Solution of the one-dimensional Dirac equation with a linear scalar potential

We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum is shown to match smoothly to the nonrelativistic spectrum in a weak-coupling limit.Comment: 7 pages, 1 figure, RevTE

Effects of a fundamental mass term in two-dimensional super Yang-Mills theory

We show that adding a vacuum expectation value to a gauge field left over from a dimensional reduction of three-dimensional pure supersymmetric Yang-Mills theory generates mass terms for the fundamental fields in the two-dimensional theory while supersymmetry stays intact. This is similar to the adjoint mass term that is generated by a Chern-Simons term in this theory. We study the spectrum of the two-dimensional theory as a function of the vacuum expectation value and of the Chern-Simons coupling. Apart from some symmetry issues a straightforward picture arises. We show that at least one massless state exists if the Chern-Simons coupling vanishes. The numerical spectrum separates into (almost) massless and very heavy states as the Chern-Simons coupling grows. We present evidence that the gap survives the continuum limit. We display structure functions and other properties of some of the bound states.Comment: 17 pp., 10 figs; substantially revised version to be published in Phys. Rev.

Debye relaxation and 250 K anomaly in glass forming monohydroxy alcohols

A previous dielectric, near-infrared (NIR), and nuclear magnetic resonance study on the hydrogen-bonded liquid 2-ethyl-1-hexanol [C. Gainaru et al., Phys. Rev. Lett. 107, 118304 (2011)] revealed anomalous behavior in various static quantities near 250 K. To check whether corresponding observations can be made for other monohydroxy alcohols as well, these experimental methods were applied to such substances with 5, 6, 7, 8, and 10 carbon atoms in their molecular backbone. All studied liquids exhibit a change of behavior near 250 K which is tentatively ascribed to effects of hydrogen bond cooperativity. By analyzing the NIR band intensities, a linear cluster size is derived that agrees with estimates from dielectric spectroscopy. All studied alcohols, except 4-methyl-3-heptanol, display a dominant Debye-like peak. Furthermore, neat 2-ethyl-1-butanol exhibits a well resolved structural relaxation in its dielectric loss spectrum which so far has only been observed for diluted monohydroxy alcohols.Comment: 39 pages including 12 figure

N=(1,1) super Yang--Mills theory in 1+1 dimensions at finite temperature

We present a formulation of N=(1,1) super Yang-Mills theory in 1+1 dimensions at finite temperature. The partition function is constructed by finding a numerical approximation to the entire spectrum. We solve numerically for the spectrum using Supersymmetric Discrete Light-Cone Quantization (SDLCQ) in the large-N_c approximation and calculate the density of states. We find that the density of states grows exponentially and the theory has a Hagedorn temperature, which we extract. We find that the Hagedorn temperature at infinite resolution is slightly less than one in units of (g^(2) N_c/pi)^(1/2). We use the density of states to also calculate a standard set of thermodynamic functions below the Hagedorn temperature. In this temperature range, we find that the thermodynamics is dominated by the massless states of the theory.Comment: 16 pages, 8 eps figures, LaTe

A GENERAL ITERATION SCHEME FOR THE CALCULATION OF LEVEL DENSITIES, AND RESULTS USING A SEMICLASSICAL APPROXIMATION

A general scheme is derived to calculate m-particle n-hole fermion level densities for any single particle Hamiltonian taking into account Pauli exclusion. This technique is applied to obtain level densities of the three dimensional isotropic Harmonic Oscillator semiclassically in the Thomas-Fermi approach

Mechanisms for Stable Sonoluminescence

A gas bubble trapped in water by an oscillating acoustic field is expected to either shrink or grow on a diffusive timescale, depending on the forcing strength and the bubble size. At high ambient gas concentration this has long been observed in experiments. However, recent sonoluminescence experiments show that in certain circumstances when the ambient gas concentration is low the bubble can be stable for days. This paper presents mechanisms leading to stability which predict parameter dependences in agreement with the sonoluminescence experiments.Comment: 4 pages, 3 figures on request (2 as .ps files