Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators

O'Connor's approach to spatial exponential decay of eigenfunctions for multiparticle Schrödinger Hamiltonians is developed from the point of view of analytic perturbations with respect to transformation groups.This framework allows an improvement of his results in some directions; in particular if interactions are dilation analytic, exponential fall-off is shown to hold for any bound-state wave-function corresponding to an eigenvalue distinct from thresholds; it is shown that the exponential decay rate depends on the distance from the bound-state energy to the nearest threshold. Applications include non existence of positive energy bound-states.     

Decay of high-frequency acoustic excitations in chain-type lattices and weak localization

The attenuation of high-frequency sound in disordered quasi-one-dimensional semiconducting and dielectric crystals, which is associated with three-phonon decay and elastic scattering by structure defects is considered theoretically. It is shown that specific interference processes occurring in the regime of weak localization of acoustic vibrational excitations considerably affect the propagation of sound. This mechanism of sound attenuation can be observed experimentally from the anomalies in the frequency dependence of the reciprocal attenuation length of sound.     

Gamma-ray multipolarity studies by the nuclear orientation of 206Bi in nickel: Perturbation in the 120 μs 2.2 MeV state of 206Pb

Measurements of the anisotropic γ-ray distribution from the decay of ²⁰⁶Bi nuclei oriented in the hyperfine field of a nickel host have been used to determine the E2 admixture into six predominantly M1 transitions in ²⁰⁶Pb. The γ-ray distribution shown by the 516 keV transition is shown to differ from that expected for the E3 transition. This is analysed in terms of a perturbation of the intermediate state eigenfunctions by an off-axis electric quadrupole interaction.     

Perturbation theory for the decay rate of eigenfunctions in the generalizedN-body problem

Simple examples are known where eigenfunctions decay faster than the usual upper bounds would lead one to believe. We develop aspects of the perturbation theory of the decay rate of eigenfunctions as measured by radial exponential weights. We show that generically (in a Baire category sense) eigenfunction decay rates are governed by the lowest threshold.Supported in part by NSF grant DMS-8807816     

Experiments on quantum chaos using microwave cavities: Results for the pseudo-integrable L-billiard

We describe microwave experiments used to study billiard geometries as model problems of non-integrability in quantum or wave mechanics. The experiments can study arbitrary 2-D geometries, including chaotic and even disordered billiards. Detailed results on an L-shaped pseudo-integrable billiard are discussed as an example. The eigenvalue statistics are well-described by empirical formulae incorporating the fraction of phase space that is non-integrable. The eigenfunctions are directly measured, and their statistical properties are shown to be influenced by non-isolated periodic orbits, similar to that for the chaotic Sinai billiard. These periodic orbits are directly observed in the Fourier transform of the eigenvalue spectrum.     

Spectral Properties of a Piecewise Linear Intermittent Map

For a piecewise linear intermittent map, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions of the Frobenius–Perron operator ^P are explicitly derived. The evolution of the averages are shown to be a superposition of the contributions from two simple eigenvalues 1 and _d (–1, 0), and a continuous spectrum on the unit interval [0,1] of ^P. Power-law decay of correlations are controlled by the continuous spectrum. Also the non-normalizable invariant measure in the non-stationary regime is shown to determine the strength of the power-law decay.     

Localization estimates for a random discrete wave equation at high frequency

It is shown that at high frequencies matrix elements of the Green's function of a random discrete wave equation decay exponentially at long distances. This is the input to the proof of dense point spectrum with localized eigenfunctions in this frequency range. The proof uses techniques of Fröhlich and Spencer. A sequence of renormalization transformations shows that large regions where wave propagation is easily maintained become increasingly sparse as resonance is approached.     

Dynamics of 2D electron wave packets with different initial spin polarization in 2D structures with spin-orbit coupling

The effect of splitting and zitterbewegung of 2D-electrons wave packets in the presence of Rashba spin-orbit coupling has been investigated. It is shown that nonstandard dynamics of wave packets occurs in the systems where the complete system of eigenfunctions is formed by states with different chirality. The time evolution of wave packets depends on the initial electron spin orientation. It is established that the oscillations of packet centers decay with time. Similar effects were studied by us previously for packets with initial spin orientation perpendicular to the 2D electron gas plane.     

