Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.Comment: 7 pages, no figures. Added proof of existence of a zero mode and two more references. Accepted for publication in Journal of Nonlinear Mathematical Physic

On Urabe's criteria of isochronicity

We give a short proof of Urabe's criteria for the isochronicity of periodical solutions of the equation $\ddot{x}+g(x)=0$. We show that apart from the harmonic oscillator there exists a large family of isochronous potentials which must all be non-polynomial and not symmetric (an even function of the coordinate x).Comment: 8 page

Evaluation of specific heat for superfluid helium between 0 - 2.1 K based on nonlinear theory

The specific heat of liquid helium was calculated theoretically in the Landau theory. The results deviate from experimental data in the temperature region of 1.3 - 2.1 K. Many theorists subsequently improved the results of the Landau theory by applying temperature dependence of the elementary excitation energy. As well known, many-body system has a total energy of Galilean covariant form. Therefore, the total energy of liquid helium has a nonlinear form for the number distribution function. The function form can be determined using the excitation energy at zero temperature and the latent heat per helium atom at zero temperature. The nonlinear form produces new temperature dependence for the excitation energy from Bose condensate. We evaluate the specific heat using iteration method. The calculation results of the second iteration show good agreement with the experimental data in the temperature region of 0 - 2.1 K, where we have only used the elementary excitation energy at 1.1 K.Comment: 6 pages, 3 figures, submitted to Journal of Physics: Conference Serie

Equilibrium topology of the intermediate state in type-I superconductors of different shapes

High-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes - cones, hemispheres and discs. Combined with the measurements of macroscopic magnetization these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to geometric barrier that results in a topological hysteresis -- flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have geometric barrier and show no hysteresis with flux tubes dominating the intermediate field region. It is concluded that flux tubes represent the equilibrium topology of the intermediate state in reversible samples, whereas laminar structure appears in samples with magnetic hysteresis (either bulk or geometric). Real-time video is available in http://www.cmpgroup.ameslab.gov/supermaglab/video/Pb.html NOTE: the submitted images were severely downsampled due to Arxiv's limitations of 1 Mb total size

Strong-coupling perturbation theory for the extended Bose-Hubbard model

We develop a strong-coupling perturbation theory for the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on ($d > 1$)-dimensional hypercubic lattices. Analytical expressions for the ground-state phase boundaries between the incompressible (Mott or charge-density-wave insulators) and the compressible (superfluid or supersolid) phases are derived up to third order in the hopping $t$. We also briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.Comment: 9 pages, 3 figures and 1 table, to be submitted for PR

Vanishing bulk viscosities and conformal invariance of unitary Fermi gas

By requiring general-coordinate and conformal invariance of the hydrodynamic equations, we show that the unitary Fermi gas has zero bulk viscosity, zeta=0, in the normal phase. In the superfluid phase, two of the bulks viscosities have to vanish, zeta_1=zeta_2=0, while the third one zeta_3 is allowed to be nonzero.Comment: 4 page

Slow light in moving media

We review the theory of light propagation in moving media with extremely low group velocity. We intend to clarify the most elementary features of monochromatic slow light in a moving medium and, whenever possible, to give an instructive simplified picture

Impact parameter dependence of heavy ion e+ e- pair production to all orders in Z alpha

The heavy ion probability for continuum e+ e- pair production has been calculated to all orders in Z alpha as a function of impact parameter. The formula resulting from an exact solution of the semiclassical Dirac equation in the ultrarelativistic limit is evaluated numerically. In a calculation of gamma = 100 colliding Au ions the probability of e+ e- pair production is reduced from the perturbation theory result throughout the impact parameter range.Comment: 20 pages, latex, revtex, 6 eps figures. Revised Phys. Rev. C version with minor additions, one figure added, and added reference

Generalized Landau-Pollak Uncertainty Relation

The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a generalization of this bound (weak version of the Landau-Pollak uncertainty relation). Our generalization covers a pair of positive operator valued measures. A nontrivial but slightly weak inequality that can treat an arbitrary number of positive operator valued measures is also presented.Comment: Simplified the proofs. To be published in Phys.Rev.

Collective Dynamics of Bose--Einstein Condensates in Optical Cavities

Recent experiments on Bose--Einstein condensates in optical cavities have reported a quantum phase transition to a coherent state of the matter-light system -- superradiance. The time dependent nature of these experiments demands consideration of collective dynamics. Here we establish a rich phase diagram, accessible by quench experiments, with distinct regimes of dynamics separated by non-equilibrium phase transitions. We include the key effects of cavity leakage and the back-reaction of the cavity field on the condensate. Proximity to some of these phase boundaries results in critical slowing down of the decay of many-body oscillations. Notably, this slow decay can be assisted by large cavity losses. Predictions include the frequency of collective oscillations, a variety of multi-phase co-existence regions, and persistent optomechanical oscillations described by a damped driven pendulum. These findings open new directions to study collective dynamics and non-equilibrium phase transitions in matter-light systems.Comment: 5 pages, 5 figure