Arpad Laszlo Lukacs

• Doctor of Philosophy
• PostDoc Position at Durham University

Polyhedral cages (or p-cages) are a generalisation of the polyhedron surface: they are objects in three-dimensional space consisting of planar polygons attached along shared edges but allowed to have holes and thus edges not shared by two polygons. The main motivation driving the research into the properties of p-cages is the structure of artificia...

Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of one family have five neighbors and P1 edges, while those of the other family have six neighbors and P2 edges. We restrict ourselves to polyhedral cages where...

Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of 1 family has 5 neighbours and P_1 edges, while those of the other family have 6 neighbours and P_2 edges. We restrict ourselves to polyhedral cages where the...

We consider quantum metrology with several copies of bipartite and multipartite quantum states. We characterize the metrological usefulness by determining how much the state outperforms separable states. We identify a large class of entangled states that become maximally useful for metrology in the limit of large number of copies, even if the state...

In two-component nonlinear Schrödinger equations, the force exerted by incident monochromatic plane waves on an embedded dark soliton and on dark-bright-type solitons is investigated, both perturbatively and by numerical simulations. When the incoming wave is nonvanishing only in the orthogonal component to that of the embedded dark soliton, its ac...

Following the discovery of an artificial protein cage with a paradoxical geometry, we extend the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages, for which all the faces are equivalent, and define bi-homogeneous symmetric polyhedral cages made of two different types of faces, where all the faces of a given type are...

In two-component non-linear Schr\"odinger equations, the force exerted by incident monochromatic plane waves on an embedded dark soliton and on dark-bright-type solitons is investigated, both perturbatively and by numerical simulations. When the incoming wave is non-vanishing only in the orthogonal component to that of the embedded dark soliton, it...

Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons numerically to construct all such polyhedral...

A generic semiclassical superconducting nanostructure connected to multiple superconducting terminals hosts a quasicontinuous spectrum of Andreev states. The spectrum is sensitive to the superconducting phases of the terminals. It can be either gapped or gapless depending on the point in the multidimensional parametric space of these phases. Specia...

We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system. For a given quantum state, our methods find the best local Hamiltonian for which the state outperforms separable states the most from the point of view of quantum metrology. We show that this problem can be reduced to maximiz...

We consider quantum metrology with several copies of bipartite and multipartite quantum states. We identify a large class of states that become maximally useful for metrology in the limit of infinite number of copies. The maximally achievable metrological usefulness is attained exponentially fast in the number of copies. We show that, on the other...

A generic semiclassical superconducting nanostructure connected to multiple superconducting terminals hosts a quasi-continuous spectrum of Andreev states. The spectrum is sensitive to the superconducting phases of the terminals. It can be either gapped or gapless depending on the point in the multi-dimensional parametric space of these phases. Spec...

In the Abelian Higgs model electric (and magnetic) fields of external charges (and currents) are screened by the scalar field. In this contribution, complementing recent investigations of Ishihara and Ogawa, we present a detailed investigation of charge screening using a perturbative approach with the charge strength as an expansion parameter. It i...

In the Abelian Higgs model electric (and magnetic) fields of external charges (and currents) are screened by the scalar field. In this contribution, complementing recent investigations of Ishihara and Ogawa, we present a detailed investigation of charge screening using a perturbative approach with the charge strength as an expansion parameter. It i...

In a series of recent works, Ishihara and Ogawa have investigated nontopological solitons (Q-balls) in a spontaneously broken Abelian gauge theory coupled to two complex scalar fields. The present paper extends their investigations to the most general U(1)×U(1) symmetric quartic potential. Also, a new class of charged Q-ball solutions with vanishin...

In a series of recent works Ishihara and Ogawa have investigated non-topological solitons (Q-balls) in a spontaneously broken Abelian gauge theory coupled to two complex scalar fields. The present paper extends their investigations to the most general U(1)$\times$U(1) symmetric quartic potential. Also a new class of charged Q-ball solutions with va...

The stability of “visible” electroweak-type cosmic strings is investigated in an extension of the Standard Model by a minimal dark sector, consisting of a U(1) gauge field, broken spontaneously by a scalar. The visible and dark sectors are coupled through a Higgs-portal and a gauge-kinetic mixing term. It is found that strings whose core is “filled...

The stability of "visible" electroweak-type cosmic strings is investigated in an extension of the Standard Model (SM) by a minimal dark sector, consisting of a U(1) gauge field, broken spontaneously by a scalar. The "visible" and dark sectors are coupled through a Higgs-portal and a gauge-kinetic mixing term. It is found that strings whose core is...