Two-dimensional graphene with structural defects: elastic mean free path, minimum conductivity, and Anderson transition

Quantum transport properties of disordered graphene with structural defects (Stone-Wales and divacancies) are investigated using a realistic π-π* tight-binding model elaborated from ab initio calculations. Mean free paths and semiclassical conductivities are then computed as a function of the nature and density of defects (using an order-N real-space Kubo-Greenwood method). By increasing the defect density, the decay of the semiclassical conductivities is predicted to saturate to a minimum value of 4e2/πh over a large range (plateau) of carrier density (>0.5×10(14) cm(-20). Additionally, strong contributions of quantum interferences suggest that the Anderson localization regime could be experimentally measurable for a defect density as low as 1%.     

GD a-Si:H主光致发光带的时间分辨研究

本文研究了低温淀积(例如T:<150℃)的GD a-Si:H在77K的时间分辨光致发光谱和荧光衰退。光致发光谱显示非对称形,荧光衰退显示出最初的快衰退,较长时间后为慢衰退。在快衰退范围内可用两个时间常数逐点分析时间分辨光谱,把主发光带分解为两个近似高斯形的发光带,对于Ts=127℃的薄膜,两发光带峰值位置在t=0时分别为1.73和1.58eV。快衰退两带的时间常数分别为10和23ns。文中还初步讨论了这两个发光带的起因。     

On line shape of electromagnetically induced transparency in a multilevel system

We present a detail analysis of the line shape of electromagnetically induced transparency (EIT) in a Doppler broadened five level atomic system based on density matrix formalism. It has been shown that the velocity averaged EIT line shape in a multilevel system is very sharp. The effect of the ground state decay rates on the EIT peak has also been investigated. The linear and non-linear variations of the EIT line width (FWHM) for different pump and probe power ratios are shown. Considering the D₂ transition of ⁸⁵Rb atom the dependence of EIT width and height on pump power has been experimentally measured. Simulated spectra are compared with the experimentally obtained one. The effect of buffer gas on the EIT peak has also been observed experimentally as well as theoretically.     

Hyperfine decoupling in electron paramagnetic resonance as a powerful tool for unraveling complicated ESEEM spectra of S=1/2, I> or =1/2 systems

Hyperfine decoupling in electron paramagnetic resonance after strong microwave radiation is studied for S=1/2, I=1/2 and S=1/2, I=1 spin systems. A new 2D pulse sequence based on the hyperfine-decoupled DEFENCE (deadtime-free ESEEM by nuclear coherence-transfer echoes) experiment is introduced, which is distinguished by a remarkable reduction of the residual hyperfine coupling. The efficiency of this new decoupling experiment in comparison to the old pulse sequence is studied by means of numerical simulations. The advantages of the new decoupling experiment and its ability to simplify ESEEM spectra are experimentally demonstrated on two disordered systems.     

用Schaefer和Harris方法计算LS耦合原子态及其简洁本征函数

应用推广Schaefer和Harris的方法(即对于给定的电子组态,在Slater行列式基上构造算符L2+λS2的矩阵,通过对角化此矩阵求得LS耦合原子态的本征函数)开发一套Fortran程序,不仅可以求得某一对称下最简洁的的LS本征函数,而且能够求得任一电子组态(同科电子组态和非同科电子组态)的所有LS耦合原子态.作为例子,具体计算Np(Z=93)电子组态5f46d的LS耦合原子态和对应于6I光谱项的最简洁的LS本征函数.     

How to measure the polarization of top quarks

The production of polarized top quarks will be reflected in the polarization of T¹ mesons and can be observed experimentally through their dominant weak decays. It is shown that energy and transverse momentum distributions of top-meson decay products are effected and eventually enhanced or depleted by a factor between 0.5 and 1.5. Parity-violating effects in the lepton distribution from top decay could be observed.     

Survival Probability of the Néel State in Clean and Disordered Systems: An Overview

In this work we provide an overview of our recent results about the quench dynamics of one-dimensional many-body quantum systems described by spin-1/2 models. To illustrate those general results, here we employ a particular and experimentally accessible initial state, namely the Néel state. Both cases are considered: clean chains without any disorder and disordered systems with static random on-site magnetic fields. The quantity used for the analysis is the probability for finding the initial state later in time, the so-called survival probability. At short times, the survival probability may decay faster than exponentially, Gaussian behaviors and even the limit established by the energy-time uncertainty relation are displayed. The dynamics at long times slows down significantly and shows a powerlaw behavior. For both scenarios, we provide analytical expressions that agree very well with our numerical results.     

