A method for approximating the eigenvalues of non self-adjoint ordinary differential operators

Eigenvalue approximation method for non-self-adjoint operators using Galerkin method for estimating eigenvalue perturbations of self-adjoint operator

Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.Comment: 4 pages, 4 figures, minor changes, as published in Phys. Rev. Let

Vibrational and electronic entropy of β-cerium and γ-cerium measured by inelastic neutron scattering

Time-of-flight (TOF) inelastic neutron-scattering spectra were measured on β-cerium (double hcp) and γ-cerium (fcc) near the phase-transition temperature. Phonon densities of states (DOS) and crystal-field levels were extracted from the TOF spectra. A softening of the phonon DOS occurs in the transition from β- to γ-cerium, accounting for an increase in vibrational entropy of ΔSvibγ-β=(0.09±0.05)kB/atom. The entropy calculated from the crystal-field levels and a fit to calorimetry data from the literature were significantly larger in β-cerium than in γ-cerium below room temperature, but the difference was found to be negligible at the experimental phase-transition temperature. A contribution to the specific heat from Kondo spin fluctuations was consistent with the quasielastic magnetic scattering, but the difference between phases was negligible. To be consistent with the latent heat of the β-γ transition, the increase in vibrational entropy at the phase transition may be accompanied by a decrease in electronic entropy not associated with the crystal-field splitting or spin fluctuations. At least three sources of entropy need to be considered for the β-γ transition in cerium

Stochastic field theory for a Dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.Comment: 4 pages, 1 figur

Forcing Adsorption of a Tethered Polymer by Pulling

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first-order. Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the reentrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled

Large harmonic softening of the phonon density of states of uranium

Phonon density-of-states curves were obtained from inelastic neutron scattering spectra from the three crystalline phases of uranium at temperatures from 50 to 1213 K. The alpha -phase showed an unusually large thermal softening of phonon frequencies. Analysis of the vibrational power spectrum showed that this phonon softening originates with the softening of a harmonic solid, as opposed to vibrations in anharmonic potentials. It follows that thermal excitations of electronic states are more significant thermodynamically than are the classical volume effects. For the alpha-beta and beta-gamma phase transitions, vibrational and electronic entropies were comparable