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Stochastic ionization of highly excited relativistic hydrogenlike atom in the monochromatic field is investigated. A theoretical analisis of chaotic dynamics of the relativistic electron based on Chirikov criterion is given for the cases of one- and three-dimensional atoms. Critical value of the external field is evaluated analitically. The diffusion coefficient and ionization time are calculated.
The harmonic inversion method is applied in the case of the hydrogen atom in a magnetic field to extract classical information from the quantum photo-ionization cross-section. The study is made close to a saddle-node bifurcation for which the usual semi-classical formulas give diverging contributions. All quantities (actions, stabilities and Maslov indices) for real orbits above the bifurcation and for complex ghost orbits below the bifurcation, are found to be in excellent agreement with the modified semi-classical predictions based on a normal form approach.
A decimation method is applied to the tight binding model describing the two dimensional electron gas with next nearest neighbor interaction in the presence of an inverse golden mean magnetic flux. The critical phase with fractal spectrum and wave function exists in a finite window in two-dimensional parameter space. There are special points on the boundaries as well as inside the critical phase where the renormalization flow exhibits higher order limit cycles. Our numerical results suggest that most of the critical phase is characterized by a strange attractor of the renormalization equations.
We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We numerically investigate models exhibiting one or both of these features, and we find in all cases an inverse power law dependence of the average transmission on the sample length. Although in all the considered cases the quadratic spread of wave packets increases linearly (or very close to linearly) in time for both types of dynamics, a proper Ohmic dependence is always observed only in the case of quasi-classical diffusion. The analysis of the statistics of transmission fluctuations in the case of a fractal spectrum exposes some new features, which mark further differences from ordinary diffusion, and enforce the conclusion that the two types of transmission are intrinsically different.
Spatio-temporal chaos is predicted to occur in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Under dc voltage bias, undamped time-dependent oscillations of the current (due to the motion and recycling of electric field domain walls) have been observed in recent experiments. Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal.
We study the spectral statistics in the center of the lowest Landau band of a 2D disordered system with smooth potential and strong transverse magnetic field. Due to the finite size of the system, the energy range in which there are extended states is finite as well. The behavior in this range can be viewed as the analogue of the Anderson metal-insulator transition for the case of the Hall system. Accordingly, we verify recent predictions regarding the exponent of the asymptotic power law of $Σ^2 (\bar N)$, $γ$, and that of the stretched exponential dominating the large $s$ behavior of the spacings distribution, $α$. Both the relations, $α= 1- γ$, and $γ= 1 - {1\over{νd}}$ where $ν$ is the critical exponent of the localization length and $d$ is the dimension, are found to hold within the accuracy of our computations. However, we find that none of several possible models of the entire spacings distribution correctly describes our situation. Finally, for very large $\bar N$, $\bar N > 60$, we find a new regime in which $Σ^2 (\bar N)$ behaves as a power law with an unexpectedly large power, $γ_1 = 1.38 \pm 0.02$.
The purpose of this work is to compare the dynamics of arrays of Josephson junctions in presence of magnetic field in two different frameworks: the so called XY frustrated model with no self inductance and an approach that takes into account the screening currents (considering self inductances only). We show that while for a range of parameters the simpler model is sufficiently accurate, in a region of the parameter space solutions arise that are not contained in the XY model equations.
Electron scattering on a thin layer where the potential depends self-consistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped brightening (darkening) appears on the layer causing diffraction of the wave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonlinearities result in different phase shifts of the wave function on the screen, which give rise to quite different diffraction patterns. Among others, the nonlinearity can cause self-focusing of the incident wave into a ``beam'', splitting in two ``beams'', single or double traces with suppressed reflection or transmission, etc.
We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the distribution of the conductance for three classes of reflection symmetry relevant for experimental ballistic microstructures. The S-matrix ensembles used fall within the general classification scheme introduced by Dyson, but because the conductance couples blocks of the S-matrix of different parity, the resulting conductance properties are highly non-trivial.
We study the lowest order conservation laws in one-dimensional (1D) integrable quantum many-body models (IQM) as the Heisenberg spin 1/2 chain, the Hubbard and t-J model. We show that the energy current is closely related to the first conservation law in these models and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero frequency component of the conductivity) and so ideal conductivity at finite temperatures.
The elastic mean free path of carriers in a recently introduced model of quantum chaotic billiards in two and three dimensions is calculated. The model incorporates surface roughness at a microscopic scale by randomly choosing the atomic levels at the surface sites between -W/2 and W/2. Surface roughness yields a mean free path l that decreases as L/W^2 as W increases, L being the linear size of the system. But this diminution ceases when the surface layer begins to decouple from the bulk for large enough values of W, leaving more or less unperturbed states on the bulk. Consequently, the mean free path shows a minimum of about L/2 for W of the order of the band width. Energy fluctuations reflect the behavior of the mean free path. At small energy scales, strong level correlations manifest themselves by small values of the number of levels variance Sigma^2(E) that are close to Random Matrix Theory (RMT) in all cases. At larger energy scales, fluctuations are below the logarithmic behavior of RMT for l > L, and above RMT value when l < L.
