Ginzburg-Landau Theory for the Jaynes-Cummings-Hubbard Model

We develop a Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model which effectively describes both static and dynamic properties of photons evolving in a cubic lattice of cavities, each filled with a two-level atom. To this end we calculate the effective action to first-order in the hopping parameter. Within a Landau description of a spatially and temporally constant order parameter we calculate the finite-temperature mean-field quantum phase boundary between a Mott insulating and a superfluid phase of polaritons. Furthermore, within the Ginzburg-Landau description of a spatio-temporal varying order parameter we determine the excitation spectra in both phases and, in particular, the sound velocity of light in the superfluid phase

A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this new method are studied and it is then applied to the calculation of relevant quantities in different $\phi^4$ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein Condensation temperature shift $\Delta T_c$ recently investigated by various authors. Our present estimates of $\Delta T_c$, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.Comment: 9 pages, no figures. v2: minor wording changes in title/abstract, to appear in Phys.Rev.

Sine-Gordon Field Theory for the Kosterlitz-Thouless Transitions on Fluctuating Membranes

In the preceding paper, we derived Coulomb-gas and sine-Gordon Hamiltonians to describe the Kosterlitz-Thouless transition on a fluctuating surface. These Hamiltonians contain couplings to Gaussian curvature not found in a rigid flat surface. In this paper, we derive renormalization-group recursion relations for the sine-Gordon model using field-theoretic techniques developed to study flat space problems.Comment: REVTEX, 14 pages with 6 postscript figures compressed using uufiles. Accepted for publication in Phys. Rev.

Global Anomalies in the Batalin Vilkovisky Quantization

The Batalin Vilkovisky (BV) quantization provides a general procedure for calculating anomalies associated to gauge symmetries. Recent results show that even higher loop order contributions can be calculated by introducing an appropriate regularization-renormalization scheme. However, in its standard form, the BV quantization is not sensible to quantum violations of the classical conservation of Noether currents, the so called global anomalies. We show here that the BV field antifield method can be extended in such a way that the Ward identities involving divergencies of global Abelian currents can be calculated from the generating functional, a result that would not be obtained by just associating constant ghosts to global symmetries. This extension, consisting of trivially gauging the global Abelian symmetries, poses no extra obstruction to the solution of the master equation, as it happens in the case of gauge anomalies. We illustrate the procedure with the axial model and also calculating the Adler Bell Jackiw anomaly.Comment: We emphasized the fact that our procedure only works for the case of Abelian global anomalies. Section 3 was rewritten and some references were added. 12 pages, LATEX. Revised version that will appear in Phys. Rev.

Langevin dynamics of the Lebowitz-Percus model

We revisit the hard-spheres lattice gas model in the spherical approximation proposed by Lebowitz and Percus (J. L. Lebowitz, J. K. Percus, Phys. Rev.{\ 144} (1966) 251). Although no disorder is present in the model, we find that the short-range dynamical restrictions in the model induce glassy behavior. We examine the off-equilibrium Langevin dynamics of this model and study the relaxation of the density as well as the correlation, response and overlap two-time functions. We find that the relaxation proceeds in two steps as well as absence of anomaly in the response function. By studying the violation of the fluctuation-dissipation ratio we conclude that the glassy scenario of this model corresponds to the dynamics of domain growth in phase ordering kinetics.Comment: 21 pages, RevTeX, 14 PS figure

Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results

We consider systems confined to a $d$-dimensional slab of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$ and are describable by an O(n) symmetrical Hamiltonian. Periodic boundary conditions are applied across the slab. We study the effects of long-range pair interactions whose potential decays as $b x^{-(d+\sigma)}$ as $x\to\infty$, with $2<\sigma<4$ and $2<d+\sigma\leq 6$, on the Casimir effect at and near the bulk critical temperature $T_{c,\infty}$, for $2<d<4$. For the scaled reduced Casimir force per unit cross-sectional area, we obtain the form L^{d} {\mathcal F}_C/k_BT \approx \Xi_0(L/\xi_\infty) + g_\omega L^{-\omega}\Xi\omega(L/\xi_\infty) + g_\sigma L^{-\omega_\sigm a} \Xi_\sigma(L \xi_\infty). The contribution $\propto g_\sigma$ decays for $T\neq T_{c,\infty}$ algebraically in $L$ rather than exponentially, and hence becomes dominant in an appropriate regime of temperatures and $L$. We derive exact results for spherical and Gaussian models which confirm these findings. In the case $d+\sigma =6$, which includes that of nonretarded van-der-Waals interactions in $d=3$ dimensions, the power laws of the corrections to scaling $\propto b$ of the spherical model are found to get modified by logarithms. Using general RG ideas, we show that these logarithmic singularities originate from the degeneracy $\omega=\omega_\sigma=4-d$ that occurs for the spherical model when $d+\sigma=6$, in conjunction with the $b$ dependence of $g_\omega$.Comment: 28 RevTeX pages, 12 eps figures, submitted to PR

Effects of surfaces on resistor percolation

We study the effects of surfaces on resistor percolation at the instance of a semi-infinite geometry. Particularly we are interested in the average resistance between two connected ports located on the surface. Based on general grounds as symmetries and relevance we introduce a field theoretic Hamiltonian for semi-infinite random resistor networks. We show that the surface contributes to the average resistance only in terms of corrections to scaling. These corrections are governed by surface resistance exponents. We carry out renormalization group improved perturbation calculations for the special and the ordinary transition. We calculate the surface resistance exponents \phi_{\mathcal S \mathnormal} and \phi_{\mathcal S \mathnormal}^\infty for the special and the ordinary transition, respectively, to one-loop order.Comment: 19 pages, 3 figure

Dynamics and geometric properties of the k-Trigonometric model

We analyze the dynamics and the geometric properties of the Potential Energy Surfaces (PES) of the k-Trigonometric Model (kTM), defined by a fully-connected k-body interaction. This model has no thermodynamic transition for k=1, a second order one for k=2, and a first order one for k>2. In this paper we i) show that the single particle dynamics can be traced back to an effective dynamical system (with only one degree of freedom); ii) compute the diffusion constant analytically; iii) determine analytically several properties of the self correlation functions apart from the relaxation times which we calculate numerically; iv) relate the collective correlation functions to the ones of the effective degree of freedom using an exact Dyson-like equation; v) using two analytical methods, calculate the saddles of the PES that are visited by the system evolving at fixed temperature. On the one hand we minimize |grad V|^2, as usually done in the numerical study of supercooled liquids and, on the other hand, we compute the saddles with minimum distance (in configuration space) from initial equilibrium configurations. We find the same result from the two calculations and we speculate that the coincidence might go beyond the specific model investigated here.Comment: 36 pages, 13 figure

Thermal properties of spacetime foam

Spacetime foam can be modeled in terms of nonlocal effective interactions in a classical nonfluctuating background. Then, the density matrix for the low-energy fields evolves, in the weak-coupling approximation, according to a master equation that contains a diffusion term. Furthermore, it is argued that spacetime foam behaves as a quantum thermal field that, apart from inducing loss of coherence, gives rise to effects such as gravitational Lamb and Stark shifts as well as quantum damping in the evolution of the low-energy observables. These effects can be, at least in principle, experimentally tested.Comment: RevTeX 3.01, 11 pages, no figure

Matrix product approach for the asymmetric random average process

We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called beta densities, of all local interactions leading to steady states of product measure form are rigorously derived. This also completes an outstanding proof given in a previous publication. Then, we present an alternative solution for the processes with factorized stationary states by using a matrix product ansatz. Due to continuous state variables we obtain a matrix algebra in form of a functional equation which can be solved exactly.Comment: 17 pages, 1 figur