Diamagnetism of the hydrogen atom in the quasi-Landau regime

Using periodic orbits to compute chaotic transport rates between resonance zones

Transport properties of chaotic systems are computable from data extracted from periodic orbits. Given a sufficient number of periodic orbits, the escape rate can be computed using the spectral determinant, a function that incorporates the eigenvalues and periods of periodic orbits. The escape rate computed from periodic orbits converges to the true value as more and more periodic orbits are included. Escape from a given region of phase space can be computed by considering only periodic orbits that lie within the region. An accurate symbolic dynamics along with a corresponding partitioning of phase space is useful for systematically obtaining all periodic orbits up to a given period, to ensure that no important periodic orbits are missing in the computation. Homotopic lobe dynamics (HLD) is an automated technique for computing accurate partitions and symbolic dynamics for maps using the topological forcing of intersections of stable and unstable manifolds of a few periodic anchor orbits. In this study, we apply the HLD technique to compute symbolic dynamics and periodic orbits, which are then used to find escape rates from different regions of phase space for the Hénon map. We focus on computing escape rates in parameter ranges spanning hyperbolic plateaus, which are parameter intervals where the dynamics is hyperbolic and the symbolic dynamics does not change. After the periodic orbits are computed for a single parameter value within a hyperbolic plateau, periodic orbit continuation is used to compute periodic orbits over an interval that spans the hyperbolic plateau. The escape rates computed from a few thousand periodic orbits agree with escape rates computed from Monte Carlo simulations requiring hundreds of billions of orbits.

Magnetic field induced dynamical chaos

In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x-y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.

Si:P as a laboratory analogue for hydrogen on high magnetic field white dwarf stars

Laboratory spectroscopy of atomic hydrogen in a magnetic flux density of 10(5) T (1 gigagauss), the maximum observed on high-field magnetic white dwarfs, is impossible because practically available fields are about a thousand times less. In this regime, the cyclotron and binding energies become equal. Here we demonstrate Lyman series spectra for phosphorus impurities in silicon up to the equivalent field, which is scaled to 32.8 T by the effective mass and dielectric constant. The spectra reproduce the high-field theory for free hydrogen, with quadratic Zeeman splitting and strong mixing of spherical harmonics. They show the way for experiments on He and H(2) analogues, and for investigation of He(2), a bound molecule predicted under extreme field conditions.

Realization of anisotropic diamagnetic kepler problem in a solid state environment

The anisotropic diamagnetic Kepler problem (ADKP) is realized experimentally by the orbital electrons of a P donor in Si under magnetic fields. The interference of electron wave packets which leads to quasi-Landau resonances (QLR) were observed. Applying the closed-orbit theory to an anisotropic solid state environment, we have identified orbits responsible for the QLR manifesting the quantum chaotic behavior in Rydberg atoms. The excellent consistency between the measured spectra and theoretical calculation provides unambiguous evidence of quantum chaotic dynamics of electrons in the ADKP.

Nonclassical paths in the recurrence spectrum of diamagnetic atoms

Using time-independent scattering matrices, we study how the effects of nonclassical paths on the recurrence spectra of diamagnetic atoms can be extracted from purely quantal calculations. This study reveals an intimate relationship between two types of nonclassical paths: exotic ghost orbits and diffractive orbits. This relationship proves to be a previously unrecognized reason for the success of semiclassical theories, such as closed-orbit theory, and permits a comprehensive reformulation of the semiclassical theory that elucidates its convergence properties.

Conductance fluctuations and quantum chaotic scattering in semiconductor microstructures

We review recent experiments on aperiodic conductance fluctuations in ballistic GaAs/AlGaAs microstructures in the shape of a stadium billiard and a circle with point-contact leads, measured at millikelvin temperatures. Much of the observed behavior can be analyzed within a semiclassical approach to quantum chaotic scattering. After a brief review of the Landauer-Buttiker formulation of coherent transport, a variety of novel experimental phenomena and comparisons to semiclassical theory are presented. In particular, we discuss quantum-enhanced backscattering, the power spectrum of conductance fluctuations, crossover to the high-magnetic-field and tunneling regimes, and an application allowing the rate of phase-randomizing scattering to be measured in chaotic ballistic microstructures.