arXiv subjects

F. K. Diakonos

Publications and source records attributed to F. K. Diakonos.

At least 37 records · Page 2Linked to original sources

arXiv2018

Life-times of quantum resonances through the Geometrical Phase Propagator Approach

We employ the recently introduced Geometric Phase Propagator Approach (GPPA) [Phys. Rev. A85, 062110 (2012)] to develop an improved perturbative scheme for the calculation of life times in driven quantum systems. This incorporates a resummation of the contributions of virtual processes starting and ending at the same state in the considered time interval. The proposed procedure allows for a strict determination of the conditions leading to finite life times in a general driven quantum system by isolating the resummed terms in the perturbative expansion contributing to their generation. To illustrate how the derived conditions apply in practice, we consider the effect of driving in a system with purely discrete energy spectrum, as well as in a system for which the eigenvalue spectrum contains a continuous part. We show that in the first case, when the driving contains a dense set of frequencies acting as a noise to the system, the corresponding bound states acquire a finite life time. When the energy spectrum contains also a continuum set of eigenvalues then the bound states, due to the driving, couple to the continuum and become quasi-bound resonances. The benchmark of this change is the appearance of a Fano-type peak in the associated transmission profile. In both cases the corresponding life-time can be efficiently estimated within the reformulated GPPA approach.

quant-ph↗

arXiv2017

Viscosity of a net-baryon fluid near the QCD critical point

In the dynamics of the QCD critical point, the net-baryon fluid, linked to the slow component of the order parameter, relaxes to a 3d Ising system in equilibrium. An analytical study of shear and bulk viscosity, with constraints imposed by the dynamics of the critical net-baryon fluid, the universality property and the requirements of a class of strong coupling theories, is performed in the neighbourhood of the critical point. It is found that the shear viscosity of the net-baryon fluid is restricted in the domain $1.6\leq 4π\fracη{s}\leq 3.7$ for $T_c < T \leq 2T_c$ whereas the bulk viscosity is small, $4π\fracζ{s} < 0.05$ (for $T>1.27 T_c$) but rising towards the singularity at $T=T_c$.

nucl-th↗

arXiv2017

Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays

We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schrödinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The framework is applied to locally inversion-(time-) and translation-(time-) symmetric one-dimensional photonic waveguide arrays with Hermitian or non-Hermitian effective tight-binding Hamiltonians. For stationary states the nonlocal currents become translationally invariant within symmetric domains, exposing different types of local symmetry. They are further employed to derive a mapping between wave amplitudes of symmetry-related sites, generalizing also the global Bloch and parity mapping to local symmetry in discrete systems. In scattering setups, perfectly transmitting states are characterized by aligned invariant currents in attached symmetry domains, whose vanishing signifies a correspondingly symmetric density. For periodically driven arrays, the invariance of the nonlocal currents is retained on period average for quasi-energy eigenstates. The proposed theory of symmetry-induced continuity and local invariants may contribute to the understanding of wave structure and response in systems with localized spatial order.

quant-ph↗

arXiv2017

Locating the QCD critical endpoint through finite-size scaling

Considering the 3d Ising universality class of the QCD critical endpoint we use a universal effective action for the description of the baryon-number density fluctuations around the critical region. Calculating the baryon-number multiplicity moments and determining their scaling with system's size we show that the critical region is very narrow in the direction of the baryon chemical potential $μ$ and wide in the temperature direction $T$ for $T > T_c$. In this context, published experimental results on local proton density-fluctuation measurements obtained by intermittency analysis in transverse momentum space in NA49 central A+A collisions at $\sqrt{s_{NN}}=17.2$ GeV (A=C,Si,Pb), restrict significantly the location $(μ_c,T_c)$ of the QCD critical endpoint. The main constraint is provided by the freeze-out chemical potential of the Si+Si system, which shows non-conventional baryon density fluctuations, restricting $(μ_c,T_c)$ within a narrow domain, $119~\textrm{MeV} \leq T_c \leq 162~\textrm{MeV}$, $252~\textrm{MeV} \leq μ_c \leq 258~\textrm{MeV}$, of the phase diagram.

