arXiv subjects

Luis M. A. Bettencourt

Publications and source records attributed to Luis M. A. Bettencourt.

43 records · Page 3Linked to original sources

arXiv1998

Time evolution of correlation functions for classical and quantum anharmonic oscillators

The time evolution of the correlation functions of an ensemble of anharmonic N-component oscillators with O(N) symmetry is described by a flow equation, exact up to corrections of order $1/N^2$. We find effective irreversibility. Nevertheless, analytical and numerical investigation reveals that the system does not reach thermal equilibrium for large times, even when $N\to \infty$. Depending on the initial distribution, the dynamics is asymptotically stable or it exhibits growing modes which break the conditions for the validity of the 1/N expansion for large time. We investigate both classical and quantum systems, the latter being the limit of an O(N) symmetric scalar quantum field theory in zero spatial dimensions.

hep-ph↗

arXiv1997

Time evolution of correlation functions in Non-equilibrium Field Theories

We investigate the non-equilibrium properties of an N-component scalar field theory. The time evolution of the correlation functions for an arbitrary ensemble of initial conditions is described by an exact functional differential equation. In leading order in the 1/N expansion the system can be understood in terms of infinitely many conserved quantities. They forbid the approach to the canonical thermal distribution. Beyond leading order only energy conservation is apparent generically. Nevertheless, we find a large manifold of stationary distributions both for classical and quantum fields. They are the fixed points of the evolution equation. For small deviations of the correlation functions from a large range of fixed points we observe stable oscillations. These results raise the question of if and in what sense the particular fixed point corresponding to thermal equilibrium dominates the large time behavior of the system.

hep-ph↗

arXiv1997

The Thermodynamics of Cosmic String densities in U(1) Scalar Field Theory

We present a full characterization of the phase transition in U(1) scalar field theory and of the associated vortex string thermodynamics in 3D. We show that phase transitions in the string densities exist and measure their critical exponents, both for the long string and the short loops. Evidence for a natural separation between these two string populations is presented. In particular our results strongly indicate that an infinite string population will only exist above the critical temperature. Canonical initial conditions for cosmic string evolution are show to correspond to the infinite temperature limit of the theory.

hep-ph↗

arXiv1997

Non-intercommuting Cosmic Strings

We perform the numerical field evolution for the collision of two Abelian type I cosmic strings. We present evidence that, for collisions at small but characteristic relative velocities and angles, these cosmic strings do not exchange ends and separate. Rather, local higher winding number bound states are formed close to the collision point, which promote multiple local scatterings at right angles and prevent intercommutation from happening. This constitutes the simplest example of the breakdown of the intercommutation rule, usually assumed in the construction of effective models for cosmic string network evolution.

hep-ph↗

arXiv1996

Multiple-Scale Analysis of Quantum Systems

Conventional weak-coupling Rayleigh-Schrödinger perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale analysis, a powerful and sophisticated perturbative method that quantitatively analyzes characteristic physical behaviors occurring on various length or time scales, avoids such problems by implicitly performing an infinite resummation of the conventional perturbation series. Multiple-scale perturbation theory provides a good description of the classical anharmonic oscillator. Here, it is extended to study (1) the Heisenberg operator equations of motion and (2) the Schrödinger equation for the quantum anharmonic oscillator. In the former case, it leads to a system of coupled operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory. In the latter case, multiple-scale analysis elucidates the connection between weak-coupling perturbative and semiclassical nonperturbative aspects of the wave function.

hep-th↗

arXiv1996

Multiple-Scale Analysis of the Quantum Anharmonic Oscillator

Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an infinite reordering and resummation of the conventional perturbation series. Multiple-scale analysis provides a good description of the classical anharmonic oscillator. Here, it is extended to study the Heisenberg operator equations of motion for the quantum anharmonic oscillator. The analysis yields a system of nonlinear operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory.

hep-th↗

arXiv1995

Coarse-Grained Fluctuation Probabilities in the Standard Model and Subcritical Bubbles

We compute systematically the probability for fluctuations of the Higgs field, averaged over a given spatial scale, to exceed a specified value, in the Standard Model. For the particular case of interest of averages over one coherence volume we show that, even in the worst possible case of taking the one-loop improved effective potential parameters, the probability for the field to fluctuate from the symmetric to the asymmetric minimum before the latter becomes stable is very small for Higgs masses of the order of those of the $W$ and $Z$ bosons, whereas the converse is more likely. As such, metastability should be satisfied dynamically at the Electroweak phase transition and its dynamics should therefore proceed by the usual mechanism of bubble nucleation with subcritical fluctuations playing no particularly relevant role in it.

hep-ph↗