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Gerald V. Dunne

Publications and source records attributed to Gerald V. Dunne.

At least 91 records · Page 5Linked to original sources
arXiv2011

The Derivative Expansion at Small Mass for the Spinor Effective Action

We study the small mass limit of the one-loop spinor effective action, comparing the derivative expansion approximation with exact numerical results that are obtained from an extension to spinor theories of the partial-wave-cutoff method. In this approach one can compute numerically the renormalized one-loop effective action, for radially separable gauge field background fields in spinor QED. We highlight an important difference between the small mass limit of the derivative expansion approximation for spinor and scalar theories.

hep-th↗
arXiv2011

Interference Effects in Schwinger Vacuum Pair Production for Time-Dependent Laser Pulses

We present simple new approximate formulas, for both scalar and spinor QED, for the number of particles produced from vacuum by a time dependent electric field, incorporating the interference effects that arise from an arbitrary number of distinct semiclassical turning points. Such interference effects are important when the temporal profile of the laser pulse has subcycle structure. We show how the resulting semiclassical intuition may be used to guide the design of temporal profiles that enhance the momentum spectrum due to interference effects. The result is easy to implement and generally applicable to time-dependent tunneling problems, such as appear in many other contexts in particle and nuclear physics, condensed matter physics, atomic physics, chemical physics, and gravitational physics.

hep-th↗
arXiv2010

Thermodynamics of photons on fractals

A thermodynamical treatment of a massless scalar field (a "photon") confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, $P V_s=U/d_s$, where $d_s$ is the spectral dimension and $V_s$ defines the "spectral volume". For regular manifolds, $V_s$ coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

cond-mat.stat-mech↗
arXiv2010

Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schrödinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.

hep-th↗
arXiv2010

The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses

Particle production due to external fields (electric, chromo-electric or gravitational) requires evolving an initial state through an interaction with a time-dependent background, with the rate being computed from a Bogoliubov transformation between the in and out vacua. When the background fields have temporal profiles with sub-structure, a semiclassical analysis of this problem confronts the full subtlety of the Stokes phenomenon: WKB solutions are only local, while the production rate requires global information. Incorporating the Stokes phenomenon, we give a simple quantitative explanation of the recently computed [Phys. Rev. Lett. 102, 150404 (2009)] oscillatory momentum spectrum of e+e- pairs produced from vacuum subjected to a time-dependent electric field with sub-cycle laser pulse structure. This approach also explains naturally why for spinor and scalar QED these oscillations are out of phase.

hep-th↗
arXiv2010

U_A(1) Anomaly at high temperature: the scalar-pseudoscalar splitting in QCD

We estimate the splitting between the spatial correlation lengths in the scalar and pseudoscalar channels in QCD at high temperature. The splitting is due to the contribution of the instanton/anti-instanton chains in the thermal ensemble, even though instanton contributions to thermodynamic quantities are suppressed. The splitting vanishes at asymptotically high temperatures as $ΔM/M\propto (Λ_{QCD}/T)^b$, where $b$ is the beta function coefficient.

hep-ph↗
arXiv2010

Chiral Magnetic Spiral

We argue that the presence of a very strong magnetic field in the chirally broken phase induces inhomogeneous expectation values, of a spiral nature along the magnetic field axis, for the currents of charge and chirality, when there is finite baryon density or an imbalance between left and right chiralities. This "chiral magnetic spiral" is a gapless excitation transporting the currents of (i) charge (at finite chirality), and (ii) chirality (at finite baryon density) along the direction of the magnetic field. In both cases it also induces in the transverse directions oscillating currents of charge and chirality. In heavy ion collisions, the chiral magnetic spiral possibly provides contributions both to the out-of-plane and the in-plane dynamical charge fluctuations recently observed at RHIC.

hep-ph↗
arXiv2009

A Gauge-Gravity Relation in the One-loop Effective Action

We identify an unusual new gauge-gravity relation: the one-loop effective action for a massive spinor in 2n dimensional AdS space is expressed in terms of precisely the same function [a certain multiple gamma function] as the one-loop effective action for a massive charged scalar in 4n dimensions in a maximally symmetric background electromagnetic field [one for which the eigenvalues of F_{μν} are maximally degenerate, corresponding in 4 dimensions to a self-dual field, equivalently to a field of definite helicity], subject to the identification F^2 <-> Λ, where Λis the gravitational curvature. Since these effective actions generate the low energy limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a nontrivial gauge-gravity relation at the non-perturbative level and at the amplitude level.

hep-th↗
arXiv2009

Physical Consequences of Complex Dimensions of Fractals

It has recently been realized that fractals may be characterized by complex dimensions, arising from complex poles of the corresponding zeta function, and we show here that these lead to oscillatory behavior in various physical quantities. We identify the physical origin of these complex poles as the exponentially large degeneracy of the iterated eigenvalues of the Laplacian, and discuss applications in quantum mesoscopic systems such as oscillations in the fluctuation $Σ^2 (E)$ of the number of levels, as a correction to results obtained in Random Matrix Theory. We present explicit expressions for these oscillations for families of diamond fractals, also studied as hierarchical lattices.

