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C. A. A. de Carvalho

Publications and source records attributed to C. A. A. de Carvalho.

At least 37 records · Page 2Linked to original sources
arXiv2004

Correlations around an interface

We compute one-loop correlation functions for the fluctuations of an interface using a field theory model. We obtain them from Feynman diagrams drawn with a propagator which is the inverse of the Hamiltonian of a Poschl-Teller problem. We derive an expression for the propagator in terms of elementary functions, show that it corresponds to the usual spectral sum, and use it to calculate quantities such as the surface tension and interface profile in two and three spatial dimensions. The three-dimensional quantities are rederived in a simple, unified manner, whereas those in two dimensions extend the existing literature, and are applicable to thin films. In addition, we compute the one-loop self-energy, which may be extracted from experiment, or from Monte Carlo simulations. Our results may be applied in various scenarios, which include fluctuations around topological defects in cosmology, supersymmetric domain walls, Z(N) bubbles in QCD, domain walls in magnetic systems, interfaces separating Bose-Einstein condensates, and interfaces in binary liquid mixtures.

hep-ph↗
arXiv2003

Alternative dimensional reduction via the density matrix: A test

We derive and analyze the perturbation series for the classical effective action in quantum statistical mechanics, treated as a toy model for the dimensionally reduced effective action in quantum field theory at finite temperature. The first few terms of the series are computed for the harmonic oscillator and the quartic potential.

hep-th↗
arXiv2002

Improved semiclassical density matrix: taming caustics

We present a simple method to deal with caustics in the semiclassical approximation to the thermal density matrix of a particle moving on the line. For simplicity, only its diagonal elements are considered. The only ingredient we require is the knowledge of the extrema of the Euclidean action. The procedure makes use of complex trajectories, and is applied to the quartic double-well potential.

quant-ph↗
arXiv2001

Alternative Dimensional Reduction via the Density Matrix

We give graphical rules, based on earlier work for the functional Schrodinger equation, for constructing the density matrix for scalar and gauge fields at finite temperature T. More useful is a dimensionally-reduced effective action (DREA) constructed from the density matrix by further functional integration over the arguments of the density matrix coupled to a source. The DREA is an effective action in one less dimension which may be computed order by order in perturbation theory or by dressed-loop expansions; it encodes all thermal matrix elements. The DREA is useful because it gives a dimensionally-reduced field theory usable at any T including infinity, where it yields the usual dimensionally-reduced field theory (DRFT). However, it cannot and does not have spurious infinities which sometimes occur in the density matrix or the DRFT; these come from ln T factors at infinite temperature. An example of spurious divergences in the DRFT occurs in d 2+1 $ϕ^4$ theory dimensionally reduced to d=2. We show that the rules for the DREA replace these "wrong" divergences in physical parameters by calculable powers of ln T; we also compute the phase transition temperature of this theory at one loop order.

hep-th↗
arXiv2000

On the effectiveness of Gamow's method for calculating decay rates

We examine Gamow's method for calculating the decay rate of a wave function initially located within a potential well. Using elementary techniques, we examine a very simple, exactly solvable model, in order to show why it is so reliable for calculating decay rates, in spite of its conceptual problems. We also discuss the regime of validity of the exponential decay law.

quant-ph↗
arXiv2000

Semiclassical approximation to the partition function of a particle in D dimensions

We use a path integral formalism to derive the semiclassical series for the partition function of a particle in D dimensions. We analyze in particular the case of attractive central potentials, obtaining explicit expressions for the fluctuation determinant and for the semiclassical two-point function in the special cases of the harmonic and single-well quartic anharmonic oscillators. The specific heat of the latter is compared to precise WKB estimates. We conclude by discussing the possible extension of our results to field theories.

quant-ph↗
arXiv1999

Semiclassical Series from Path Integrals

We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a simple derivation of the exact result for the harmonic oscillator, and an accurate estimate of ground-state energy and specific heat for a single-well quartic anharmonic oscillator. As QSM can be regarded as finite temperature field theory at a point, we make use of Feynman diagrams to illustrate the non-perturbative character of the series: it contains all powers of $\hbar$ and graphs with any number of loops; the usual perturbative series corresponds to a subset of the diagrams of the semiclassical series. We comment on the application of our results to other potentials, to correlation functions and to field theories in higher dimensions.

