Super Multi-Instantons in Conformal Chiral Superspace

We reformulate self-dual supersymmetric theories directly in conformal chiral superspace, where superconformal invariance is manifest. The superspace can be interpreted as the generalization of the usual Atiyah-Drinfel'd-Hitchin-Manin twistors (the quaternionic projective line), the real projective light-cone in six dimensions, or harmonic superspace, but can be reduced immediately to four-dimensional chiral superspace. As an example, we give the 't Hooft and ADHM multi-instanton constructions for self-dual super Yang-Mills theory. In both cases, all the parameters are represented as a single, irreducible, constant tensor.Comment: 21 pg., uuencoded compressed postscript file (twist.ps.Z.uu), other formats (.dvi, .ps, .ps.Z, 8-bit .tex) available at http://insti.physics.sunysb.edu/~siegel/preprints or at ftp://max.physics.sunysb.edu/preprints/siege

Accurate numerical verification of the instanton method for macroscopic quantum tunneling: dynamics of phase slips

Instanton methods, in which imaginary-time evolution gives the tunneling rate, have been widely used for studying quantum tunneling in various contexts. Nevertheless, how accurate instanton methods are for the problems of macroscopic quantum tunneling (MQT) still remains unclear because of lack of their direct comparison with exact time evolution of the many-body Schroedinger equation. Here, we verify instanton methods applied to coherent MQT. Specifically applying the quasi-exact numerical method of time-evolving block decimation to the system of bosons in a ring lattice, we directly simulate the real-time quantum dynamics of supercurrents, where a coherent oscillation between two macroscopically distinct current states occurs due to MQT. The tunneling rate extracted from the coherent oscillation is compared with that given by the instanton method. We show that the error is within 10% when the effective Planck's constant is sufficiently small. We also discuss phase slip dynamics associated with the coherent oscillations.Comment: 19 pages, 14 figures, 1 tabl

Novel approach to a perfect lens

Within the framework of an exact analytical solution of Maxwell equations in a space domain, it is shown that optical scheme based on a slab with negative refractive index ($n=-1$) (Veselago lens or Pendry lens) does not possess focusing properties in the usual sense . In fact, the energy in such systems does not go from object to its "image", but from object and its "image" to an intersection point inside a metamaterial layer, or vice versa. A possibility of applying this phenomenon to a creation of entangled states of two atoms is discussed.Comment: 4 pages, 6 figure

Finite-Range Gravity and Its Role in Gravitational Waves, Black Holes and Cosmology

Theoretical considerations of fundamental physics, as well as certain cosmological observations, persistently point out to permissibility, and maybe necessity, of macroscopic modifications of the Einstein general relativity. The field-theoretical formulation of general relativity helped us to identify the phenomenological seeds of such modifications. They take place in the form of very specific mass-terms, which appear in addition to the field-theoretical analog of the usual Hilbert-Einstein Lagrangian. We interpret the added terms as masses of the spin-2 and spin-0 gravitons. The arising finite-range gravity is a fully consistent theory, which smoothly approaches general relativity in the massless limit, that is, when both masses tend to zero and the range of gravity tends to infinity. We show that all local weak-field predictions of the theory are in perfect agreement with the available experimental data. However, some other conclusions of the non-linear massive theory are in a striking contrast with those of general relativity. We show in detail how the arbitrarily small mass-terms eliminate the black hole event horizon and replace a permanent power-law expansion of a homogeneous isotropic universe with an oscillatory behaviour. One variant of the theory allows the cosmological scale factor to exhibit an `accelerated expansion'instead of slowing down to a regular maximum of expansion. We show in detail why the traditional, Fierz-Pauli, massive gravity is in conflict not only with the static-field experiments but also with the available indirect gravitational-wave observations. At the same time, we demonstrate the incorrectness of the widely held belief that the non-Fierz-Pauli theories possess `negative energies' and `instabilities'.Comment: 56 pages including 11 figures; significant modifications; in particular, we demonstrate the incorrectness of the widely held belief that the non-Fierz-Pauli theories should suffer from negative energies and instabilities; to appear in Int. J. Mod. Phys.

Neutrino conversions in random magnetic fields and ν~e\tilde{\nu}_e from the Sun

The magnetic field in the convective zone of the Sun has a random small-scale component with the r.m.s. value substantially exceeding the strength of a regular large-scale field. For two Majorana neutrino flavors $\times$ two helicities in the presence of a neutrino transition magnetic moment and nonzero neutrino mixing we analyze the displacement of the allowed ($\Delta m^2- \sin^22\theta$)-parameter region reconciled for the SuperKamiokande(SK) and radiochemical (GALLEX, SAGE, Homestake) experiments in dependence on the r.m.s. magnetic field value $b$, or more precisely, on a value $\mu b$ assuming the transition magnetic moment $\mu = 10^{-11}\mu_B$. In contrast to RSFP in regular magnetic fields we find an effective production of electron antineutrinos in the Sun even for small neutrino mixing through cascade conversions $\nu_{eL}\to \nu_{\mu L}\to \tilde{\nu}_{eR}$, $\nu_{eL}\to \nu_{\mu R}\to \tilde{\nu}_{eR}$ in a random magnetic field that would be a signature of the Majorana nature of neutrino if $\tilde{\nu}_{eR}$ will be registered. Basing on the present SK bound on electron antineutrinos we have also found an excluded area in the same $\Delta m^2,~\sin^22\theta$-plane and revealed a strong sensitivity to the random magnetic field correlation length $L_0$.Comment: LaTex 36 pages including 14 PostScript figure

