High field magnetoresistance of impure semimetals

The theory of the longitudinal magnetoresistance at high magnetic fields and low temperatures is reformulated to incorporate screened impurities or a random potential of rather arbitrary shape. Analytical expressions are derived for the density of states, the chemical potential, the quasi particle damping and the longitudinal conductivity. They include vertex corrections and are valid from the higher field Shubnikov-de Haas regime up to arbitrarily high fields. The theory contains no adjustible parameter except the potential correlation function. InSb is studied as an example and a comparison with the experiment yields field dependent screening parameters.     

Effects of collisions on linear and non-linear spectroscopic line shapes

A fundamental physical problem is the determination of atom-atom, atom-molecule and molecule-molecule differential and total scattering cross sections. In this work, a technique for studying atomic and molecular collisions using spectroscopic line shape analysis is discussed. Collisions occuring within an atomic or molecular sample influence the sample's absorptive or emissive properties. Consequently the line shapes associated with the linear or non-linear absorption of external fields by an atomic system reflect the collisional processes occuring in the gas. Explicit line shape expressions are derived characterizing linear or saturated absorption by two- or three-level “active” atoms which are undergoing collisions with perturber atoms. The line shapes may be broadened, shifted, narrowed, or distorted as a result of collisions which may be “phase-interrupting” or “velocity-changing” in nature. Systematic line shape studies can be used to obtain information on both the differential and total active atom-perturber scattering cross sections.     

Spectral Sum Rules for the Circular Aharonov-Bohm Quantum Billiard

This work presents the results of a quantitative investigation of the “sum rule method” recently proposed by the author for calculating low-lying energy levels. The system considered in detail is the circular Aharonov-Bohm quantum billiard recently introduced by Berry and Robnik. Exact, expressions are derived for the spectral zeta function at positiveinteger values as a function of the magnetic flux. Using the zeta function for fixed angular momentum, we observe a very fast convergence to the exact ground state energy (“precocious convergence”).     

Scattering of waves by irregularities in periodic discrete lattice spaces. I. Reduction of problem to quadratures on a discrete model of the Schrödinger equation

The scattering of plane waves and of point source pulses by irregularities in a discrete lattice model of the Schrödinger equation is considered. Closed form expressions are derived for the scattered wave function in terms of lattice Green's functions in the case that a finite number of lattice points or “bonds” are defective. The scattered wave function appears in the form of the ratio of two determinants. While in continuum scattering theory the scatterer must have some symmetry, perhaps spherical, cylindrical or elliptical, in order to allow separation of variables in the basic scattering differential equation, such symmetries are not necessary for the construction of scattered wave functions on discrete lattices. When the number of irregularities becomes large, the determinants in the solution of the scattering problem become large.     

Two-dimensional quantum antiferromagnet in a strong magnetic field

The behaviour of the two-dimensional quantum antiferromagnet of arbitrary spin in a strong transversal magnetic field on a square lattice is studied in terms of the equivalent Bose gas problem. The existence of phase transition from the state characterized by “quasi-long-range” magnetic order to the disordered ferromagnetic state is demonstrated. The expressions for correlation functions, thermodynamical and magnetic characteristics are derived.     

Bose-Einstein correlations in thermal field theory

Two-particle correlation functions are calculated for bosons emitted from a localized thermal source (the “glow” of a “hot spot”). In contrast to existing work, non-equilibrium effects up to first order in gradients of the particle distribution function are taken into account. The spectral width of the bosons is shown to be an important quantity: if it is too small, they do not equilibrate locally and therefore strongly increase the measured correlation radius.     

An Enskog repeated-ring kinetic equation; Long-time tails and the Brownian limit

A kinetic equation for the motion of a particle of arbitrary size and mass through a moderately dense gas is derived and discussed. The “long-time tail” of the velocity correlation function is calculated and found to agree with existing results. For a Brownian particle, the theory gives the Stokes-Einstein law for the self-diffusion coefficient, with the shear viscosity given by its Enskog value.     

Correlation of ultrasonic scatterer size estimates for the statistical analysis and optimization of angular compounding

Ultrasonic scatterer size estimates generally have large variances due to the inherent noise of spectral estimates used to calculate size. Compounding partially correlated size estimates associated with the same tissue, but produced with data acquired from different angles of incidence, is an effective way to reduce the variance without making dramatic sacrifices in spatial resolution. This work derives theoretical approximations for the correlation between these size estimates, and the coherence between their associated spectral estimates, as functions of ultrasonic system parameters. A Gaussian spatial autocorrelation function is assumed to adequately model scatterer shape. Both approximations compare favorably with simulation results, which consider validation near the focus. Utilization of the correlation/coherence expressions for statistical analysis and optimization is discussed. Approximations, such as the invariance of phase and amplitude terms with angle, are made to obtain closed-form solutions to the derived spectral coherence near the focus and permit analytical optimization analysis. Results indicate that recommended parameter adjustments for performance improvement generally depend upon whether, for the system under consideration, the primary source of change in total coherence with rotation is phase term variation due to the change in the relative position of scattering sites, or field amplitude term variation due to beam movement.     

“Spreading” of a biphoton in a group-velocity-dispersion medium and two-photon interference

It is shown that two-photon Bell states can be prepared by “spreading” of a two-photon wave packet (biphoton) in a dispersive medium without compensating for group delays between photons with orthogonal polarizations or using narrow-band filters but by selecting the time correlation function. This is possible because two-photon interference effects are manifested in the shape of the time correlation function of intensity due to its spreading.     

