Radiation and Relaxation of Oscillons

We study oscillons, extremely long-lived localized oscillations of a scalar field, with three different potentials: quartic, sine-Gordon model and in a new class of convex potentials. We use an absorbing boundary at the end of the lattice to remove emitted radiation. The energy and the frequency of an oscillon evolve in time and are well fitted by a constant component and a decaying, radiative part obeying a power law as a function time. The power spectra of the emitted radiation show several distinct frequency peaks where oscillons release energy. In two dimensions, and with suitable initial conditions, oscillons do not decay within the range of the simulations, which in quartic theory reach 10^8 time units. While it is known that oscillons in three-dimensional quartic theory and sine-Gordon model decay relatively quickly, we observe a surprising persistence of the oscillons in the convex potential with no sign of demise up to 10^7 time units. This leads us to speculate that an oscillon in such a potential could actually live infinitely long both in two and three dimensions.Comment: 16 pages, 28 eps figure

Numerical Investigations of Oscillons in 2 Dimensions

Oscillons, extremely long-living localized oscillations of a scalar field, are studied in theories with quartic and sine-Gordon potentials in two spatial dimensions. We present qualitative results concentrating largely on a study in frequency space via Fourier analysis of oscillations. Oscillations take place at a fundamental frequency just below the threshold for the production of radiation, with exponentially suppressed harmonics. The time evolution of the oscillation frequency points indirectly to a life time of at least 10 million oscillations. We study also elliptical perturbations of the oscillon, which are shown to decay. We finish by presenting results for boosted and collided oscillons, which point to a surprising persistence and soliton-like behaviour.Comment: Matches the published version (12 pages, 34 figures

Oscillons and Domain Walls

Oscillons, extremely long-lived localized oscillations of a scalar field, are shown to be produced by evolving domain wall networks in quartic theory in two spatial dimensions. We study the oscillons in frequency space using the classical spectral function at zero momentum, and obtain approximate information of their velocity distribution. In order to gain some insight onto the dilute oscillon 'gas' produced by the domain walls, we prepare a denser gas by filling the simulation volume with oscillons boosted in random directions. We finish the study by revisiting collisions between oscillons and between an oscillon and a domain wall, showing that in the latter case they can pass straight through with minimal distortion.Comment: 11 pages, 28 eps figure

Flat-top oscillons in an expanding universe

Oscillons are extremely long lived, oscillatory, spatially localized field configurations that arise from generic initial conditions in a large number of non-linear field theories. With an eye towards their cosmological implications, we investigate their properties in an expanding universe. We (1) provide an analytic solution for one dimensional oscillons (for the models under consideration) and discuss their generalization to 3 dimensions, (2) discuss their stability against long wavelength perturbations and (3) estimate the effects of expansion on their shapes and life-times. In particular, we discuss a new, extended class of oscillons with surprisingly flat tops. We show that these flat topped oscillons are more robust against collapse instabilities in (3+1) dimensions than their usual counterparts. Unlike the solutions found in the small amplitude analysis, the width of these configurations is a non-monotonic function of their amplitudes.Comment: v2-matches version published in Phys. Rev D. Updated references and minor modification to section 4.

Oscillon resonances and creation of kinks in particle collisions

We present a numerical study of the process of production of kink-antikink pairs in the collision of particle-like states in the one-dimensional $\phi^4$ model. It is shown that there are 3 steps in the process, the first step is to excite the oscillon intermediate state in the particle collision, the second step is a resonance excitation of the oscillon by the incoming perturbations, and finally, the soliton-antisoliton pair can be created from the resonantly excited oscillon. It is shown that the process depends fractally on the amplitude of the perturbations and the wave number of the perturbation. We also present the effective collective coordinate model for this process.Comment: 4 pages, 4 figures, revtex