Tunneling in a uniform one-dimensional superfluid: emergence of a complex instanton

In a uniform ring-shaped one-dimensional superfluid, quantum fluctuations that unwind the order parameter need to transfer momentum to quasiparticles (phonons). We present a detailed calculation of the leading exponential factor governing the rate of such phonon-assisted tunneling in a weakly-coupled Bose gas at a low temperature $T$. We also estimate the preexponent. We find that for small superfluid velocities the $T$-dependence of the rate is given mainly by $\exp(-c_s P/ 2T)$, where $P$ is the momentum transfer, and $c_s$ is the phonon speed. At low $T$, this represents a strong suppression of the rate, compared to the non-uniform case. As a part of our calculation, we identify a complex instanton, whose analytical continuation to suitable real-time segments is real and describes formation and decay of coherent quasiparticle states with nonzero total momenta.Comment: 15 pages, 3 figures; to be published in Phys. Rev.

Anomalous diffusion in the dynamics of complex processes

Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively small time intervals. This paper proposes an interpolation expression for the identification of anomalous diffusion in complex signals for the cases when the dynamics of the system under study reaches a steady state (large time intervals). This interpolation expression uses the chaotic difference moment (transient structural function) of the second order as an average characteristic of displacements. A general procedure for identifying anomalous diffusion and calculating its parameters in real stochastic signals, which includes the removal of the regular (low-frequency) components from the source signal and the fitting of the chaotic part of the experimental difference moment of the second order to the interpolation expression, is presented. The procedure was applied to the analysis of the dynamics of magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray emission from accreting objects. For all three applications, the interpolation was able to adequately describe the chaotic part of the experimental difference moment, which implies that anomalous diffusion manifests itself in these natural signals. The results of this study make it possible to broaden the range of complex natural processes in which anomalous diffusion can be identified. The relation between the interpolation expression and a diffusion model, which is derived in the paper, allows one to simulate the chaotic processes in the open complex systems with anomalous diffusion.Comment: 47 pages, 15 figures; Submitted to Physical Review

The Origin of Magnetic Fields in Galaxies

Microgauss magnetic fields are observed in all galaxies at low and high redshifts. The origin of these intense magnetic fields is a challenging question in astrophysics. We show here that the natural plasma fluctuations in the primordial universe (assumed to be random), predicted by the Fluctuation-Dissipation-Theorem, predicts $\sim 0.034 \mu G$ fields over $\sim 0.3$ kpc regions in galaxies. If the dipole magnetic fields predicted by the Fluctuation-Dissipation-Theorem are not completely random, microgauss fields over regions $\gtrsim 0.34$ kpc are easily obtained. The model is thus a strong candidate for resolving the problem of the origin of magnetic fields in $\lesssim 10^{9}$ years in high redshift galaxies.Comment: 10 pages, 3 figure

Influence of helicity on scaling regimes in the extended Kraichnan model

We have investigated the advection of a passive scalar quantity by incompressible helical turbulent flow in the frame of extended Kraichnan model. Turbulent fluctuations of velocity field are assumed to have the Gaussian statistics with zero mean and defined noise with finite time-correlation. Actual calculations have been done up to two-loop approximation in the frame of field-theoretic renormalization group approach. It turned out that space parity violation (helicity) of turbulent environment does not affect anomalous scaling which is peculiar attribute of corresponding model without helicity. However, stability of asymptotic regimes, where anomalous scaling takes place, strongly depends on the amount of helicity. Moreover, helicity gives rise to the turbulent diffusivity, which has been calculated in one-loop approximation.Comment: 16 pages, talk given by M. Hnatich at "Renormalization Group 2005", Helsinki, Finland 30 August - 3 September 2005. To apear in J. Phys. A: Math. Ge

High orders of perturbation theory: are renormalons significant?

According to Lipatov, the high orders of perturbation theory are determined by saddle-point configurations (instantons) of the corresponding functional integrals. According to t'Hooft, some individual large diagrams, renormalons, are also significant and they are not contained in the Lipatov contribution. The history of the conception of renormalons is presented, and the arguments in favor of and against their significance are discussed. The analytic properties of the Borel transforms of functional integrals, Green functions, vertex parts, and scaling functions are investigated in the case of \phi^4 theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou - Zinn-Justin hypothesis) is proved. It rules out the existence of the renormalon singularities pointed out by t'Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of \phi^4 theory.Comment: 28 pages, 8 figures include