On the spin-phonon interaction in anharmonic crystals

In this paper, a theory is developed for examining the influence of the spin-phonon interaction on the phonon dynamics in anharmonic crystals. In contrast to a harmonic approximation such an approach allows for comparing the role of the direct interaction between lattice vibrations with that of the indirect interaction via spins in the propagation and attenuation of sound as well as in the behaviour of thermodynamic quantities. Explicit expressions are derived for the phonon self-energy using successively higher approximations obtained from a cumulant expansion of the density of interparticle distances. It is shown that even in the harmonic approximation the two-spin correlation function and the four-spin correlation function enter into the expression of the generalized dynamical matrix in deviation from previous results. The modification of this harmonic dynamical matrix due to the renormalization of the harmonic phonons and due to phonon-phonon scattering processes is given employing a “weak coupling” approximation between the localized spins and the interparticle-distance density of the crystal. The resemblance of the present approach to an earlier microscopic treatment of electronic contributions to phonon dynamics in anharmonic crystals is pointed out.     

Observation of a lambda-shaped ultrasonic attenuation peak in superconducting UPt3

We report measurements of the temperature dependence of the ultrasonic attenuation in superconducting UPt₃. In the vicinity of the superconducting transition temperature a pronounced longitudinal attenuation peak is observed. Such a peak does not appear for transverse ultrasound. Our experimental results can be explained by a “correlation hump” of the density-density correlation function.     

Almost-adiabatic collisions of quantum systems

Expressions are derived for corrections resulting from a small variation of the “slow” internal degrees of freedom during an almost-adiabatic quantum collision. First-order non-adiabatic contributions to the scattering wave function and scattering T-matrix element are derived making use of (a) Wronskian surface terms, and (b) converging factors. Advantages of method (a) are indicated. Modifications of the expressions necessary to include a possible projectile intrinsic spin are described. A one-dimensional model illustrating the range of validity of the adiabatic approximation is presented.     

Uplifting the Iwasawa

The Iwasawa manifold is uplifted to seven‐folds of either G₂ holonomy or SU(3) structure, explicit new metrics for the same having been constructed in this work. We uplift the Iwasawa manifold to a G₂ manifold through “size” deformation (of the Iwasawa metric), via Hitchin's Flow equations, showing also the impossibility of the uplift for “shape” and “size” deformations (of the Iwasawa metric). Using results of Dall'Agata and Prezas, Phys. Rev. D 69 , 066004 (2004) [arXiv:hep‐th/0311146] [1], we also uplift the Iwasawa manifold to a 7‐fold with SU(3) structure through “size” and “shape” deformations via generalisation of Hitchin's Flow equations. For seven‐folds with SU(3)‐structure, the result could be interpreted as M5‐branes wrapping two‐cycles embedded in the seven‐fold (as in [1]) ‐ a warped product of either a special hermitian six‐fold or a balanced six‐fold with the unit interval. There can be no uplift to seven‐folds of SU(3) structure involving non‐trivial “size” and “shape” deformations (of the Iwasawa metric) retaining the “standard complex structure” ‐ the uplift generically makes one move in the space of almost complex structures such that one is neither at the standard complex structure point nor at the “edge”. Using the results of Konopelchenko and Landolfi, J. Geom. Phys. 29 , 319 (1999) [arXiv:math.DG/9804144] [2], we show that given two “shape deformation” functions, and the dilaton, one can construct a Riemann surface obtained via Weierstraß representation for the conformal immersion of a surface in R ^l, for a suitable l, with the condition of having conformal immersion being a quadric in CP ^l‐1.     

Grundlagen der Polarisationsmessung in polarisierten Targets mit Hilfe des inneren Feldes

It is shown how the difficulties with the “Lorentz field” method of Abragamet al. for the measurement of nuclear polarization can be resolved. The observable field shift is derived as a function of nuclear polarization, target shape and some other parameters. For purposes of practical application numerical results are presented for polarized targets of lanthanum magnesium nitrate (1% Nd) having the shape of thin square slabs.     

Classical stochastic model of laser-stimulated surface processes and the selective nature of laser excitation via multiphonon couplings

The dynamical behavior of laser-stimulated surface processes (LSSP) is studied by the generalized Langevin equation via the memory effects of the damping kernel, the dephasing kernel and mode-mode interactions. The temperature-dependent averaged energy absorption rate (which characterizes the line shape) is calculated by solving the Laplace-Fourier transform of the velocity correlation function. The features of the response function and its overall line broadening are discussed in terms of Markovian processes. The nature of LSSP and laser-selective effects are discussed in terms of the multiphonon coupling strength and the related “internal resonant” condition. It is shown that laser-selective bond breaking is possible for a slow intramolecular vibrational relaxation rate which is governed by a high-order multiphonon process or a far off “internal resonance”.     

The relativistic Burnett equations and sound propagation

A relaxation-time model for the relativistic Boltzmann equation of a single-component gas is solved to second, or “Burnett”, order using the relativistic version of the Chapman-Enskog method developed by Marle. Expressions are obtained from this second order solution for the “Burnett” contributions to the heat flux and pressure tensor of the gas. Using the “Burnett” equations, which incorporate these contributions, expressions are then derived for the dispersion and absorption of sound in the gas which agree, in the classical limit, with the results of Wang Chang and Uhlenbeck.     

Luminosity of a Collider with Asymmetric Beams

A formula for the collider luminosity is derived for a head-on collision of two beams with different parameters. The formula is valid for colliding and partially separated (“merging”) beams. Three particular cases are presented: the collision of two identical axially symmetric bunches, the collision of a bunch with a disbanded beam, and the collision of two disbanded bunches. The colliding beams have coinciding longitudinal axes. The formula is valid for colliding both counter propagating and co-propagating beams.