Árpád Lukács

Small amplitude quasibreathers and oscillons

Quasibreathers (QB) are time-periodic solutions with weak spatial localization introduced in G. Fodor et al. in [Phys. Rev. D 74, 124003 (2006)]. QBs provide a simple description of oscillons (very long-living spatially localized time dependent solutions). The small amplitude limit of QBs 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 QBs is reduced to a universal elliptic partial differential equation. It is also found that there is the critical dimension, D{sub crit}=4, above which no small amplitude QBs exist. The QBs obtained this way are shown to provide very good initial data for oscillons. Thus these QBs provide the solution of the complicated, nonlinear time dependent problem of small amplitude oscillons in scalar theories.

Instabilities of twisted strings

A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory ? an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry ? is carried out. Here the twist refers to a relative phase between the two complex scalars (with linear dependence on, say, the z coordinate), and importantly it leads to a global current flowing along the the string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO) solution embedded in the semilocal theory. Our numerical investigations of the small fluctuation spectrum confirm previous results that twisted strings exhibit instabilities whose amplitudes grow exponentially in time. More precisely twisted strings with a single magnetic flux quantum admit a continuous family of unstable eigenmodes with harmonic z dependence, indexed by a wavenumber k[?km, km]. Carrying out a perturbative semi-analytic analysis of the bifurcation, it is found that the purely numerical results are very well reproduced. This way one obtains not only a good qualitative description of the twisted solutions themselves as well as of their instabilities, but also a quantitative description of the numerical results. Our semi-analytic results indicate that in close analogy to the known instability of the embedded ANO vortex a twisted string is also likely to expand in size caused by the spreading out of its magnetic flux.A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory — an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry — is carried out. Here the twist refers to a relative phase between the two complex scalars (with linear dependence on, say, the z coordinate), and importantly it leads to a global current flowing along the the string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO) solution embedded in the semilocal theory. Our numerical investigations of the small fluctuation spectrum confirm previous results that twisted strings exhibit instabilities whose amplitudes grow exponentially in time. More precisely twisted strings with a single magnetic flux quantum admit a continuous family of unstable eigenmodes with harmonic z dependence, indexed by a wavenumber k[−km, km]. Carrying out a perturbative semi-analytic analysis of the bifurcation, it is found that the purely numerical results are very well reproduced. This way one obtains not only a good qualitative description of the twisted solutions themselves as well as of their instabilities, but also a quantitative description of the numerical results. Our semi-analytic results indicate that in close analogy to the known instability of the embedded ANO vortex a twisted string is also likely to expand in size caused by the spreading out of its magnetic flux.

Vortices and magnetic bags in Abelian models with extended scalar sectors and some of their applications

A detailed study of vortices is presented in Ginzburg-Landau (or Abelian Higgs) models with two complex scalars (order parameters) assuming a general U(1)×U(1) symmetric potential. Particular emphasis is given to the case in which only one of the scalars obtains a vacuum expectation value (VEV). It is found that for a significantly large domain in parameter space vortices with a scalar field condensate in their core [condensate core (CC)] coexist with Abrikosov-Nielsen-Olesen (ANO) vortices. Importantly, CC vortices are stable and have lower energy than the ANO ones. Magnetic bags or giant vortices of the order of 1000 flux quanta are favored to form for the range of parameters (“strong couplings”) appearing for the superconducting state of liquid metallic hydrogen (LMH). Furthermore, it is argued that finite energy/unit length 1VEV vortices are smoothly connected to fractional flux 2VEV ones. Stable, finite energy CC-type vortices are also exhibited in the case when one of the scalar fields is neutral.

Time-dependent Bogomolny-Prasad-Sommerfeld skyrmions

An extended version of the BPS Skyrme model that admits time-dependent solutions is discussed. Initially, by introducing a power law at the original potential term of the BPS Skyrme model the existence, stability and structure of the corresponding solutions is investigated. Then, the frequencies and half-lifes of the radial oscillations of the constructed time-dependent solutions are determined.An extended version of the Bogomolny-Prasad-Sommerfeld (BPS) Skyrme model that admits time-dependent solutions is discussed. Initially, by introducing a power law at the original potential term of the BPS Skyrme model, the existence, stability, and structure of the corresponding solutions are investigated. Then, the frequency and half-lifes of the radial oscillations of the constructed time-dependent solutions are determined.

Negative radiation pressure exerted on kinks

The interaction of a kink and a monochromatic plane wave in one dimensional scalar field theories is studied. It is shown that in a large class of models the radiation pressure exerted on the kink is negative, i.e. the kink is pulled towards the source of the radiation. This effect has been observed by numerical simulations in the

Stabilization of semilocal strings by dark scalar condensates

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“Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model

model, and it is explained by a perturbative calculation assuming that the amplitude of the incoming wave is small. Quite importantly the effect is shown to be robust against small perturbations of the

AN ANALYTIC APPROACH TO THE LATE ISW EFFECT IN A Λ DOMINATED UNIVERSE

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Canonical Quantization and Black Hole Perturbations

model. In the sine-Gordon (SG) model the time-averaged radiation pressure acting on the kink turns out to be zero. The results of the perturbative computations in the SG model are shown to be in full agreement with an analytical solution corresponding to the superposition of a SG kink with a cnoidal wave. It is also demonstrated that the acceleration of the kink satisfies Newtons law.

Twisted non-Abelian vortices

Semilocal and electroweak strings are well known to be unstable against unwinding by the condensation of the second Higgs component in their cores. A large class of current models of dark matter contains dark scalar fields coupled to the Higgs sector of the Standard Model (Higgs portal) and/or dark U(1) gauge fields. It is shown that Higgs-portal-type couplings and a gauge kinetic mixing term of the dark U(1) gauge field have a significant stabilizing effect on semilocal strings in the “visible” sector.