hep-ph↗

arXiv2017

Condensation of Lee-Yang zeros in scalar field theory

We show that, at the critical temperature, there is a class of Lee-Yang zeros of the partition function in a general scalar field theory, which location scales with the size of the system with a characteristic exponent expressed in terms of the isothermal critical exponent $δ$. In the thermodynamic limit the zeros belonging to this class condense to the critical point ζ=1 on the real axis in the complex fugacity plane while the complementary set of zeros (with Re ζ < 1) covers uniformly the unit circle. Although the aforementioned class degenerates to a single point for an infinite system, when the size is finite it dominates in the partition function and determines the self-similar structure (fractal geometry, scaling laws) of the critical system. This property opens up the perspective to formulate finite-size scaling theory in effective QCD, near the chiral critical point, in terms of the location of Lee-Yang zeros.

hep-th↗

arXiv2017

Emitter and absorber assembly for multiple self-dual operation and directional transparency

A recursive scheme for the design of scatterers acting simultaneously as emitters and absorbers, such as lasers and coherent perfect absorbers in optics, at multiple prescribed frequencies is proposed. The approach is based on the assembly of non-Hermitian emitter and absorber units into self-dual emitter-absorber trimers at different composition levels, exploiting the simple structure of the corresponding transfer matrices. In particular, lifting the restriction to parity-time-symmetric setups enables the realization of emitter and absorber action at distinct frequencies and provides flexibility in the choice of realistic parameters. We further show how the same assembled scatterers can be rearranged to produce unidirectional and bidirectional transparency at the selected frequencies. With the design procedure being generically applicable to wave scattering in single-channel settings, we demonstrate it with concrete examples of photonic multilayer setups.

physics.optics↗

arXiv2016

A non-abelian quasi-particle model for gluon plasma

We propose a quasi-particle model for the thermodynamic description of the gluon plasma which takes into account non-abelian characteristics of the gluonic field. This is accomplished utilizing massive non-linear plane wave solutions of the classical equations of motion with a variable mass parameter, reflecting the scale invariance of the Yang-Mills Lagrangian. For the statistical description of the gluon plasma we interpret these non-linear waves as quasi-particles with a temperature dependent mass distribution. Quasi-Gaussian distributions with a common variance but different temperature dependent mean masses for the longitudinal and transverse modes are employed. We use recent Lattice results to fix the mean transverse and longitudinal masses while the variance is fitted to the equation of state of pure $SU(3)$ on the Lattice. Thus, our model succeeds to obtain both a consistent description of the gluon plasma energy density as well as a correct behaviour of the mass parameters near the critical point.

hep-ph↗

arXiv2016

Non-local Lagrangians: a variational approach to non-local conservation laws for wave mechanics

We introduce a class of non-local Lagrangians which allow for the variational derivation of non-local conser- vation laws in a self-consistent manner. The formalism developed here generalizes previous approaches, used in the context of $\mathcal{PT}$ symmetric quantum mechanics and optics in the paraxial approximation in a twofold way: firstly it is valid for a larger set of linear symmetry transforms and secondly it enables the derivation of additional non-local conservation laws for general higher dimensional wave mechanical systems.

quant-ph↗

arXiv2016

Has the QCD critical point been observed at RHIC?

The experimental search for the location of the QCD critical point in the phase diagram is of primary importance. In a recent publication it is claimed that measurements at RHIC lead not only to the location of the critical point ($μ_{cep}=95$ MeV, $T_{cep}=165$ MeV) but also to the verification of its universality class ($3d$ Ising system) by extracting the values of the critical exponents ($γ=1.2$, $ν=0.66$). We argue that this claim is based on an erroneous treatment of scaling relations near the critical point. As a result, the correct interpretation of the measurements cannot be linked to the QCD critical point.

nucl-th↗

arXiv2016

${\mathcal{PT}}$ symmetry breaking in waveguide arrays with competing loss/gain pairs

We consider a periodic waveguide array whose unit cell consists of a $\mathcal{PT}$-symmetric quadrimer with two competing loss/gain parameter pairs which lead to qualitatively different symmetry-broken phases. It is shown that the transitions between the phases are described by a symmetry-adapted nonlocal current which maps the spectral properties to the spatially resolved field, for the lattice as well as for the isolated quadrimer. Its site-average acts like a natural order parameter for the general class of one-dimensional $\mathcal{PT}$-symmetric Hamiltonians, vanishing in the unbroken phase and being nonzero in the broken phase. We investigate how the beam dynamics in the array is affected by the presence of competing loss/gain rates in the unit cell, showing that the enriched band structure yields the possibility to control the propagation length before divergence when the system resides in the broken $\mathcal{PT}$ phase.

