Small amplitude quasibreathers and oscillons

Abstract

Quasi-breathers (QB) are time-periodic solutions with weak spatial localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006). QB's provide a simple description of oscillons (very long-living spatially localized time dependent solutions). The small amplitude limit of QB's is worked out in a large class of scalar theories with a general self-interaction potential, in D spatial dimensions. It is shown that the problem of small amplitude QB's is reduced to a universal elliptic partial differential equation. It is also found that there is the critical dimension, Dcrit = 4, above which no small amplitude QB's exist. The QB's obtained this way are shown to provide very good initial data for oscillons. Thus these QB's provide the solution of the complicated, nonlinear time dependent problem of small amplitude oscillons in scalar theories.

Creating Kinks from Particles

“…Then, if we depart weakly from the sine-Gordon model, we expect long-lived "breather-like" states that can transition to both widely separated kink-antikink pair and also to particles. Such long-lived states have been discovered in various systems and have been termed "bions" in certain contexts and "oscillons" in others [9,10,11,12,13,14,15,16,17,18,19,20,21].…”

Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) inDdimensions

“…We recall that in all known examples the stability pattern of oscillons is the same, namely if dE/dε > 0 oscillons are stable, while when dE/dε < 0 oscillons are unstable, where E = E(ε) is the total energy of the oscillon [14][15][16]25]. Therefore we conjecture that the same stability pattern holds true for oscillatons, except that the energy, E is replaced by the total mass M = M (ε) of the oscillaton.…”

“…Later it has been generalized for D + 1 dimensional spherically symmetric systems in [14], and to a scalar-dilaton system in [25]. In this section we generalize the method for the case when the scalar field is coupled to gravity.…”

“…It has been shown in Refs. [13], [14], that slowly radiating oscillons can be well described by a special class of exactly time-periodic "quasibreathers" (QB). Being time periodic, QBs are easier to describe mathematically by ordinary Fourier analysis than the long time asymptotics of oscillons.…”

“…It is the incoming radiation that maintains the time periodicity of the QBs by compensating the energy loss through the outgoing waves. In a series of papers [14][15][16] a method has been developed to compute the leading part of the exponentially suppressed tail amplitude of QBs, in a large class of scalar theories in various dimensions, in the limit when the QB core amplitude is small. Although oscillons continuously loose energy through radiation, many of them are remarkably stable.…”