3,561 research outputs found
Peakompactons: Peaked compact nonlinear waves
This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. These peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vries-type models. Peakompactons, like the now-well-known compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly by reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. A simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solu..
Chiral Asymmetry from a 5D Higgs Mechanism
An intriguing feature of the Standard Model is that the representations of
the unbroken gauge symmetries are vector-like whereas those of the
spontaneously broken gauge symmetries are chiral. Here we provide a toy model
which shows that a natural explanation of this property could emerge in higher
dimensional field theories and discuss the difficulties that arise in the
attempt to construct a realistic theory. An interesting aspect of this type of
models is that the 4D low energy effective theory is not generically gauge
invariant. However, the non-invariant contributions to the observable
quantities are very small, of the order of the square of the ratio between the
light particle mass scale and the Kaluza-Klein mass scale. Remarkably, when we
take the unbroken limit both the chiral asymmetry and the non-invariant terms
disappear.Comment: 30 pages, 5 figures, uses axodraw.sty. Extended version, matches the
article published on JHE
Nonequilibrium Quantum Dynamics of Second Order Phase Transitions
We use the so-called Liouville-von Neumann (LvN) approach to study the
nonequilibrium quantum dynamics of time-dependent second order phase
transitions. The LvN approach is a canonical method that unifies the functional
Schr\"{o}dinger equation for the quantum evolution of pure states and the LvN
equation for the quantum description of mixed states of either equilibrium or
nonequilibrium. As nonequilibrium quantum mechanical systems we study a
time-dependent harmonic and an anharmonic oscillator and find the exact Fock
space and density operator for the harmonic oscillator and the nonperturbative
Gaussian Fock space and density operator for the anharmonic oscillator. The
density matrix and the coherent, thermal and coherent-thermal states are found
in terms of their classical solutions, for which the effective Hamiltonians and
equations of motion are derived. The LvN approach is further extended to
quantum fields undergoing time-dependent second order phase transitions. We
study an exactly solvable model with a finite smooth quench and find the
two-point correlation functions. Due to the spinodal instability of long
wavelength modes the two-point correlation functions lead to the
-scaling relation during the quench and the Cahn-Allen scaling
relation after the completion of quench. Further, after the finite
quench the domain formation shows a time-lag behavior at the cubic power of
quench period. Finally we study the time-dependent phase transition of a
self-interacting scalar field.Comment: discussion on back-reaction added, typos corrected, references added,
final version for PR
CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions
CMB anisotropy measurements have brought the issue of global topology of the
universe from the realm of theoretical possibility to within the grasp of
observations. The global topology of the universe modifies the correlation
properties of cosmic fields. In particular, strong correlations are predicted
in CMB anisotropy patterns on the largest observable scales if the size of the
Universe is comparable to the distance to the CMB last scattering surface. We
describe in detail our completely general scheme using a regularized method of
images for calculating such correlation functions in models with nontrivial
topology, and apply it to the computationally challenging compact hyperbolic
spaces. Our procedure directly sums over images within a specified radius,
ideally many times the diameter of the space, effectively treats more distant
images in a continuous approximation, and uses Cesaro resummation to further
sharpen the results. At all levels of approximation the symmetries of the space
are preserved in the correlation function. This new technique eliminates the
need for the difficult task of spatial eigenmode decomposition on these spaces.
Although the eigenspectrum can be obtained by this method if desired, at a
given level of approximation the correlation functions are more accurately
determined. We use the 3-torus example to demonstrate that the method works
very well. We apply it to power spectrum as well as correlation function
evaluations in a number of compact hyperbolic (CH) spaces. Application to the
computation of CMB anisotropy correlations on CH spaces, and the observational
constraints following from them, are given in a companion paper.Comment: 27 pages, Latex, 11 figures, submitted to Phys. Rev. D, March 11,
199
Electron-Positron Pair Production in Space- or Time-Dependent Electric Fields
Treating the production of electron and positron pairs by a strong electric
field from the vacuum as a quantum tunneling process we derive, in
semiclassical approximation, a general expression for the pair production rate
in a -dependent electric field pointing in the -direction. We also
allow for a smoothly varying magnetic field parallel to . The result is
applied to a confined field for , a
semi-confined field for , and a linearly increasing
field . The boundary effects of the confined fields on
pair-production rates are exhibited. A simple variable change in all formulas
leads to results for electric fields depending on time rather than space.
In addition, we discuss tunneling processes in which empty atomic bound
states are spontaneously filled by negative-energy electrons from the vacuum
under positron emission. In particular, we calculate the rate at which the
atomic levels of a bare nucleus of finite size and large
are filled by spontaneous pair creation.Comment: 33 pages and 9 figures. to appear in Phys. Rev.
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