38 research outputs found
Oscillons in Scalar Field Theories: Applications in Higher Dimensions and Inflation
The basic properties of oscillons -- localized, long-lived, time-dependent
scalar field configurations -- are briefly reviewed, including recent results
demonstrating how their existence depends on the dimensionality of spacetime.
Their role on the dynamics of phase transitions is discussed, and it is shown
that oscillons may greatly accelerate the decay of metastable vacuum states.
This mechanism for vacuum decay -- resonant nucleation -- is then applied to
cosmological inflation. A new inflationary model is proposed which terminates
with fast bubble nucleation.Comment: 11 pages, 4 figures, to appear in Int. J. Mod. Phys.
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 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 () larger than scalar masses
(). 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 -- where such configurations exist and to
follow them for times t \sim \O(10^5) m^{-1}. An investigation of their
properties for -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
Topological quantum numbers and curvature -- examples and applications
Using the idea of the degree of a smooth mapping between two manifolds of the
same dimension we present here the topological (homotopical) classification of
the mappings between spheres of the same dimension, vector fields, monopole and
instanton solutions. Starting with a review of the elements of Riemannian
geometry we also present an original elementary proof of the Gauss-Bonnet
theorem and the Poincar\'{e}-Hopf theorem.Comment: LaTeX2e, 26 pages, 4 figure
On certain classes of solutions of the Weierstrass-Enneper system inducing constant mean curvature surfaces
Analysis of the generalized Weierstrass-Enneper system includes the
estimation of the degree of indeterminancy of the general analytic solution and
the discussion of the boundary value problem. Several different procedures for
constructing certain classes of solutions to this system, including potential,
harmonic and separable types of solutions, are proposed. A technique for
reduction of the Weierstrass-Enneper system to decoupled linear equations, by
subjecting it to certain differential constraints, is presented as well. New
elementary and doubly periodic solutions are found, among them kinks, bumps and
multi-soliton solutions
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
d-dimensional Oscillating Scalar Field Lumps and the Dimensionality of Space
Extremely long-lived, time-dependent, spatially-bound scalar field
configurations are shown to exist in spatial dimensions for a wide class of
polynomial interactions parameterized as . Assuming spherical symmetry and if
for a range of values of , such configurations exist if: i) spatial
dimensionality is below an upper-critical dimension ; ii) their radii are
above a certain value . Both and are uniquely
determined by . For example, symmetric double-well potentials only
sustain such configurations if and . Asymmetries may modify the value of . All
main analytical results are confirmed numerically. Such objects may offer novel
ways to probe the dimensionality of space.Comment: In press, Physics Letters B. 6 pages, 2 Postscript figures, uses
revtex4.st
Affine Toda Solitons and Vertex Operators
Affine Toda theories with imaginary couplings associate with any simple Lie
algebra generalisations of Sine Gordon theory which are likewise
integrable and possess soliton solutions. The solitons are \lq\lq created" by
exponentials of quantities which lie in the untwisted affine
Kac-Moody algebra and ad-diagonalise the principal Heisenberg
subalgebra. When is simply-laced and highest weight irreducible
representations at level one are considered, can be expressed as
a vertex operator whose square vanishes. This nilpotency property is extended
to all highest weight representations of all affine untwisted Kac-Moody
algebras in the sense that the highest non vanishing power becomes proportional
to the level. As a consequence, the exponential series mentioned terminates and
the soliton solutions have a relatively simple algebraic expression whose
properties can be studied in a general way. This means that various physical
properties of the soliton solutions can be directly related to the algebraic
structure. For example, a classical version of Dorey's fusing rule follows from
the operator product expansion of two 's, at least when is
simply laced. This adds to the list of resemblances of the solitons with
respect to the particles which are the quantum excitations of the fields.Comment: Imperial/TP/92-93/29 SWAT/92-93/5 PU-PH-93/1392, requires newma
Quantum kink and its excitations
We show how detailed properties of a kink in quantum field theory can be
extracted from field correlation functions. This makes it possible to study
quantum kinks in a fully non-perturbative way using Monte Carlo simulations. We
demonstrate this by calculating the kink mass as well as the spectrum and
approximate wave functions of its excitations. This way of measuring the kink
mass has clear advantages over the existing approaches based on creation and
annihilation operators or the kink free energy. Our methods are straightforward
to generalise to more realistic theories and other defect types.Comment: 21 pages, 11 figures, v2: typos corrected, references adde