Glass Transition of Hard Sphere Systems: Molecular Dynamics and Density Functional Theory

The glass transition of a hard sphere system is investigated within the framework of the density functional theory (DFT). Molecular dynamics (MD) simulations are performed to study dynamical behavior of the system on the one hand and to provide the data to produce the density field for the DFT on the other hand. Energy landscape analysis based on the DFT shows that there appears a metastable (local) free energy minimum representing an amorphous state as the density is increased. This state turns out to become stable, compared with the uniform liquid, at some density, around which we also observe sharp slowing down of the $alpha$ relaxation in MD simulations.Comment: 5 pages, 5 figure

Star-graph expansions for bond-diluted Potts models

We derive high-temperature series expansions for the free energy and the susceptibility of random-bond $q$-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength $p$ as well as the dimension $d$ as symbolic parameters. By applying several series analysis techniques to the new series expansions, one can scan large regions of the $(p,d)$ parameter space for any value of $q$. For the bond-diluted 4-state Potts model in three dimensions, which exhibits a rather strong first-order phase transition in the undiluted case, we present results for the transition temperature and the effective critical exponent $\gamma$ as a function of $p$ as obtained from the analysis of susceptibility series up to order 18. A comparison with recent Monte Carlo data (Chatelain {\em et al.}, Phys. Rev. E64, 036120(2001)) shows signals for the softening to a second-order transition at finite disorder strength.Comment: 8 pages, 6 figure

Elementary excitations of trapped Bose gas in the large-gas-parameter regime

We study the effect of going beyond the Gross-Pitaevskii theory on the frequencies of collective oscillations of a trapped Bose gas in the large gas parameter regime. We go beyond the Gross-Pitaevskii regime by including a higher-order term in the interatomic correlation energy. To calculate the frequencies we employ the sum-rule approach of many-body response theory coupled with a variational method for the determination of ground-state properties. We show that going beyond the Gross-Pitaevskii approximation introduces significant corrections to the collective frequencies of the compressional mode.Comment: 17 pages with 4 figures. To be published in Phys. Rev.

Relativistic nuclear structure effects in quasielastic neutrino scattering

Charged-current cross sections are calculated for quasielastic neutrino and antineutrino scattering using a relativistic meson-nucleon model. We examine how nuclear-structure effects, such as relativistic random-phase-approximation (RPA) corrections and momentum-dependent nucleon self-energies, influence the extraction of the axial form factor of the nucleon. RPA corrections are important only at low-momentum transfers. In contrast, the momentum dependence of the relativistic self-energies changes appreciably the value of the axial-mass parameter, $M_A$, extracted from dipole fits to the axial form factor. Using Brookhaven's experimental neutrino spectrum we estimate the sensitivity of M$_A$ to various relativistic nuclear-structure effects.Comment: 26 pages, revtex, 6 postscript figures (available upon request

Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps

Interaction between collective monopole oscillations of a trapped Bose-Einstein condensate and thermal excitations is investigated by means of perturbation theory. We assume spherical symmetry to calculate the matrix elements by solving the linearized Gross-Pitaevskii equations. We use them to study the resonances of the condensate induced by temperature when an external perturbation of the trapping frequency is applied and to calculate the Landau damping of the oscillations.Comment: revtex, 9 pages, 5 figure

Universal Magnetic Properties of La2−δSrδCuO4La_{2-\delta} Sr_{\delta} Cu O_4 at Intermediate Temperatures

We present the theory of two-dimensional, clean quantum antiferromagnets with a small, positive, zero temperature ($T$) stiffness $\rho_s$, but with the ratio $k_B T / \rho_s$ arbitrary. Universal scaling forms for the uniform susceptibility ($\chi_u$), correlation length($\xi$), and NMR relaxation rate ($1/T_1$) are proposed and computed in a $1/N$ expansion and by Mont\'{e}-Carlo simulations. For large $k_B T/\rho_s$, $\chi_u (T)/T$ and $T\xi(T)$ asymptote to universal values, while $1/T_{1}(T)$ is nearly $T$-independent. We find good quantitative agreement with experiments and some numerical studies on $La_{2-\delta} Sr_{\delta} Cu O_4$.Comment: 14 pages, REVTEX, 1 postscript figure appende

Collective excitations of a two-dimensional interacting Bose gas in anti-trap and linear external potentials

We present a method of finding approximate analytical solutions for the spectra and eigenvectors of collective modes in a two-dimensional system of interacting bosons subjected to a linear external potential or the potential of a special form $u(x,y)=\mu -u \cosh^2 x/l$, where $\mu$ is the chemical potential. The eigenvalue problem is solved analytically for an artificial model allowing the unbounded density of the particles. The spectra of collective modes are calculated numerically for the stripe, the rare density valley and the edge geometry and compared with the analytical results. It is shown that the energies of the modes localized at the rare density region and at the edge are well approximated by the analytical expressions. We discuss Bose-Einstein condensation (BEC) in the systems under investigations at $T\ne 0$ and find that in case of a finite number of the particles the regime of BEC can be realized, whereas the condensate disappears in the thermodynamic limit.Comment: 10 pages, 2 figures include

Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State

We present the general theory of clean, two-dimensional, quantum Heisenberg antiferromagnets which are close to the zero-temperature quantum transition between ground states with and without long-range N\'{e}el order. For N\'{e}el-ordered states, `nearly-critical' means that the ground state spin-stiffness, $\rho_s$, satisfies $\rho_s \ll J$, where $J$ is the nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered ground states have a energy-gap, $\Delta$, towards excitations with spin-1, which satisfies $\Delta \ll J$. Under these circumstances, we show that the wavevector/frequency-dependent uniform and staggered spin susceptibilities, and the specific heat, are completely universal functions of just three thermodynamic parameters. Explicit results for the universal scaling functions are obtained by a $1/N$ expansion on the $O(N)$ quantum non-linear sigma model, and by Monte Carlo simulations. These calculations lead to a variety of testable predictions for neutron scattering, NMR, and magnetization measurements. Our results are in good agreement with a number of numerical simulations and experiments on undoped and lightly-doped $La_{2-\delta} Sr_{\delta}Cu O_4$.Comment: 81 pages, REVTEX 3.0, smaller updated version, YCTP-xxx