Nonlinear localized excitations in one-dimensional diatomic lattices with cubic and quartic nonlinearity are considered analytically by a quasi-discreteness approach. The criteria for the occurence of asymmetric gap solitons (with vibrating frequency lying in the gap of phonon bands) and small-amplitude, asymmetric intrinsic localized modes (with the vibrating frequency being above all the phonon bands) are obtained explicitly based on the modulational instabilities of corresponding linear lattice plane waves. The expressions of particle displacement for all these nonlinear localized excitations are also given. The result is applied to standard two-body potentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. The comparison with previous numerical study of the anharmonic gap modes in diatomic lattices for the standard two-body potentials is made and good agreement is found.
The conductance of a waveguide containing finite number of periodically placed identical point-like impurities is investigated. It has been calculated as a function of both the impurity strength and the number of impurities using the Landauer-Büttiker formula. In the case of few impurities the conductance is proportional to the number of the open channels $N$ of the empty waveguide and shows a regular staircase like behavior with step heights $\approx 2e^2/h$. For large number of impurities the influence of the band structure of the infinite periodic chain can be observed and the conductance is approximately the number of energy bands (smaller than $N$) times the universal constant $2e^2/h$. This lower value is reached exponentially with increasing number of impurities. As the strength of the impurity is increased the system passes from integrable to quantum-chaotic. The conductance, in units of $2e^2/h$, changes from $N$ corresponding to the empty waveguide to $\sim N/2 $ corresponding to chaotic or disordered system. It turnes out, that the conductance can be expressed as $(1-c/2)N$ where the parameter $0<c<1$ measures the chaoticity of the system.
Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain driven by a constant external force are investigated. Resonant steplike transitions of the average velocity occur due to the competitions between the moving kinks and their radiated phasonlike modes. A mean-field consideration is introduced to give a precise prediction of the resonant steps. Slip-stick motion and spatiotemporal dynamics on those resonant steps are discussed. Our results can be applied to studies of the fluxon dynamics of 1D Josephson-junction arrays and ladders, dislocations, tribology and other fields.
The persistent current of ballistic chaotic billiards is considered with the help of the Gutzwiller trace formula. We derive the semiclassical formula of a typical persistent current $I^{typ}$ for a single billiard and an average persistent current $ $ for an ensemble of billiards at finite temperature. These formulas are used to show that the persistent current for chaotic billiards is much smaller than that for integrable ones. The persistent currents in the ballistic regime therefore become an experimental tool to search for the quantum signature of classical chaotic and regular dynamics.
We study the transmission coefficient of a plane wave through a 1D finite quasi-periodic system -- the Frenkel-Kontorova (FK) model -- embedding in an infinite uniform harmonic chain. By varying the mass of atoms in the infinite uniform chain, we obtain the transmission coefficients for {\it all} eigenfrequencies. The phonon localization of the incommensurated FK chain is also studied in terms of the transmission coefficients and the Thouless exponents. Moreover, the heat conduction of Rubin-Greer-like model for FK chain at low temperature is calculated. It is found that the stationary heat flux $J(N)\sim N^α$, and $α$ depends on the strength of the external potential.
The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory for the time evolution of the order parameter in systems undergoing first-order phase transformations has been extended by Sekimoto to the level of two-point correlation functions. Here, this extended KJMA theory is applied to a kinetic Ising lattice-gas model, in which the elementary kinetic processes act on microscopic length and time scales. The theoretical framework is used to analyze data from extensive Monte Carlo simulations. The theory is inherently a mesoscopic continuum picture, and in principle it requires a large separation between the microscopic scales and the mesoscopic scales characteristic of the evolving two-phase structure. Nevertheless, we find excellent quantitative agreement with the simulations in a large parameter regime, extending remarkably far towards strong fields (large supersaturations) and correspondingly small nucleation barriers. The original KJMA theory permits direct measurement of the order parameter in the metastable phase, and using the extension to correlation functions one can also perform separate measurements of the nucleation rate and the average velocity of the convoluted interface between the metastable and stable phase regions. The values obtained for all three quantities are verified by other theoretical and computational methods. As these quantities are often difficult to measure directly during a process of phase transformation, data analysis using the extended KJMA theory may provide a useful experimental alternative.
We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j|^{-μ}$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the parameter $μ$. The model is critical at $μ=1$ and the eigenstates are multifractals. Based on numerical simulations we demonstrate that the spectral statistics at criticality differs from semi-Poisson statistics which is expected to be a general feature of systems exhibiting a LDT or `weak chaos'.