A variety of quantum systems exhibit Weyl points in their spectra where two bands cross in a point of three-dimensional parameter space with conical dispersion in the vicinity of the point. We consider theoretically the soft constraint regime where the parameters are dynamical quantum variables. We have shown that in general the soft constraints, i...

A variety of quantum systems exhibits Weyl points in their spectra where two bands cross in a point of three-dimensional parameters space with conical dispersion in the vicinity of the point. We consider theoretically the soft constraint regime where the parameters are dynamical quantum variables. We have shown that in general the soft constraints,...

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-...

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-...

Twisted non-Abelian flux-tube solutions are considered in the bosonic sector of a 4-dimensional 𝒩 = 2 super-symmetric gauge theory with U(2)local ×SU(2)global symmetry, with two scalar doublets in the fundamental representation. Twist refers to a time-dependent matrix phase between the two doublets, and twisted strings have nonzero (global) charge,...

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)$\times$U(1) symmetric potential. Particular emphasis is given to the case, when only one of the scalars obtains a vacuum expectation value (VEV). It is found that for a significantly large domain...

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)$\times$U(1) symmetric potential. Particular emphasis is given to the case, when only one of the scalars obtains a vacuum expectation value (VEV). It is found that for a significantly large domain...

In a class of two-component Ginzburg-Landau models (TCGL) with a U(1)$\times$U(1) symmetric potential, vortices with a condensate at their core may have significantly lower energies than the Abrikosov-Nielsen-Olesen (ANO) ones. On the example of liquid metallic hydrogen (LMH) above the critical temperature for protons we show that the ANO vortices...

In a class of two-component Ginzburg-Landau models (TCGL) with a U(1)$\times$U(1) symmetric potential, vortices with a condensate at their core may have significantly lower energies than the Abrikosov-Nielsen-Olesen (ANO) ones. On the example of liquid metallic hydrogen (LMH) above the critical temperature for protons we show that the ANO vortices...

The BPS Skyrme model is a model containing an $SU(2)$-valued scalar field, in which a Bogomol'nyi-type inequality can be satisfied by soliton solutions. In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-b...

The BPS Skyrme model is a model containing an $SU(2)$-valued scalar field, in which a Bogomol'nyi-type inequality can be satisfied by soliton solutions. In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-b...

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...

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 cons...

Non-Abelian flux-tube (string) solutions carrying global currents are found in the bosonic sector of 4-dimensional N=2 super-symmetric gauge theories. The specific model considered here posseses U(2)local x SU(2)global symmetry, with two scalar doublets in the fundamental representation of SU(2). We construct string solutions that are stationary an...

We present an effective model, which is an extension of the usual linear sigma model, that contains a low energy multiplet for every hadronic particle type. These multiplets are a scalar nonet, a pseudoscalar nonet, a vector nonet, an axialvector nonet, a baryon octet and a baryon decuplet. Tree level baryon masses and possible two body decuplet de...

We study string solutions in two-component Abelian Higgs models with globally U(1) × U(1) symmetric potentials. Two component Abelian Higgs models with spontaneous symmetry breaking are divided into two classes, according to the number of Higgs field components obtaining a nonzero vacuum expectation value. In one class, where one field component is...

It is shown that in a large class of systems plane waves can act as tractor beams: i.e., an incident plane wave can exert a pulling force on the scatterer. The underlying physical mechanism for the pulling force is due to the sufficiently strong scattering of the incoming wave into another mode having a larger wave number, in which case excess mome...

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...

Quasibreathers (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 g...

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 {\sl pulled} towards the source of the radiation. This effect has been observed by numerical simulations in the $\phi^4$ mo...

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 g...

The integrated Sachs–Wolfe (ISW) effect in a Λ dominated universe can be an important factor in the evolution of cosmic microwave background fluctuations. With the inclusion of cosmological constant we present the complete analytic solution of the covariant linear perturbations of the Einstein equations in the Newtonian gauge, in the case of a spat...

We present the complete solution of the first order metric and density perturbation equations in a spatially flat (K = 0), Friedmann–Robertson–Walker (FRW) universe filled with pressureless ideal fluid, in the presence of cosmological constant. We use covariant linear perturbation formalism and the comoving gauge condition to obtain the field and c...

We examine the possibility of a constraint‐free quantization of linearized gravity, based on the Teukolsky equation for black hole perturbations. We exhibit a simple quadratic (but complex) Lagrangian for the Teukolsky equation, leading to the interpretation that the elementary excitations (gravitons bound to the Kerr black hole) are unstable.