Numerical Simulation of an Electroweak Oscillon

Numerical simulations of the bosonic sector of the $SU(2)\times U(1)$ electroweak Standard Model in 3+1 dimensions have demonstrated the existence of an oscillon -- an extremely long-lived, localized, oscillatory solution to the equations of motion -- when the Higgs mass is equal to twice the $W^\pm$ boson mass. It contains total energy roughly 30 TeV localized in a region of radius 0.05 fm. A detailed description of these numerical results is presented.Comment: 12 pages, 8 figures, uses RevTeX4; v2: expanded results section, fixed typo

Kink-Antikink Formation from an Oscillation Mode by Sudden Distortion of the Evolution Potential

We demonstrate numerically that an oscillation mode in 1+1 dimensions (eg a breather or an oscillon) can decay into a kink-antikink pair by a sudden distortion of the evolution potential which occurs within a certain time or space domain. In particular, we consider the transition of a sine-Gordon potential into a \Phi^4 potential. The breather field configuration is assumed to initially evolve in a sine-Gordon potential with velocity $v$ and oscillation frequency $\omega$. We then consider two types of numerical experiments: a. An abrupt transition of the potential to a $\Phi^4$ form at t_0=0 over the whole 1-dimensional lattice and b. The impact of the breather on a region x>x_0=0 where the potential has the \Phi^4 form which is different from the sine-Gordon form valid at x<x_0=0. We find that in both cases there is a region of parameters (v,\omega) such that the breather decays to a kink-antikink pair. This region of parameters for kink-antikink formation is qualitatively similar with the parameter region where the energy of the breather exceeds the energy of the kink-antikink pair in the \Phi^4 potential. We demonstrate that the same mechanism for soliton formation is realized when using a gaussian oscillator (oscillon) instead of a breather. We briefly discuss the implications of our results for realistic experiments as well as their extension to soliton formation in two and three space dimensions.Comment: 8 pages, 9 figures. The Mathematica files used for the production of the figures may be downloaded from http://leandros.physics.uoi.gr/partkinks.zi

A Class of Nonperturbative Configurations in Abelian-Higgs Models: Complexity from Dynamical Symmetry Breaking

We present a numerical investigation of the dynamics of symmetry breaking in both Abelian and non-Abelian $[S U (2)]$ Higgs models in three spatial dimensions. We find a class of time-dependent, long-lived nonperturbative field configurations within the range of parameters corresponding to type-1 superconductors, that is, with vector masses ($m_v$) larger than scalar masses ($m_s$). We argue that these emergent nontopological configurations are related to oscillons found previously in other contexts. For the Abelian-Higgs model, our lattice implementation allows us to map the range of parameter space -- the values of $\beta = (m_s /m_v)^2$ -- where such configurations exist and to follow them for times t \sim \O(10^5) m^{-1}. An investigation of their properties for $\hat z$-symmetric models reveals an enormously rich structure of resonances and mode-mode oscillations reminiscent of excited atomic states. For the SU(2) case, we present preliminary results indicating the presence of similar oscillonic configurations.Comment: 21 pages, 19 figures, prd, revte

Information Content of Spontaneous Symmetry Breaking

We propose a measure of order in the context of nonequilibrium field theory and argue that this measure, which we call relative configurational entropy (RCE), may be used to quantify the emergence of coherent low-entropy configurations, such as time-dependent or time-independent topological and nontopological spatially-extended structures. As an illustration, we investigate the nonequilibrium dynamics of spontaneous symmetry-breaking in three spatial dimensions. In particular, we focus on a model where a real scalar field, prepared initially in a symmetric thermal state, is quenched to a broken-symmetric state. For a certain range of initial temperatures, spatially-localized, long-lived structures known as oscillons emerge in synchrony and remain until the field reaches equilibrium again. We show that the RCE correlates with the number-density of oscillons, thus offering a quantitative measure of the emergence of nonperturbative spatiotemporal patterns that can be generalized to a variety of physical systems.Comment: LaTeX, 9 pages, 5 figures, 1 tabl