arXiv subjects

Gerald V. Dunne

Publications and source records attributed to Gerald V. Dunne.

At least 145 records · Page 8Linked to original sources

arXiv2002

Finite Temperature Induced Fermion Number In The Nonlinear sigma Model In (2+1) Dimensions

We compute the finite temperature induced fermion number for fermions coupled to a static nonlinear sigma model background in (2+1) dimensions, in the derivative expansion limit. While the zero temperature induced fermion number is well known to be topological (it is the winding number of the background), at finite temperature there is a temperature dependent correction that is nontopological -- this finite T correction is sensitive to the detailed shape of the background. At low temperature we resum the derivative expansion to all orders, and we consider explicit forms of the background as a CP^1 instanton or as a baby skyrmion.

hep-th↗

arXiv2002

Particle number fractionization of an atomic Fermi-Dirac gas in an optical lattice

We show that a dilute 2-species gas of Fermi-Dirac alkali-metal atoms in a periodic optical lattice may exhibit fractionization of particle number when the two components are coupled via a coherent electromagnetic field with a topologically nontrivial phase profile. This results in fractional eigenvalues of the spin operator with vanishing fluctuations. The fractional part can be accurately controlled by modifying the effective detuning of the electromagnetic field.

cond-mat↗

arXiv2002

Chiral Extrapolation: An Analogy with Effective Field Theory

We draw an analogy between the chiral extrapolation of lattice QCD calculations from large to small quark masses and the interpolation between the large mass (weak field) and small mass (strong field) limits of the Euler--Heisenberg QED effective action. In the latter case, where the exact answer is known, a simple extrapolation of a form analogous to those proposed for the QCD applications is shown to be surprisingly accurate over the entire parameter range.

hep-th↗

arXiv2001

Finite temperature induced fermion number

The induced fractional fermion number at zero temperature is topological (in the sense that it is only sensitive to global asymptotic properties of the background field), and is a sharp observable (in the sense that it has vanishing rms fluctuations). In contrast, at finite temperature, it is shown to be generically nontopological, and not a sharp observable.

hep-th↗

arXiv2001

Non-Abelian Thermal Large Gauge Transformations in 2+1 Dimensions

We discuss several different constructions of non-Abelian large gauge transformations at finite temperature. Pisarski's ansatz with even winding number is related to Hopf mappings, and we present a simple new ansatz that has any integer winding number at finite temperature.

hep-th↗

arXiv2001

Closed-form two-loop Euler-Heisenberg Lagrangian in a self-dual background

We show that the two-loop Euler-Heisenberg effective Lagrangian for scalar QED in a constant Euclidean self-dual background has a simple explicit closed form expression in terms of the digamma function. This result leads to a simple analysis of the weak- and strong-field expansions, the two-loop scalar QED beta function, and the analytic continuation properties of the effective Lagrangian and its imaginary part.

hep-th↗

arXiv2001

Parity Violating Bosonic Loops at Finite Temperature

The finite temperature parity-violating contributions to the polarization tensor are computed at one loop in a system without fermions. The system studied is a Maxwell-Chern-Simons-Higgs system in the broken phase, for which the parity-violating terms are well known at zero temperature. At nonzero temperature the static and long-wavelength limits of the parity violating terms have very different structure, and involve non-analytic log terms depending on the various mass scales. At high temperature the boson loop contribution to the Chern-Simons term goes like T in the static limit and like T log T in the long-wavelength limit, in contrast to the fermion loop contribution which behaves like 1/T in the static limit and like log T/T in the long wavelength limit.

hep-th↗

arXiv2001

Thermal Fluctuations of Induced Fermion Number

We analyze the phemomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number $ $ is a thermal expectation value, and we compute the finite temperature fluctuations, $(ΔN)^2= - ^2$. While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopological, and is not a sharp observable. The fluctuations are due to the mixing of states inherent in any finite temperature expectation value. We analyze in detail two different cases in 1+1 dimensional field theory: fermions in a kink background, and fermions in a chiral sigma model background. At zero temperature the induced fermion numbers for these two cases are very similar, but at finite temperature they are very different. The sigma model case is generic and the induced fermion number is nontopological, but the kink case is special and the fermion number is topological, even at finite temperature. There is a simple physical interpretation of all these results in terms of the spectrum of the fermions in the relevant background, and many of the results generalize to higher dimensional models.

hep-th↗

arXiv2001

Calorons in Weyl Gauge

We demonstrate by explicit construction that while the untwisted Harrington-Shepard caloron $A_μ$ is manifestly periodic in Euclidean time, with period $β=\frac{1}{T}$, when transformed to the Weyl ($A_0=0$) gauge, the caloron gauge field $A_i$ is periodic only up to a large gauge transformation, with winding number equal to the caloron's topological charge. This helps clarify the tunneling interpretation of these solutions, and their relation to Chern-Simons numbers and winding numbers.

