Phase Equilibration and Magnetic Field Generation in U(1) Bubble Collisions

We present the results of lattice computations of collisions of two expanding bubbles of true vacuum in the Abelian Higgs model with a first-order phase transition. New time-dependent analytical solutions for the Abelian field strength and the phase of the complex field are derived from initial conditions inferred from linear superposition and are shown to be in excellent agreement with the numerical solutions especially for the case where the initial phase difference between the bubbles is small. With a step-function approximation for the initial phase of the complex field, solutions for the Abelian field strength and other gauge-invariant quantities are obtained in closed form. Possible extensions of the solution to the case of the electroweak phase transition and the generation of primordial magnetic fields are briefly discussed.Comment: LaTeX, 41 pages, 6 figures, submitted to Physical Review

Auxiliary particle theory of threshold singularities in photoemission and X-ray absorption spectra: Test of a conserving T-matrix approximation

We calculate the exponents of the threshold singularities in the photoemission spectrum of a deep core hole and its X-ray absorption spectrum in the framework of a systematic many-body theory of slave bosons and pseudofermions (for the empty and occupied core level). In this representation, photoemission and X-ray absorption can be understood on the same footing; no distinction between orthogonality catastrophe and excitonic effects is necessary. We apply the conserving slave particle T-matrix approximation (CTMA), recently developed to describe both Fermi and non-Fermi liquid behavior systems with strong local correlations, to the X-ray problem as a test case. The numerical results for both photoemission and X-ray absorption are found to be in agreement with the exact infrared powerlaw behavior in the weak as well as in the strong coupling regions. We point out a close relation of the CTMA with the parquet equation approach of Nozi{\`e}res et al.Comment: 10 pages, 9 figures, published versio

Bosonization in Particle Physics

Path integral techniques in collective fields are shown to be a useful analytical tool to reformulate a field theory defined in terms of microscopic quark (gluon) degrees of freedom as an effective theory of collective boson (meson) fields. For illustrations, the path integral bosonization approach is applied to derive a (non)linear sigma model from a Nambu-Jona-Lasinio (NJL) quark model. The method can be extended to include higher order derivative terms in meson fields or heavy-quark symmetries. It is also approximately applicable to QCD.Comment: 12 pages, LaTeX, uses lamuphys.sty, 5 LaTeX figures, talk given at the Workshop "Field Theoretical Tools in Polymer and Particle Physics", University Wuppertal, June 17-19, 199

First-order cosmological phase transitions in the radiation dominated era

We consider first-order phase transitions of the Universe in the radiation-dominated era. We argue that in general the velocity of interfaces is non-relativistic due to the interaction with the plasma and the release of latent heat. We study the general evolution of such slow phase transitions, which comprise essentially a short reheating stage and a longer phase equilibrium stage. We perform a completely analytical description of both stages. Some rough approximations are needed for the first stage, due to the non-trivial relations between the quantities that determine the variation of temperature with time. The second stage, instead, is considerably simplified by the fact that it develops at a constant temperature, close to the critical one. Indeed, in this case the equations can be solved exactly, including back-reaction on the expansion of the Universe. This treatment also applies to phase transitions mediated by impurities. We also investigate the relations between the different parameters that govern the characteristics of the phase transition and its cosmological consequences, and discuss the dependence of these parameters with the particle content of the theory.Comment: 38 pages, 3 figures; v2: Minor changes, references added; v3: several typos correcte

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution

The self-consistent bounce: an improved nucleation rate

We generalize the standard computation of homogeneous nucleation theory at zero temperature to a scenario in which the bubble shape is determined self-consistently with its quantum fluctuations. Studying two scalar models in 1+1 dimensions, we find the self-consistent bounce by employing a two-particle irreducible (2PI) effective action in imaginary time at the level of the Hartree approximation. We thus obtain an effective single bounce action which determines the rate exponent. We use collective coordinates to account for the translational invariance and the growth instability of the bubble and finally present a new nucleation rate prefactor. We compare the results with those obtained using the standard 1-loop approximation and show that the self-consistent rate can differ by several orders of magnitude.Comment: 28 pages, revtex, 7 eps figure