Measurement of wave chaotic eigenfunctions in the time-reversal symmetry-breaking crossover regime

We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a two-dimensional microwave resonator are analyzed as a function of an experimentally determined time-reversal symmetry-breaking parameter. We test four theories of one-point eigenfunction statistics and introduce a new theory relating the one-point and two-point statistical properties in the crossover regime. We also find a universal correlation between the one-point and two-point statistical parameters for the crossover eigenfunctions.     

From chaos to disorder: Statistics of the eigenfunctions of microwave cavities

We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the inverse participation ratio (IPR) and density-density auto-correlation. A path from chaos to disorder is described in terms of increasing IPR. In the chaotic, ballistic limit, the data correspond well with universal results from random matrix theory. Deviations from universal distributions are observed due to disorder induced localization, and for the weakly disordered case the data are well-described by including finite conductance and mean free path contributions in the framework of nonlinear sigma models of supersymmetry.     

Anderson Localization in Dissipative Lattices

Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for dynamical localization. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal disorder, there is a one-to-one correspondence between dynamical localization and spectral localization, that is, the exponential localization of all the Hamiltonian eigenfunctions. This correspondence can be broken when dealing with disordered dissipative lattices. When the system exchanges particles with the surrounding environment and random fluctuations of the dissipation are introduced, spectral localization is observed but without dynamical localization. Previous studies consider lattices with mixed conservative (Hamiltonian) and dissipative dynamics and are restricted to a semiclassical analysis. However, Anderson localization in purely dissipative lattices, displaying an entirely Lindbladian dynamics, remains largely unexplored. Here the purely-dissipative Anderson model in the framework of a Lindblad master equation is considered, and it is shown that, akin to the semiclassical models with conservative hopping and random dissipation, one observes dynamical delocalization in spite of strong spectral localization of the Liouvillian superoperator. This result is very distinct from delocalization observed in the Anderson model with dephasing, where dynamical delocalization arises from the delocalization of the stationary state of the Liouvillian.     

Decay of correlations. IV. Necessary and sufficient conditions for a rapid decay of correlations

We considerN-particle systems whose probability distributions obey the master equation. For these systems, we derive the necessary and sufficient conditions under which the reducedn-particle (n) probabilities also obey master equations and under which the Ursell functions decay to their equilibrium values faster than the probability distributions. These conditions impose restrictions on the form of the transition rate matrix and thus on the form of its eigenfunctions. We first consider systems in which the eigenfunctions of theN-particle transition rate matrix are completely factorized and demonstrate that for such systems, the reduced probabilities obey master equations and the Ursell functions decay rapidly if certain additional conditions are imposed. As an example of such a system, we discuss a random walk ofN pairwise interacting walkers. We then demonstrate that for systems whoseN-particle transition matrix can be written as a sum of one-particle, two-particle, etc. contributions, and for which the reduced probabilities obey master equations, the reduced master equations become, in the thermodynamic limit, those for independent particles, which have been discussed by us previously. As an example of suchN-particle systems, we discuss the relaxation of a gas of interacting harmonic oscillators.Supported in part (grants to D.B. and K.E.S.) by the Advanced Research Projects Agency of the Department of Defense as monitored by the U.S. Office of Naval Research under Contract N00014-69-A-0200-6018, and in part (grant to I.O.) by the National Science Foundation.     

On the evaluation of gluon condensate effects in the holographic approach to QCD

In holographic QCD the effects of gluonic condensate can be encoded in a suitable deformation of the 5D metric. We develop two different methods for the evaluation of first order perturbative corrections to masses and decay constants of vector resonances in 5D Hard-Wall models of QCD due to small deformations of the metric. They are extracted either from a novel compact form for the first order correction to the vector two-point function, or from perturbation theory for vector bound-state eigenfunctions: the equivalence of the two methods is shown. Our procedures are then applied to flat and to AdS 5D Hard-Wall models; we complement results of existing literature evaluating the corrections to vector decay constant and to two-pion–one-vector couplings: this is particularly relevant to satisfy the sum rules. We concentrate our attention on the effects for the Gasser–Leutwyler coefficients; we show that as in the Chiral Quark model, the addition of the gluonic condensate improves the consistency, the understanding and the agreement with phenomenology of the holographic model.