modes is possible if the classical relaxation rate is slow. Connections are made with upper bounds on semiclassical accuracy and with fidelity decay in the presence of a weak perturbation.Comment: 13 pages, 6 figures, submitted to Phys Rev

Spectral correlations : understanding oscillatory contributions

We give a different derivation of a relation obtained using a supersymmetric nonlinear sigma model by Andreev and Altshuler [Phys. Rev. Lett. 72, 902 (1995)], which connects smooth and oscillatory components of spectral correlation functions. We show that their result is not specific to the random matrix theory. Also, we show that despite an apparent contradiction, the results obtained using their formula are consistent with earlier perspectives on random matrix models

The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems

The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is proportional to the rate of dissipation. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall off is inversely proportional to time for the Gaussian orthogonal ensemble. The correlation function is found to be dominated by the nearest neighbor level spacings. It was calculated for a variety of nearest neighbor level spacing distributions, including ones that do not originate from RMT ensembles. The various approximate formulas obtained are tested numerically in RMT. The results shed light on the quantum to classical crossover for chaotic systems. The implications on the possibility to experimentally observe deterministic friction are discussed.Comment: 26 pages, including 6 figure

Oxygen Moment Formation and Canting in Li2CuO2

The possibilities of oxygen moment formation and canting in the quasi-1D cuprate Li2CuO2 are investigated using single crystal neutron diffraction at 2 K. The observed magnetic intensities could not be explained without the inclusion of a large ordered oxygen moment of 0.11(1) Bohr magnetons. Least-squares refinement of the magnetic structure of Li2CuO2 in combination with a spin-density Patterson analysis shows that the magnetization densities of the Cu and O atoms are highly aspherical, forming quasi-1D ribbons of localised Cu and O moments. Magnetic structure refinements and low-field magnetization measurements both suggest that the magnetic structure of Li2CuO2 at 2 K may be canted. A possible model for the canted configuration is proposed.Comment: 10 pages, 8 figures (screen resolution

Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle

Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy-spreading is studied. The associated irreversible growth of the average energy has the meaning of dissipation. It is found that a dimensionless velocity $v_{PR}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence (QCC). A perturbative regime and a non-perturbative semiclassical regime are distinguished.Comment: 4 pages, clear presentation of the main poin

The potential of the ground state of NaRb

The X$^{1}\Sigma ^{+}$ state of NaRb was studied by Fourier transform spectroscopy. An accurate potential energy curve was derived from more than 8800 transitions in isotopomers $^{23}$Na$^{85}$Rb and $^{23}$Na$^{87}$Rb. This potential reproduces the experimental observations within their uncertainties of 0.003 \rcm to 0.007 \rcm. The outer classical turning point of the last observed energy level ($v''=76$, $J''=27$) lies at $\approx 12.4$ \AA, leading to a energy of 4.5 \rcm below the ground state asymptote.Comment: 8 pages, 6 figures and 2 table

Modeling skull-face anatomical/morphological correspondence for craniofacial superimposition-based identification

Craniofacial superimposition (CFS) is a forensic identification technique which studies the anatomical and morphological correspondence between a skull and a face. It involves the process of overlaying a variable number of facial images with the skull. This technique has great potential since nowadays the wide majority of the people have photographs where their faces are clearly visible. In addition, the skull is a bone that hardly degrades under the effect of fire, humidity, temperature changes, etc. Three consecutive stages for the CFS process have been distinguished: the acquisition and processing of the materials; the skull-face overlay; and the decision making. This final stage consists of determining the degree of support for a match based on the previous overlays. The final decision is guided by different criteria depending on the anatomical relations between the skull and the face. In previous approaches, we proposed a framework for automating this stage at different levels taking into consideration all the information and uncertainty sources involved. In this study, we model new anatomical skull-face regions and we tackle the last level of the hierarchical decision support system. For the first time, we present a complete system which provides a final degree of craniofacial correspondence. Furthermore, we validate our system as an automatic identification tool analyzing its capabilities in closed (known information or a potential list of those involved) and open lists (little or no idea at first who may be involved) and comparing its performance with the manual results achieved by experts, obtaining a remarkable performance. The proposed system has been demonstrated to be valid for sortlisting a given data set of initial candidates (in 62,5% of the cases the positive one is ranked in the first position) and to serve as an exclusion method (97,4% and 96% of true negatives in training and test, respectively)

Collective versus single-particle effects in the optical spectra of finite electronic quantum systems

We study optical spectra of finite electronic quantum systems at frequencies smaller than the plasma frequency using a quasi-classical approach. This approach includes collective effects and enables us to analyze how the nature of the (single-particle) electron dynamics influences the optical spectra in finite electronic quantum systems. We derive an analytical expression for the low-frequency absorption coefficient of electro-magnetic radiation in a finite quantum system with ballistic electron dynamics and specular reflection at the boundaries: a two-dimensional electron gas confined to a strip of width a (the approach can be applied to systems of any shape and electron dynamics -- diffusive or ballistic, regular or irregular motion). By comparing with results of numerical computations using the random-phase approximation we show that our analytical approach provides a qualitative and quantitative understanding of the optical spectrum.Comment: 4 pages, 3 figure

Quantal Brownian Motion - Dephasing and Dissipation

We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an equivalent Master equation. Unlike the case of the Zwanzig-Caldeira-Leggett model, genuine quantum mechanical effects manifest themselves due to the disordered nature of the environment. Using Wigner picture of the dynamics we distinguish between two different mechanisms for destruction of coherence. The analysis of dephasing is extended to the low temperature regime by using a semiclassical strategy. Various results are derived for ballistic, chaotic, diffusive, both ergodic and non-ergodic motion. We also analyze loss of coherence at the limit of zero temperature and clarify the limitations of the semiclassical approach. The condition for having coherent effect due to scattering by low-frequency fluctuations is also pointed out. It is interesting that the dephasing rate can be either larger or smaller than the dissipation rate, depending on the physical circumstances.Comment: LaTex, 23 pages, 4 figures, published vesio

Signatures of chaotic tunnelling

Recent experiments with cold atoms provide a significant step toward a better understanding of tunnelling when irregular dynamics is present at the classical level. In this paper, we lay out numerical studies which shed light on the previous experiments, help to clarify the underlying physics and have the ambition to be guidelines for future experiments.Comment: 11 pages, 9 figures, submitted to Phys. Rev. E. Figures of better quality can be found at http://www.phys.univ-tours.fr/~mouchet