Magnetic monopoles from gauge theory phase transitions

Thermal fluctuations of the gauge field lead to monopole formation at the grand unified phase transition in the early Universe, even if the transition is merely a smooth crossover. The dependence of the produced monopole density on various parameters is qualitatively different from theories with global symmetries, and the monopoles have a positive correlation at short distances. The number density of monopoles may be suppressed if the grand unified symmetry is only restored for a short time by, for instance, nonthermal symmetry restoration after preheating.Comment: 5 pages, updated to match the version published in PRD (http://link.aps.org/abstract/PRD/v68/e021301) on 11 July 200

Ghost Condensation and a Consistent Infrared Modification of Gravity

We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of Higgs mechanism in general relativity, and can be thought of as arising from ghost condensation--a background where a scalar field \phi has a constant velocity, = M^2. The ghost condensate is a new kind of fluid that can fill the universe, which has the same equation of state, \rho = -p, as a cosmological constant, and can hence drive de Sitter expansion of the universe. However, unlike a cosmological constant, it is a physical fluid with a physical scalar excitation, which can be described by a systematic effective field theory at low energies. The excitation has an unusual low-energy dispersion relation \omega^2 \sim k^4 / M^2. If coupled to matter directly, it gives rise to small Lorentz-violating effects and a new long-range 1/r^2 spin dependent force. In the ghost condensate, the energy that gravitates is not the same as the particle physics energy, leading to the possibility of both sources that can gravitate and antigravitate. The Newtonian potential is modified with an oscillatory behavior starting at the distance scale M_{Pl}/M^2 and the time scale M_{Pl}^2/M^3. This theory opens up a number of new avenues for attacking cosmological problems, including inflation, dark matter and dark energy.Comment: 42 pages, LaTeX 2

AMPK is essential for energy homeostasis regulation and glucose sensing by POMC and AgRP neurons

Hypothalamic AMP-activated protein kinase (AMPK) has been suggested to act as a key sensing mechanism, responding to hormones and nutrients in the regulation of energy homeostasis. However, the precise neuronal populations and cellular mechanisms involved are unclear. The effects of long-term manipulation of hypothalamic AMPK on energy balance are also unknown. To directly address such issues, we generated POMC alpha 2KO and AgRP alpha 2KO mice lacking AMPK alpha 2 in proopiomelanocortin- (POMC-) and agouti-related protein-expressing (AgRP-expressing) neurons, key regulators of energy homeostasis. POMC alpha 2KO mice developed obesity due to reduced energy expenditure and dysregulated food intake but remained sensitive to leptin. in contrast, AgRPa2KO mice developed an age-dependent lean phenotype with increased sensitivity to a melanocortin agonist. Electrophysiological studies in AMPK alpha 2-deficient POMC or AgRP neurons revealed normal leptin or insulin action but absent responses to alterations in extracellular glucose levels, showing that glucose-sensing signaling mechanisms in these neurons are distinct from those pathways utilized by leptin or insulin. Taken together with the divergent phenotypes of POMC alpha 2KO and AgRP alpha 2KO mice, our findings suggest that while AMPK plays a key role in hypothalamic function, it does not act as a general sensor and integrator of energy homeostasis in the mediobasal hypothalamus

Self-consistent quantal treatment of decay rates within the perturbed static path approximation

The framework of the Perturbed Static Path Approximation (PSPA) is used to calculate the partition function of a finite Fermi system from a Hamiltonian with a separable two body interaction. Therein, the collective degree of freedom is introduced in self-consistent fashion through a Hubbard-Stratonovich transformation. In this way all transport coefficients which dominate the decay of a meta-stable system are defined and calculated microscopically. Otherwise the same formalism is applied as in the Caldeira-Leggett model to deduce the decay rate from the free energy above the so called crossover temperature $T_0$.Comment: 17 pages, LaTex, no figures; final version, accepted for publication in PRE; e-mail: [email protected]