hep-th↗

arXiv2001

Quantum Complex Henon-Heiles Potentials

Quantum-mechanical PT-symmetric theories associated with complex cubic potentials such as V=x^2+y^2+igxy^2 and V=x^2+y^2+z^2+igxyz, where g is a real parameter, are investigated. These theories appear to possess real, positive spectra. Low-lying energy levels are calculated to very high order in perturbation theory. The large-order behavior of the perturbation coefficients is determined using multidimensional WKB tunneling techniques. This approach is also applied to the complex Henon-Heiles potential V=x^2+y^2+ig(xy^2-x^3/3).

quant-ph↗

arXiv2000

QED Effective Actions in Inhomogeneous Backgrounds: Summing the Derivative Expansion

The QED effective action encodes nonlinear interactions due to quantum vacuum polarization effects. While much is known for the special case of electrons in a constant electromagnetic field (the Euler-Heisenberg case), much less is known for inhomogeneous backgrounds. Such backgrounds are more relevant to experimental situations. One way to treat inhomogeneous backgrounds is the "derivative expansion", in which one formally expands around the soluble constant-field case. In this talk I use some recent exactly soluble inhomogeneous backgrounds to perform precision tests on the derivative expansion, to learn in what sense it converges or diverges. A closely related question is to find the exponential correction to Schwinger's pair-production formula for a constant electric field, when the electric background is inhomogeneous.

hep-th↗

arXiv1999

Derivative Expansion and Soliton Masses

We present a simple algorithm to implement the generalized derivative expansion introduced previously by L-H. Chan, and apply it to the calculation of the one-loop mass correction to the classical soliton mass in the 1+1 dimensional Jacobi model. We then show how this derivative expansion approach implies that the total (bosonic plus fermionic) mass correction in an N=1 supersymmetric soliton model is determined solely by the asymptotic values (and derivatives) of the fermionic background potential. For a static soliton the total mass correction is $-m/(2π)$, in agreement with recent analyses using phase-shift methods.

hep-th↗

arXiv1999

Two-Loop Euler-Heisenberg QED Pair-Production Rate

We study the divergence of large-order perturbation theory in the worldline expression for the two-loop Euler-Heisenberg QED effective Lagrangian in a constant magnetic field. The leading rate of divergence is identical, up to an overall factor, to that of the one-loop case. From this we deduce, using Borel summation techniques, that the leading behaviour of the imaginary part of the two-loop effective Lagrangian for a constant E field, giving the pair-production rate, is proportional to the one-loop result. This also serves as a test of the mass renormalization, and confirms the earlier analysis by Ritus.

hep-th↗

arXiv1999

Lam'e Instantons

We perform a precise analytic test of the instanton approximation by comparing the exact band spectrum of the periodic Lamé potential to the tight-binding, instanton and WKB approximations. The instanton result gives the correct leading behavior in the semiclassical limit, while the tight-binding approximation does even better. WKB is off by an overall factor of $\sqrt{e/π}$.

hep-th↗

arXiv1999

Aspects of Chern-Simons Theory

Lectures at the 1998 Les Houches Summer School: Topological Aspects of Low Dimensional Systems. These lectures contain an introduction to various aspects of Chern-Simons gauge theory: (i) basics of planar field theory, (ii) canonical quantization of Chern-Simons theory, (iii) Chern-Simons vortices, and (iv) radiatively induced Chern-Simons terms.

hep-th↗

arXiv1999

Borel Summation of the Derivative Expansion and Effective Actions

We give an explicit demonstration that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B\to iE gives a non-Borel-summable perturbative series for a time dependent background electric field, and Borel dispersion relations yield the non-perturbative imaginary part of the effective action, which determines the pair production probability. Resummations of leading Borel approximations exponentiate to give perturbative corrections to the exponents in the non-perturbative pair production rates. Comparison with a WKB analysis suggests that these divergence properties are general features of derivative expansions and effective actions.

hep-th↗

arXiv1998

Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian

A precise calculation of the ground-state energy of the complex PT-symmetric Hamiltonian $H=p^2+{1/4}x^2+i λx^3$, is performed using high-order Rayleigh-Schrödinger perturbation theory. The energy spectrum of this Hamiltonian has recently been shown to be real using numerical methods. The Rayleigh-Schrödinger perturbation series is Borel summable, and Padé summation provides excellent agreement with the real energy spectrum. Padé analysis provides strong numerical evidence that the once-subtracted ground-state energy considered as a function of $λ^2$ is a Stieltjes function. The analyticity properties of this Stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-εx^3$.

quant-ph↗

arXiv1998

Complex periodic potentials with real band spectra

This paper demonstrates that complex PT-symmetric periodic potentials possess real band spectra. However, there are significant qualitative differences in the band structure for these potentials when compared with conventional real periodic potentials. For example, while the potentials V(x)=i\sin^{2N+1}(x), (N=0, 1, 2, ...), have infinitely many gaps, at the band edges there are periodic wave functions but no antiperiodic wave functions. Numerical analysis and higher-order WKB techniques are used to establish these results.

cond-mat↗