arXiv subjects

Gerald Dunne

Publications and source records attributed to Gerald Dunne.

At least 19 recordsLinked to original sources

arXiv2021

Uniformizing Lee-Yang Singularities

Motivated by the search for the QCD critical point, we discuss how to obtain the singular behavior of a thermodynamic system near a critical point, namely the Lee-Yang singularities, from a limited amount of local data generated in a different region of the phase diagram. We show that by using a limited number of Taylor series coefficients, it is possible to reconstruct the equation of state past the radius of convergence, in particular in the critical region. Furthermore we also show that it is possible to extend this reconstruction to go from a crossover region to the first-order transition region in the phase diagram, using a uniformizing map to pass between Riemann sheets. We illustrate these ideas via the Chiral Random Matrix Model and the Ising Model.

hep-th↗

arXiv2018

Fractal AC circuits and propagating waves on fractals

We extend Feynman's analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the individual impedances inside the circuit are purely imaginary. This provides a physical setting for analyzing wave propagation of signals on fractals, by analogy with the Telegrapher's Equation, and generalizes the real resistance metric on a fractal, which provides a measure of distance on a fractal, to complex impedances.

math-ph↗

arXiv2012

Wave propagation in one-dimension: Methods and applications to complex and fractal structures

This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We present examples for transport through finite-sized layered dielectric systems with periodic, quasi-periodic, fractal, disordered, and random structure, illustrating how can spatial structure affect the spectrum of modes as well as the local mode intensity.

physics.optics↗

arXiv2012

Spatial Log Periodic Oscillations of First-Passage Observables in Fractals

For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For transport in self-similar fractal structures, we obtain a new expression for the source-target distance dependence of the MFPT that exhibits both the leading power law behavior, depending on the Hausdorff and spectral dimension of the fractal, as well as small log periodic oscillations that are a clear and definitive signal of the underlying fractal structure. We also present refined numerical results for the Sierpinski gasket that confirm this oscillatory behavior.

cond-mat.stat-mech↗

arXiv2009

Worldline Monte Carlo for fermion models at large N_f

Strongly-coupled fermionic systems can support a variety of low-energy phenomena, giving rise to collective condensation, symmetry breaking and a rich phase structure. We explore the potential of worldline Monte Carlo methods for analyzing the effective action of fermionic systems at large flavor number N_f, using the Gross-Neveu model as an example. Since the worldline Monte Carlo approach does not require a discretized spacetime, fermion doubling problems are absent, and chiral symmetry can manifestly be maintained. As a particular advantage, fluctuations in general inhomogeneous condensates can conveniently be dealt with analytically or numerically, while the renormalization can always be uniquely performed analytically. We also critically examine the limitations of a straightforward implementation of the algorithms, identifying potential convergence problems in the presence of fermionic zero modes as well as in the high-density region.

hep-th↗

arXiv2008

Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls

We extend our previous results of simplified expressions for functional determinants for radial Schrödinger operators to the computation of vacuum energy, or mass corrections, for static but spatially radial backgrounds, and for domain wall configurations. Our method is based on the zeta function approach to the Gel'fand-Yaglom theorem, suitably extended to higher dimensional systems on separable manifolds. We find new expressions that are easy to implement numerically, for both zero and nonzero temperature.

hep-th↗

arXiv2008

Dynamically assisted Schwinger mechanism

We study electron-positron pair creation {from} the Dirac vacuum induced by a strong and slowly varying electric field (Schwinger effect) which is superimposed by a weak and rapidly changing electromagnetic field (dynamical pair creation). In the sub-critical regime where both mechanisms separately are strongly suppressed, their combined impact yields a pair creation rate which is {dramatically} enhanced. Intuitively speaking, the strong electric field lowers the threshold for dynamical particle creation -- or, alternatively, the fast electromagnetic field generates additional seeds for the Schwinger mechanism. These findings could be relevant for planned ultra-high intensity lasers.

hep-th↗

arXiv2007

Worldline Approach to Chiral Fermions

We propose to apply ``worldline numerics'' to a numerical calculation of quark determinants. The Gross-Neveu model with a U(1) chiral symmetry is considered as a first test. The worldline approach allows for an analytic renormalisation, and only finite parts of the determinant require a numerical calculation. It is shown that the discretisation of the worldlines, which is central to the numerical treatment, preserves chiral symmetry exactly. Numerical results for a kink configuration as a scalar background field are shown and compared with analytical results. The case of finite fermion chemical potential is also briefly discussed.

hep-lat↗

arXiv2001

Deconfining Phase Transition in 2+1 D: the Georgi-Glashow Model

We analyze the finite temperature deconfining phase transition in 2+1 dimensional Georgi-Glashow model. We show explicitly that the transition is due to the restoration of the magnetic $Z_2$ symmetry and that it is in the Ising universality class. We find that neglecting effects of the charged $W$ bosons leads to incorrect predictions for the value of the critical temperature and the universality class of the transition, as well as for various correlation functions in the high temperature phase. We derive the effective action for the Polyakov loop in the high temperature phase and calculate the correlation functions of magnetic vortex operators.

