Oscillons: Resonant configurations during bubble collapse

Abstract

Oscillons are localized, nonsingular, time-dependent, spherically symmetric solutions of nonlinear scalar field theories which, although unstable, are extremely long lived. We show that they naturally appear during the collapse of subcritical bubbles in models with symmetric and asymmetric doublewell potentials. By a combination of analytical and numerical work we explain several of their properties, including the conditions for their existence, their longevity, and their final demise. We discuss several contexts in which we expect oscillons to be relevant. In particular, their nucleation during cosmological phase transitions may have wide-ranging consequences.PACS number(s): 98.80.Cq, ll.lO.Lm, 11.27.+d, 64.60.Cn I. I N T R O D U C T I O NThe search for static, localized, nonsingular solutions of nonlinear field theories has by now a long history [I].In 1+1 dimensions, it is possible t o find exact static solutions to the nonlinear Klein-Gordon field equations for certain interacting potentials, such as the kink solutions of sine-Gordon or 44 models. For a larger number of spatial dimensions, Derrick's theorem forbids the existence of static solutions for models involving only real scalar fields [ 2 ] . There are several ways t o circumvent Derrick's theorem, by invoking more complicated models with two or more interacting fields. Well-known examples include topological defects such as the 't Hooft-Polyakov monopole or the Nielsen-Olesen vortices [3]. Topological conservation laws guarantee the stability of these configurations.It is also possible t o find localized time-dependent but nondissipative solutions of nontopological nature, the socalled nontopological solitons [4]. The simplest model of a noritopological soliton in the context of renormalizable theories has a complex scalar field quadratically coupled to a real scalar field with quartic potential. The stability of the configuration comes from the conserved global charge Q carried by the complex field which is confined within a spherically symmetric domain formed by the real scalar field. One can show that for Q larger than a critical value, the energy of the configuration is smaller than the energy of Q free particles. There has been a recent upsurge of interest on nontopological solitons due to their potential relevance t o cosmology and astrophysics 'On leave from Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755.[ 5 ] . If one waives the requirement of renormalizability, it is possible to find nontopological solitons for models with a single complex scalar field, by invoking, e.g., a 46 term in the potential. These are the so-called Q-ball solutions discovered by Coleman and collaborators [6].In the present work we will go back to the simple models involving only a self-interacting real scalar field and study the properties of time-dependent spherically symmetric solutions. Because of the constraint imposed by Derrick's theorem, these configurations have been somewhat overlooked in the literature (but not completely, as we w...

Numerical investigations of oscillons in 2 dimensions

“…where r is the distance to the center of an oscillon r = (x 2 1 +x 2 2 ) 1/2 and the width of the distribution was set to be r 0 ≃ 2.9 (in units of ( √ λ v) −1 ), suggested an optimal choice for a long living oscillon in [10]. Earlier studies have established the sensitivity both to the spatial size r 0 and the amplitude of the deviation from vacuum.…”

“…In higher dimensions, the long life time of certain oscillations was pointed out 30 years ago in [7,8] and then re-discovered [9] when the dynamics of first order phase transitions and bubble nucleation was studied. More extended investigations were carried out in [10], where conditions, like the size of the initial bubble, for long living oscillations were examined. In [8] oscillating objects were called pulsons, we adopt hereafter the definition oscillon according to [10].…”

“…More extended investigations were carried out in [10], where conditions, like the size of the initial bubble, for long living oscillations were examined. In [8] oscillating objects were called pulsons, we adopt hereafter the definition oscillon according to [10].…”

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].…”

Oscillon in Einstein-scalar system with double well potential and its properties.

“…When the gravity is turned off, there is localized, longevity, nonsingular solutions, which are called "oscillons", in this theory. On flat space, the oscillons have been studied by Bogolyubsky et al [1], and Copeland et al [2]. They found that the oscillons can be formed after a bubble collapses.…”