From Disordered Crystal to Glass: Exact Theory

We calculate thermodynamic properties of a disordered model insulator, starting from the ideal simple-cubic lattice ($g = 0$) and increasing the disorder parameter $g$ to $\gg 1/2$. As in earlier Einstein- and Debye- approximations, there is a phase transition at $g_{c} = 1/2$. For $g<g_{c}$ the low-T heat-capacity $C \sim T^{3}$ whereas for $g>g_{c}$, $C \sim T$. The van Hove singularities disappear at {\em any finite $g$}. For $g>1/2$ we discover novel {\em fixed points} in the self-energy and spectral density of this model glass.Comment: Submitted to Phys. Rev. Lett., 8 pages, 4 figure

The Trapped Polarized Fermi Gas at Unitarity

We consider population-imbalanced two-component Fermi gases under external harmonic confinement interacting through short-range two-body potentials with diverging s-wave scattering length. Using the fixed-node diffusion Monte Carlo method, the energies of the "normal state" are determined as functions of the population-imbalance and the number of particles. The energies of the trapped system follow, to a good approximation, a universal curve even for fairly small systems. A simple parameterization of the universal curve is presented and related to the equation of state of the bulk system.Comment: 4 pages, 2 tables, 2 figure

Bohr-Sommerfeld quantization of spin Hamiltonians

The Bohr-Sommerfeld rule for a spin system is obtained, including the first quantum corrections. The rule applies to both integer and half-integer spin, and respects Kramers degeneracy for time-reversal invariant systems. It is tested for various models, in particular the Lipkin-Meshkov-Glick model, and found to agree very well with exact results.Comment: Revtex 4, no figures, 1 tabl

Third Order Renormalization Group applied to the attractive one-dimensional Fermi Gas

We consider a Callan-Symanzik and a Wilson Renormalization Group approach to the infrared problem for interacting fermions in one dimension with backscattering. We compute the third order (two-loop) approximation of the beta function using both methods and compare it with the well known multiplicative Gell-Mann Low approach. We point out a previously unnoticed qualitative dependence of the third order fixed point on an arbitrary dimensionless parameter, which strongly suggest the spurious nature of the fixed point.Comment: 16 pages, Revised version, added comment

Ferromagnetic transition in a double-exchange system containing impurities in the Dynamical Mean Field Approximation

We formulate the Dynamical Mean Field Approximation equations for the double-exchange system with quenched disorder for arbitrary relation between Hund exchange coupling and electron band width. Close to the ferromagnetic-paramagnetic transition point the DMFA equations can be reduced to the ordinary mean field equation of Curie-Weiss type. We solve the equation to find the transition temperature and present the magnetic phase diagram of the system.Comment: 5 pages, latex, 2 eps figures. We explicitely present the magnetic phase diagram of the syste

Soliton quantization and internal symmetry

We apply the method of collective coordinate quantization to a model of solitons in two spacetime dimensions with a global $U(1)$ symmetry. In particular we consider the dynamics of the charged states associated with rotational excitations of the soliton in the internal space and their interactions with the quanta of the background field (mesons). By solving a system of coupled saddle-point equations we effectively sum all tree-graphs contributing to the one-point Green's function of the meson field in the background of a rotating soliton. We find that the resulting one-point function evaluated between soliton states of definite $U(1)$ charge exhibits a pole on the meson mass shell and we extract the corresponding S-matrix element for the decay of an excited state via the emission of a single meson using the standard LSZ reduction formula. This S-matrix element has a natural interpretation in terms of an effective Lagrangian for the charged soliton states with an explicit Yukawa coupling to the meson field. We calculate the leading-order semi-classical decay width of the excited soliton states discuss the consequences of these results for the hadronic decay of the $\Delta$ resonance in the Skyrme model.Comment: 23 pages, LA-UR-93-299

Pion-Nucleon Scattering in a Large-N Sigma Model

We review the large-N_c approach to meson-baryon scattering, including recent interesting developments. We then study pion-nucleon scattering in a particular variant of the linear sigma-model, in which the couplings of the sigma and pi mesons to the nucleon are echoed by couplings to the entire tower of I=J baryons (including the Delta) as dictated by large-N_c group theory. We sum the complete set of multi-loop meson-exchange \pi N --> \pi N and \pi N --> \sigma N Feynman diagrams, to leading order in 1/N_c. The key idea, reviewed in detail, is that large-N_c allows the approximation of LOOP graphs by TREE graphs, so long as the loops contain at least one baryon leg; trees, in turn, can be summed by solving classical equations of motion. We exhibit the resulting partial-wave S-matrix and the rich nucleon and Delta resonance spectrum of this simple model, comparing not only to experiment but also to pion-nucleon scattering in the Skyrme model. The moral is that much of the detailed structure of the meson-baryon S-matrix which hitherto has been uncovered only with skyrmion methods, can also be described by models with explicit baryon fields, thanks to the 1/N_c expansion.Comment: This LaTeX file inputs the ReVTeX macropackage; figures accompany i

Dynamics and Control of a Quasi-1D Spin System

We study experimentally a system comprised of linear chains of spin-1/2 nuclei that provides a test-bed for multi-body dynamics and quantum information processing. This system is a paradigm for a new class of quantum information devices that can perform particular tasks even without universal control of the whole quantum system. We investigate the extent of control achievable on the system with current experimental apparatus and methods to gain information on the system state, when full tomography is not possible and in any case highly inefficient

Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires

Upon increasing the electron density in a quantum wire, the one-dimensional electron system undergoes a transition to a quasi-one-dimensional state. In the absence of interactions between electrons, this corresponds to filling up the second subband of transverse quantization, and there are two gapless excitation modes above the transition. On the other hand, strongly interacting one-dimensional electrons form a Wigner crystal, and the transition corresponds to it splitting into two chains (zigzag crystal). The two chains are locked, so their relative motion is gapped, and only one gapless mode remains. We study the evolution of the system as the interaction strength changes, and show that only one gapless mode exists near the transition at any interaction strength.Comment: 4 pages, 2 figure