Dynamics of particle production by strong electric fields in non-Abelian plasmas

We develop methods for computing the dynamics of fermion pair production by strong color electric fields using the semi-classical Boltzmann-Vlasov equation. We present numerical results for a model with SU(2) symmetry in (1+1) dimension.Comment: 10 pages, 8 figure

Casimir dependence of transverse distribution of pairs produced from a strong constant chromo-electric background field

The transverse distribution of gluon and quark-antiquark pairs produced from a strong constant chromo-electric field depends on two gauge invariant quantities, $C_1=E^aE^a$ and $C_2=[d_{abc}E^aE^bE^c]^2$, as shown earlier in [G.C. Nayak and P. van Nieuwenhuizen, Phys. Rev. D 71, 125001 (2005)] for gluons and in [G.C. Nayak, Phys. Rev. D 72, 125010 (2005)] for quarks. Here, we discuss the explicit dependence of the distribution on the second Casimir invariant, C_2, and show the dependence is at most a 15% effect.Comment: 5 fig

Leading-Order Auxiliary Field Theory of the Bose-Hubbard Model

We discuss the phase diagram of the Bose-Hubbard (BH) model in the leading-order auxiliary field (LOAF) theory. LOAF is a conserving non-perturbative approximation that treats on equal footing the normal and anomalous density condensates. The mean-field solutions in LOAF correspond to first-order and second-order phase transition solutions with two critical temperatures corresponding to a vanishing Bose-Einstein condensate, $T_c$, and a vanishing diatom condensate, $T^\star$. The \emph{second-order} phase transition solution predicts the correct order of the transition in continuum Bose gases. For either solution, the superfluid state is tied to the presence of the diatom condensate related to the anomalous density in the system. In ultracold Bose atomic gases confined on a three-dimensional lattice, the critical temperature $T_c$ exhibits a quantum phase transition, where $T_c$ goes to zero at a finite coupling. The BH phase diagram in LOAF features a line of first-order transitions ending in a critical point beyond which the transition is second order while approaching the quantum phase transition. We identify a region where a diatom condensate is expected for temperatures higher than $T_c$ and less than $T_0$, the critical temperature of the non-interacting system. The LOAF phase diagram for the BH model compares qualitatively well with existing experimental data and results of \emph{ab initio} Monte Carlo simulations.Comment: 10 pages, 6 figure

Supersymmetric approximations to the 3D supersymmetric O(N) model

We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well as in the Hartree approximation, and derive the finite temperature renormalized effective potential. We derive the exact Schwinger-Dyson equations for the superfield Green functions and develop the machinery for going beyond the next to leading order in large-N approximation using a truncation of these equations which can also be derived from a two-particle irreducible effective action.Comment: 16 pages, 3 figure