Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis

We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 dimensional case. The 1d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis.Comment: version 3: additional appendix explains how the $\nu$ to $1-\nu$ duality of Riemann's $\zeta (\nu)$ follows from a special modular transformation in a massless relativistic theor

Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models

We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with rotational spin of spin-1/2 particles. Since the spin-1/2 representation is not promoted to a representation of the Lorentz group, the model is not fully Lorentz invariant, although it has a relativistic dispersion relation. The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a unitary time evolution. Renormalization-group analysis shows the model has a low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed points. The critical exponents are computed to two-loop order. Possible applications to condensed matter physics in 3 space-time dimensions are discussed.Comment: v2: Published version, minor typose correcte

Elastic electron scattering by laser-excited 138Ba( ... 6s6p 1P1) atoms

The results of a joint experimental and theoretical study concerning elastic electron scattering by laser-excited 138Ba( ... 6s6p 1P1) atoms are described. These studies demonstrate several important aspects of elastic electron collisions with coherently excited atoms, and are the first such studies. From the measurements, collision and coherence parameters, as well as cross sections associated with an atomic ensemble prepared with an arbitrary in-plane laser geometry and linear polarization (with respect to the collision frame), or equivalently with any magnetic sublevel superposition, have been obtained at 20 eV impact energy and at 10°, 15° and 20° scattering angles. The convergent close-coupling (CCC) method was used within the non-relativistic LS-coupling framework to calculate the magnetic sublevel scattering amplitudes. From these amplitudes all the parameters and cross sections at 20 eV impact energy were extracted in the full angular range in 1° steps. The experimental and theoretical results were found to be in good agreement, indicating that the CCC method can be reliably applied to elastic scattering by 138Ba( ... 6s6p 1P1) atoms, and possibly to other heavy elements when spin-orbit coupling effects are negligible. Small but significant asymmetry was observed in the cross sections for scattering to the left and to the right. It was also found that elastic electron scattering by the initially isotropic atomic ensemble resulted in the creation of significant alignment. As a byproduct of the present studies, elastic scattering cross sections for metastable 138Ba atoms were also obtained

Non-Local Virasoro Symmetries in the mKdV Hierarchy

We generalize the dressing symmetry construction in mKdV hierarchy. This leads to non-local vector fields (expressed in terms of vertex operators) closing a Virasoro algebra. We argue that this algebra realization should play an important role in the study of 2D integrable field theories and in particular should be related to the Deformed Virasoro Algebra (DVA) when the construction is perturbed out of the critical theory.Comment: 11 pages, LaTex fil

Complex Role of Secondary Electron Emissions in Dust Grain Charging in Space Environments: Measurements on Apollo 11 and 17 Dust Grains

Dust grains in various astrophysical environments are generally charged electrostatically by photoelectric emissions with radiation from nearby sources, or by electron/ion collisions by sticking or secondary electron emissions. Knowledge of the dust grain charges and equilibrium potentials is important for understanding of a variety of physical and dynamical processes in the interstellar medium (ISM), and heliospheric, interplanetary, planetary, and lunar environments. The high vacuum environment on the lunar surface leads to some unusual physical and dynamical phenomena involving dust grains with high adhesive characteristics, and levitation and transportation over long distances. It has been well recognized that the charging properties of individual micron/submicron size dust grains are expected to be substantially different from the corresponding values for bulk materials and theoretical models. In this paper we present experimental results on charging of individual dust grains selected from Apollo 11 and Apollo 17 dust samples by exposing them to mono-energetic electron beams in the 10- 400 eV energy range. The charging rates of positively and negatively charged particles of approximately 0.2 to 13 microns diameters are discussed in terms of the secondary electron emission (SEE) process, which is found to be a complex charging process at electron energies as low as 10-25 eV, with strong particle size dependence. The measurements indicate substantial differences between dust charging properties of individual small size dust grains and of bulk materials

Lunar Dust Charging by Secondary Electron Emission and its Complex Role in the Lunar Environment

The lunar surface is covered with a thick layer of micron/sub-micron size dust grains formed by billions of years of meteoritic impact. With virtually no atmosphere and exposed to the solar wind plasma and solar electromagnetic radiation, the lunar surface and the dust grains are electrostatically charged. The dominant charging processes include: photoelectric emissions (UV, X-rays), impact of solar wind electrons and ions, and secondary electron emissions (SEE) induced by energetic solar wind electrons. During the Apollo missions, the astronauts found the lunar dust to be extraordinarily high in its adhesive characteristics, sticking to the suits and the mechanical equipment. Electrostatically charged lunar dust is believed to be transported over long distances by the induced electric fields, as indicated by the observed dust streamers and the horizon glow [e.g., 1-3]. The hazardous effects of dust in the lunar environment are recognized to be one of the major issues that must be addressed in planning the forthcoming missions for robotic and human exploration of the Moon. Theoretical studies are being performed along with the development of analytical models and a variety of experimental investigations, to better understand the lunar dust phenomena. [e.g., 4-6]. The lunar dust is believed to be charged negatively on the lunar night-side by interaction With solar wind electrons. However, rigorous theoretical expressions for calculation of SEE yields and the sticking efficiencies of individual micron size dust grains are not yet available, and the information has to be obtained by experiment. On theoretical considerations, however, it is well recognized that SEE yields, similar to the photoelectric yields for small-size grains, would be totally different from the corresponding bulk values [e.g., 7-9]. Some theoretical models for charging of individual small spherical particles have been developed [e.g., 10], and some limited measurements on individual metallic dust grains at keV electron energies have been made [e.g., i 1]. In this paper, we present the first measurements of the secondary electron emission yields of individual micron/sub-micron size dust grains selected from sample returns of Apollo 11 and Apollo 17 missions

Witten's Vertex Made Simple

The infinite matrices in Witten's vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s=0 limit. We find that s=1 eigenfunctions just acquire a p term, and x gets replaced by the midpoint position.Comment: 24 pages, 2 figures, RevTeX style, typos correcte

Finite temperature spectral function of Mott insulators and CDW States

We calculate the low temperature spectral function of one-dimensional incommensurate charge density wave (CDW) states and half-filled Mott insulators (MI). At $T=0$ there are two dispersing features associated with the spin and charge degrees of freedom respectively. We show that already at very low temperatures (compared to the gap) one of these features gets severely damped. We comment on implications of this result for photoemission experiments.Comment: 4 pages, 2 figures, published versio

The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity

The recently proposed Russian doll BCS model provides a simple example of a many body system whose renormalization group analysis reveals the existence of limit cycles in the running coupling constants of the model. The model was first studied using RG, mean field and numerical methods showing the Russian doll scaling of the spectrum, E(n) ~ E0 exp(-l n}, where l is the RG period. In this paper we use the recently discovered exact solution of this model to study the low energy spectrum. We find that, in addition to the standard quasiparticles, the electrons can bind into Cooper pairs that are different from those forming the condensate and with higher energy. These excited Cooper pairs can be described by a quantum number Q which appears in the Bethe ansatz equation and has a RG interpretation.Comment: 36 pages, 12 figure

Quantum statistical mechanics of gases in terms of dynamical filling fractions and scattering amplitudes

We develop a finite temperature field theory formalism in any dimension that has the filling fractions as the basic dynamical variables. The formalism efficiently decouples zero temperature dynamics from the quantum statistical sums. The zero temperature `data' is the scattering amplitudes. A saddle point condition leads to an integral equation which is similar in spirit to the thermodynamic Bethe ansatz for integrable models, and effectively resums infinite classes of diagrams. We present both relativistic and non-relativistic versions