hep-th↗

arXiv2000

Magnetic Symmetries and Vortices In Chern-Simons Theories

We study the locality properties of the vortex operators in compact U(1) Maxwell-Chern-Simons and SU(N) Yang-Mills-Chern-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically UV divergent. Nevertheless the classical analysis shows that at small values of CS coefficient $κ$ the vortices become light. It is conceivable that they in fact become massless and condense due to quantum effects below some small $κ$. If this happens the magnetic symmetry breaks spontaneously and the theory is confining.

hep-th↗

arXiv2000

Finite Temperature Effective Action in Monopole Background

We compute the CP-odd part of the finite temperature effective action for massive Dirac fermions in the presence of a Dirac monopole. We confirm that the induced charge is temperature dependent, and in the effective action we find an infinite series of CP-violating terms that generalize the familiar zero temperature $F\tilde{F}$ term. These results are analogous to recent results concerning finite temperature induced Chern-Simons terms.

hep-th↗

arXiv1999

Large Gauge Ward Identity

We study the question of the Ward identity for "large" gauge invariance in 0+1 dimensional theories. We derive the relevant Ward identities for a single flavor fermion and a single flavor complex scalar field interacting with an Abelian gauge field. These identities are nonlinear. The Ward identity for any other complicated theory can be derived from these basic sets of identities. However, the structure of the Ward identity changes since these are nonlinear identities. In particular, we work out the "large" gauge Ward identity for a supersymmetric theory involving a single flavor of fermion as well as a complex scalar field. Contrary to the effective action for the individual theories, the solution of the Ward identity in the supersymmetric theory involves an infinity of Fourier component modes. We comment on which features of this analysis are likely/unlikely to generalize to the 2+1 dimensional theory.

hep-th↗

arXiv1999

Non-static Dimensional Reduction of QED_3 at Finite Temperature

We study an extreme non-static limit of 2+1-dimensional QED obtained by making a dimensional reduction so that all fields are spatially uniform but time dependent. This dimensional reduction leads to a 0+1-dimensional field theory that inherits many of the features of the 2+1-dimensional model, such as Chern-Simons terms, time-reversal violation, an analogue of parity violation, and global U(2) flavor symmetry. At one-loop level, interactions induce a Chern-Simons term at finite T with coefficient tanh(beta m_F/2), where m_F is the fermion mass. The finite temperature two loop self-energies are also computed, and are non-zero for all temperatures.

hep-th↗

arXiv1998

On the QED Effective Action in Time Dependent Electric Backgrounds

We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds. The effective action has both real and imaginary parts, and the imaginary part is related to the pair production probability in such a background. The resolvent technique has been applied previously to spatially inhomogeneous magnetic backgrounds, for which the effective action is real. We explain how dispersion relations connect these two cases, the magnetic case which is essentially perturbative in nature, and the electric case where the imaginary part is nonperturbative. Finally, we use a uniform semiclassical approximation to find an expression for very general time dependence for the background field. This expression is remarkably similar in form to Schwinger's classic result for the constant electric background.

hep-th↗

arXiv1997

Finite Temperature Perturbation Theory and Large Gauge Invariance

We examine finite temperature perturbation theory for Chern-Simons theories, in the context of an analogue 0+1-dimensional model. In particular, we show how nonextensive terms arise in the perturbative finite temperature effective action, using both the real-time and imaginary-time formalisms. We illustrate how large gauge invariance is restored at all orders, despite being broken at any given order in perturbation theory. We discuss which aspects generalize to a perturbative analysis of finite temperature Chern-Simons terms in higher dimensions.

hep-th↗

arXiv1997

Planar QED in Magnetic or Electric Solitonic Backgrounds

We review the resolvent technique for computing the effective action in planar QED. For static magnetic backgrounds the effective action yields (minus) the effective energy of the fermions, while for electric backgrounds the imaginary part of the effective action gives (half) the probability of fermion-antifermion pair creation. For some special `solitonic' background profiles, these effective actions can be computed exactly.

hep-th↗

arXiv1997

An Exact QED_{3+1} Effective Action

We compute the exact QED_{3+1} effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. An asymptotic expansion of this exact effective action yields an all-orders derivative expansion, the first terms of which agree with independent derivative expansion computations. These results generalize analogous earlier results by Cangemi et al in QED_{2+1}.

hep-th↗

arXiv1997

Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics

We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast to the standard nonperiodic case where either one or neither (but not both) of the isospectral pair has a zero mode. Thus it is possible to have supersymmetry unbroken and yet also have a vanishing Witten index. We present some explicit exactly soluble examples for which the isospectral potentials have identical band spectra, and which are ``self-isospectral'' in the sense that the potentials have identical shape, but are translated by one half period relative to one another.

hep-th↗