Nonlocal anomaly of the axial-vector current for bound states

We argue that the amplitude does not vanish in the limit of zero quark masses. This represents a new kind of violation of the classical equation of motion for the axial current and should be interpreted as the axial anomaly for bound states. The anomaly emerges in spite of the fact that the one loop integrals are ultraviolet finite as guaranteed by the finite size of bound-state wave functions. As a result, the amplitude behaves like approximately 1/p(2) in the limit of a large momentum p of the current. The observed effect requires the modification of the classical equation of motion of the axial-vector current by nonlocal operators.     

Point-like structure and off-shell dual strings

We argue that in a consistent off-shell dual formalism the amplitude for the emission of a scalar off-shell state by a string consists of two components. One of these contains the particle poles in the off-shell leg and the other is intimately related to the insertion of a point-like energy density on the string. As a result, the amplitude for a string to emit a zero momentum scalar state into the vacuum (which may be relevant for spontaneous symmetry breaking) is described by the amplitude for a finite fraction of the energy in the string to collapse to a spatial point at some time (this fraction and its space-time position being integrated over). The off-shell amplitudes have an elegant formulation in terms of a set of “confined modes” which can be assigned quark flavour quantum numbers to reproduce the Chan-Paton scheme.We suggest the dual model be modified by allowing for the coupling of scalar closed strings to the vacuum and the resulting effect on the space-time structure of dual Green functions is described.We find that even the emission of a single zero-momentum closed string modifies the elastic amplitude in a significant manner, leading to a power-behaved fixed-angle cross section in contrast to the usual exponential decrease of the dual model. This arises from point-like scattering between energy densities accumulating in the colliding strings. The relationship between the fixed angle and Regge limits is discussed. The fixed angle behaviour is found to be the asymptotic limit in momentum transfer of a fixed pole that arises in the Regge limit.     

A note on anomaly matching for finite density QCD

We note that the QCD phases at large finite density respect 't Hooft anomaly matching conditions. Specifically the spectrum of the light excitations possesses the correct quantum numbers required to obey global anomaly constraints. We argue that 't Hooft constraints can be used at finite density along with non perturbative methods to help selecting the correct phase.     

Landau–Ginzburg theory for ‘star’-shaped droplets

ABSTRACT

Molecular simulations have shown that when a nano-drop comprising a single spherical central ion and a dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology. A linear continuum model of the ‘star’-shapes comprised electrostatic and surface energy is not sufficient to describe these shapes. We employ combined molecular dynamics, continuum electrostatics and macroscopic modelling in order to construct a unified free energy functional that describes the observed star-shaped droplets. We demonstrate that the Landau free energy coupled to the third-order Steinhardt invariant mimics the shapes of droplets detected in molecular simulations. Using the maximum likelihood technique we build a universal free energy functional that describes droplets for a range of Rayleigh fissility parameter. The analysis of the macroscopic free energy demonstrates the origin of the finite amplitude perturbations just above the Rayleigh limit. We argue that the presence of the finite amplitude perturbations precludes the use of the small parameter perturbation method for the analysis of the shapes above the Rayleigh limit of the corresponding spherical shape.     

Cancellations beyond finiteness in N=8 supergravity at three loops

We construct the three-loop four-point amplitude of N=8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions no worse than that of N=4 super-Yang-Mills theory--a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N=8 supergravity may be a perturbatively finite theory of quantum gravity.     

The principle of equivalence at finite temperature

We demonstrate that the equivalence principle is violated by radiative corrections to the gravitational and inertial masses at finite temperature. We argue that this result can be attributed to the Lorentz noninvariance of the finite temperature vacuum.Research supported in part by the National Science Foundation.This essay received the fourth award from the Gravity Research Foundation for the year 1984-Ed.     

From chemical freeze-out to critical conditions in heavy ion collisions

We compare the statistical thermodynamics of hadron resonance gas with recent LGT results at finite chemical potential. We argue that for T≤T _cthe equation of state derived from Monte-Carlo simulations of 2-quark-flavor QCD at finite chemical potential is consistent with that of a hadron resonance gas when applying the same set of approximations as used in LGT calculations. We indicate the relation of chemical freeze-out conditions obtained from a detailed analysis of particle production in heavy ion collisions with the critical conditions required for deconfinement. We argue that the position of a hadron quark-gluon boundary line in temperature chemical potential plane can be determined in terms of the resonance gas model by the condition of fixed energy density.     

Comment on: “Confined states in two-dimensional flat elliptic quantum dots and elliptic quantum wires” [Physica E 11 (2001) 345]

We argue that the two-dimensional elliptic quantum dot problem with finite barrier cannot be exactly solved, contrary to a recent assertion (van den Broek and Peeters, Physica E 11 (2001) 345. We also prove it explicitly by numerically calculating the correct energy spectrum.     

Poisson Sigma Model on the Sphere

We evaluate the path integral of the Poisson sigma model on the sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kähler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.     

Amplitude-mode dynamics of polariton condensates

We study the stability of collective amplitude excitations in nonequilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors. They would be present following a quantum quench or could be created directly by resonant excitation. We show that uniform amplitude excitations are unstable to the production of excitations at finite wave vectors, leading to the formation of density-modulated phases. The physical processes causing the instabilities can be understood by analogy to optical parametric oscillators and the atomic Bose supernova.     