cond-mat.mes-hall↗
arXiv2009

New Strong-Field QED Effects at ELI: Nonperturbative Vacuum Pair Production

Since the work of Sauter, and Heisenberg, Euler and Köckel, it has been understood that vacuum polarization effects in quantum electrodynamics (QED) predict remarkable new phenomena such as light-light scattering and pair production from vacuum. However, these fundamental effects are difficult to probe experimentally because they are very weak, and they are difficult to analyze theoretically because they are highly nonlinear and/or nonperturbative. The Extreme Light Infrastructure (ELI) project offers the possibility of a new window into this largely unexplored world. I review these ideas, along with some new results, explaining why quantum field theorists are so interested in this rapidly developing field of laser science. I concentrate on the theoretical tools that have been developed to analyze nonperturbative vacuum pair production.

hep-th↗
arXiv2009

Catalysis of Schwinger Vacuum Pair Production

We propose a new catalysis mechanism for non-perturbative vacuum electron-positron pair production, by superimposing a plane-wave X-ray probe beam with a strongly focused optical laser pulse, such as is planned at the Extreme Light Infrastructure (ELI) facility. We compute the absorption coefficient arising from vacuum polarization effects for photons below threshold in a strong electric field. This set-up should facilitate the (first) observation of this non-perturbative QED effect with planned light sources such as ELI yielding an envisioned intensity of order 10^{26}W/cm^2.

hep-ph↗
arXiv2009

Quantum statistics effect in Schwinger pair production in short laser pulses

We investigate non-perturbative pair production from vacuum (the Schwinger effect) in the focal region of two counter-propagating, ultra-short laser pulses with sub-cycle structure. We use the quantum kinetic formulation to calculate the momentum spectrum of created particles and show the extreme sensitivity to the laser frequency $ω$, the pulse length $τ$ and the carrier-envelope absolute phase $ϕ$. We apply this formalism to both fermions and bosons to illustrate the influence of quantum statistics in this type of electric background field.

hep-ph↗
arXiv2009

Momentum signatures for Schwinger pair production in short laser pulses with a sub-cycle structure

We investigate electron-positron pair production from vacuum for short laser pulses with sub-cycle structure, in the nonperturbative regime (Schwinger pair production). We use the non-equilibrium quantum kinetic approach, and show that the momentum spectrum of the created electron-positron pairs is extremely sensitive to the sub-cycle dynamics -- depending on the laser frequency $ω$, the pulse length $τ$, and the carrier phase $ϕ$ -- and shows several distinctive new signatures. This observation could help not only in the design of laser pulses to optimize the experimental signature of Schwinger pair production, but also ultimately lead to new probes of light pulses at extremely short time scales.

hep-ph↗
arXiv2009

Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model

We analyze the thermodynamical properties, at finite density and nonzero temperature, of the (1+1)-dimensional chiral Gross-Neveu model (the NJL_2 model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the "chiral spiral", as a thermodynamically preferred limit of the more general "twisted kink crystal" solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a discrete chiral symmetry, and for which the phase diagram has a crystalline phase with a periodic kink crystal. We use a combination of analytic, numerical and Ginzburg-Landau techniques to study various parts of the phase diagram.

hep-th↗
arXiv2008

A Twisted Kink Crystal in the Chiral Gross-Neveu model

We present the detailed properties of a self-consistent crystalline chiral condensate in the massless chiral Gross-Neveu model. We show that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schrödinger equation, which is exactly soluble. The general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation. Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with this inhomogeneous chiral condensate, and the exact spectral properties are derived. We find an all-orders expansion of the Ginzburg-Landau effective Lagrangian and show how the gap equation is solved order-by-order.

hep-th↗
arXiv2008

Abelian Zero Modes in Odd Dimensions

We show that the Loss-Yau zero modes of the 3d abelian Dirac operator may be interpreted in a simple manner in terms of a stereographic projection from a 4d Dirac operator with a constant field strength of definite helicity. This is an alternative to the conventional viewpoint involving Hopf maps from S^3 to S^2. Furthermore, our construction generalizes in a straightforward way to any odd dimension. The number of zero modes is related to the Chern-Simons number in a nonlinear manner.

hep-th↗
arXiv2008

Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems

We derive a new exact self-consistent crystalline condensate in the 1+1 dimensional chiral Gross-Neveu model. This also yields a new exact crystalline solution for the one dimensional Bogoliubov-de Gennes equations and the Eilenberger equation of semiclassical superconductivity. We show that the functional gap equation can be reduced to a solvable nonlinear equation, and discuss implications for the temperature-chemical potential phase diagram.

hep-th↗