quant-ph↗
arXiv1999

Dynamical Viscosity of Nucleating Bubbles

We study the viscosity corrections to the growth rate of nucleating bubbles in a first order phase transition in scalar field theory. We obtain the non-equilibrium equation of motion of the coordinate that describes small departures from the critical bubble and extract the growth rate consistently in weak coupling and in the thin wall limit. Viscosity effects arise from the interaction of this coordinate with the stable quantum and thermal fluctuations around a critical bubble. In the case of 1+1 dimensions we provide an estimate for the growth rate that depends on the details of the free energy functional. In 3+1 dimensions we recognize robust features that are a direct consequence of the thin wall approximation and give the leading viscosity corrections.These are long-wavelength hydrodynamic fluctuations that describe surface waves, quasi-Goldstone modes which are related to ripples on interfaces in phase ordered Ising-like systems. We discuss the applicability of our results to describe the growth rate of hadron bubbles in a quark-hadron first order transition.

hep-ph↗
arXiv1999

Two-dimensional electron gas in a uniform magnetic field in the presence of a delta-impurity

The density of states and the Hall conductivity of a two-dimensional electron gas in a uniform magnetic field and in the presence of a delta impurity are exactly calculated using elementary field theoretic techniques. Although these results are not new, our treatment is explicitly gauge-invariant, and can be easily adapted to other problems involving a delta potential.

cond-mat.mes-hall↗
arXiv1999

The weakly disordered 2D electron gas in a magnetic field

We study a relativistic two-dimensional free electron gas in the presence of a uniform external magnetic field and a random static scalar potential. We compute the expectation values of the charge density and the conductivity tensor, averaged over the random potential in first order perturbation theory. We discuss the effect of a zero vs. finite range correlation length of the random potential.

hep-th↗
arXiv1998

Semiclassical Series at Finite Temperature

We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral representation of the partition function, and we present a systematic procedure to generate the terms of the series using the minima of the Euclidean action as the only input. For the particular case of a quartic anharmonic oscillator, we compute the first two terms of the series, and investigate their high and low temperature limits. We also exhibit the nonperturbative character of the terms, as each corresponds to sums over infinite subsets of perturbative graphs. We illustrate the power of such resummations by extracting from the first term an accurate nonperturbative estimate of the ground-state energy of the system and a curve for the specific heat. We conclude by pointing out possible extensions of our results which include field theories with spherically symmetric classical solutions.

quant-ph↗
arXiv1998

Bound states of a spin-1/2 charged particle in a magnetic flux tube

We study a spin-1/2 charged particle with gyromagnetic factor g>2 moving in a plane threaded by a magnetic flux tube. We prove that, if the magnetic field (i) has radial symmetry, (ii) has compact support and (iii) does not change sign, there is at least one bound state for each angular momentum l in the interval [0,v], where v (assumed positive) is the total magnetic flux in units of the quantum of flux.

quant-ph↗
arXiv1998

Semiclassical Statistical Mechanics

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema and use it to compute the fluctuation determinant and to develop a (nonperturbative) semiclassical expansion which allows for the calculation of correlation functions. We discuss the examples of the single and double-well quartic anharmonic oscillators, and the implications of our results for higher dimensions.

quant-ph↗
arXiv1998

Perturbative Evidence of Non-Universality in the Quantized Hall Conductivity of a Disordered Relativistic 2D Electron Gas

We study a relativistic two-dimensional electron gas in the presence of a uniform external magnetic field and a random static scalar potential. We compute, in first order perturbation theory, the averages of the charge density and of the transverse conductivity for a white-noise potential, and show that, within this treatment, their quantized values are modified by the disorder.

cond-mat.mes-hall↗
arXiv1998

Tunneling catastrophes of the partition function

We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the potential. For high temperatures, the semiclassical expression is dominated by single closed paths. As we lower the temperature, new closed paths may appear, including tunneling paths. The transition from single to multiple-path regime corresponds to well-defined catastrophes. Tunneling sets in whenever they occur. Our formula fully accounts for this feature.

quant-ph↗
arXiv1997

Subtleties in Quantum Mechanical Metastability

We present a detailed discussion of some features of quantum mechanical metastability. We analyze the nature of decaying (quasistationary) states and the regime of validity of the exponencial law, as well as decays at finite temperature. We resort to very simple systems and elementary techniques to emphasize subtle aspects of the problem.

quant-ph↗
arXiv1997

Electron localization by a magnetic vortex

We study the problem of an electron in two dimensions in the presence of a magnetic vortex with a step-like profile. Dependending on the values of the effective mass and gyromagnetic factor of the electron, it may be trapped by the vortex. The bound state spectrum is obtained numerically, and some limiting cases are treated analytically.

cond-mat↗