Quantum phase slips in superconducting wires with weak inhomogeneities

Quantum phase slips are traditionally considered in diffusive superconducting wires which are assumed homogeneous. We present a definite estimate for the amplitude of phase slips that occur at a weak inhomogeneity in the wire where local resistivity is slightly increased. We model such a weak link as a general coherent conductor and show that the amplitude is dominated by the topological part of the action. We argue that such weak links occur naturally in apparently homogeneous wires and adjust the estimate to that case. The fabrication of an artificial weak link would localize phase slips and facilitate a better control of the phase-slip amplitude.     

Two-loop graviton scattering relation and IR behavior in supergravity

We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in supergravity. Specifically we show that the infrared-divergent part of the two-loop amplitude is one-half the square of the one-loop amplitude, suggesting an exponential structure for IR divergences. The difference between the two-loop amplitude and one-half the square of the full one-loop amplitude is therefore finite, and expressible in a relatively simple form. We give arguments for generalizations to higher loops and n-point functions, suggesting that the exponential of the full one-loop amplitude may be corrected, to low orders, by only simple finite terms.     

Smoothness of pion amplitudes and PCAC

We point out the essentially obvious result that if the massless pion amplitude is the smooth finite limit of the massive pion world, the Adler self-consistency condition must be true.     

Finite-size Berezinskii-Kosterlitz-Thouless transition at grain boundaries in solid 4He and the role of 3He impurities

We analyze the complex phenomenology of the nonclassical rotational inertia (NCRI) observed at low temperature in solid 4He within the context of a two-dimensional Berezinskii-Kosterlitz-Thouless transition in a premelted 4He film at the grain boundaries. We show that both the temperature and 3He doping dependence of the NCRI fraction (NCRIF) can be ascribed to finite size effects induced by the finite grain size. We give an estimate of the average size of the grains which we argue to be limited by the isotopic 3He impurities and we provide a simple power-law relation between the NCRIF and the 3He concentration.     

Wetting layer thickness and early evolution of epitaxially strained thin films

We propose a physical model which explains the existence of finite thickness wetting layers in epitaxially strained films. The finite wetting layer is shown to be stable due to the variation of the nonlinear elastic free energy with film thickness. We show that anisotropic surface tension gives rise to a metastable enlarged wetting layer. The perturbation amplitude needed to destabilize this wetting layer decreases with increasing lattice mismatch. We observe the development of faceted islands in unstable films.     

Pseudo-spectral methods and linear instabilities in reaction-diffusion fronts

We explore the application of a pseudo-spectral Fourier method to a set of reaction-diffusion equations and compare it with a second-order finite difference method. The prototype cubic autocatalytic reaction-diffusion model as discussed by Gray and Scott [Chem. Eng. Sci. 42, 307 (1987)] with a nonequilibrium constraint is adopted. In a spatial resolution study we find that the phase speeds of one-dimensional finite amplitude waves converge more rapidly for the spectral method than for the finite difference method. Furthermore, in two dimensions the symmetry preserving properties of the spectral method are shown to be superior to those of the finite difference method. In studies of plane/axisymmetric nonlinear waves a symmetry breaking linear instability is shown to occur and is one possible route for the formation of patterns from infinitesimal perturbations to finite amplitude waves in this set of reaction-diffusion equations. (c) 1996 American Institute of Physics.     

Quantum spin glass and the dipolar interaction

Anisotropic dipolar systems are considered. Such systems in an external magnetic field are expected to be a good experimental realization of the transverse field Ising model. With random interactions, this model yields a spin glass to paramagnet phase transition as a function of the transverse field. We show that the off-diagonal dipolar interaction, although effectively reduced, induces a finite correlation length and thus destroys the spin-glass order at any finite transverse field. We thus explain the behavior of the nonlinear susceptibility in the experiments on LiHo(x)Y(1-x)F(4), and argue that a crossover to the paramagnetic phase, and not quantum criticality, is observed.     

Exploring modulated amplitudes in the resistive regime of a one-dimensional superconductor

We propose a new method to explore the modulated amplitude associated with formation of phase slip centers in a one-dimensional superconductor. With this method we probe finite amplitude modulations that generally induce transitions between different metastable superconducting phases. We derive a central relationship between the modulated amplitude of the SC phase and corresponding electrochemical potential and this relation captures various dynamic and static solutions in closed analytic form.     

Superradiance resonance cavity outside rapidly rotating black holes

We discuss the late-time behavior of a dynamically perturbed Kerr black hole. We present analytic results for near-extreme Kerr black holes that show that the large number of virtually undamped quasinormal modes that exist for nonzero values of the azimuthal eigenvalue m combine in such a way that the field oscillates with an amplitude that decays as 1/t at late times. This prediction is verified using numerical time evolutions of the Teukolsky equation. We argue that the observed behavior can be understood in terms of the presence of a "superradiance resonance cavity" immediately outside the black hole, and discuss whether it may be relevant for astrophysical black holes.