physics.optics↗

arXiv2016

Gauss' Law and Non-Linear Plane Waves for Yang-Mills Theory

We investigate Non-Linear Plane-Wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the $SU(3)$ theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary non-zero mass and are exact extrema of the non-linear YM action. Among them, a unique harmonic plane wave with a non-trivial pattern in phase, spin and color is identified. Similar solutions are present in the $SU(4)$ case while are absent from the $SU(2)$ theory.

hep-th↗

arXiv2016

Invariant current approach to wave propagation in locally symmetric structures

A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schrödinger equation. The local symmetries of the potential are encoded into corresponding local basis vectors in terms of symmetry-induced two-point invariant currents which map the basis amplitudes between symmetry-related points. A universal wavefunction structure in locally symmetric potentials is revealed, independently of the physical boundary conditions, by using special local bases which are adapted to the existing local symmetries. The local symmetry bases enable efficient computation of spatially resolved wave amplitudes in systems with arbitrary combinations of local inversion and translation symmetries. The approach opens the perspective of a flexible analysis and control of wave localization in structurally complex systems.

quant-ph↗

arXiv2016

Domain magnetization approach to the isothermal critical exponent

We propose a method for calculating the isothermal critical exponent $δ$ in Ising systems undergoing a second-order phase transition. It is based on the calculation of the mean magnetization time series within a small connected domain of a lattice after equilibrium is reached. At the pseudocritical point, the magnetization time series attains intermittent characteristics and the probability density for consecutive values of mean magnetization within a region around zero becomes a power law. Typically the size of this region is of the order of the standard deviation of the magnetization. The emerging power-law exponent is directly related to the isothermal critical exponent $δ$ through a simple analytical expression. We employ this method to calculate with remarkable accuracy the exponent $δ$ for the square-lattice Ising model where traditional approaches, like the constrained effective potential, typically fail to provide accurate results.

cond-mat.stat-mech↗

arXiv2015

Critical fluctuations of the proton density in A+A collisions at $158A$ GeV

We look for fluctuations expected for the QCD critical point using an intermittency analysis in the transverse momentum phase space of protons produced around midrapidity in the 12.5\% most central C+C, Si+Si and Pb+Pb collisions at the maximum SPS energy of 158$A$~GeV. We find evidence of power-law fluctuations for the Si+Si data. The fitted power-law exponent $ϕ_{2} = 0.96^{+0.38}_{-0.25}\text{ (stat.)}$ $\pm 0.16\text{ (syst.)}$ is consistent with the va\-lue expected for critical fluctuations. Power-law fluctuations had previously also been observed in low-mass $π^+ π^-$ pairs in the same Si+Si collisions.

nucl-ex↗

arXiv2015

Invariant currents in lossy acoustic waveguides with complete local symmetry

We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate how this invariant current leads to the generalization of the Bloch and parity theorems for lossy systems defining a mapping of the pressure field between symmetry related spatial domains. Using experimental data we verify this mapping with remarkable accuracy. For the performed experiment we employ a construction technique based on local symmetries which allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results reveal the fundamental role of symmetries in restricted spatial domains and clearly indicate that completely locally symmetric devices constitute a promising class of setups, regarding the manipulation of wave propagation.

physics.class-ph↗

arXiv2015

Systematic pathway to ${\mathcal{PT}}$ symmetry breaking in scattering systems

Recently [Phys. Rev. Lett. {\bf 106}, 093902 (2011)] it has been shown that $\mathcal{PT}$-symmetric scattering systems with balanced gain and loss, undergo a transition from $\mathcal{PT}$-symmetric scattering eigenstates, which are norm preserving, to symmetry broken pairs of eigenstates exhibiting net amplification and loss. In the present work we derive the existence of an invariant non-local current which can be directly associated with the observed transition playing the role of an "order parameter". The use of this current for the description of the $\mathcal{PT}$-symmetry breaking allows the extension of the known phase diagram to higher dimensions incorporating scattering states which are not eigenstates of the scattering matrix.

physics.optics↗

arXiv2015

Oscillons and oscillating kinks in the Abelian-Higgs model

We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schrödinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the obtained solutions with the phenomenology of superconductors is discussed.

hep-th↗

arXiv2015

Symmetric solitonic excitations of the (1+1)-dimensional Abelian-Higgs "classical vacuum"

We study the classical dynamics of the Abelian-Higgs model in (1+1) space-time dimensions bf for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrodinger equations (CNLS). Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter which is the ratio of the Higgs mass to the gauge field mass . We show that only oscillons oscillating symmetrically with respect to the "classical vacuum", for both the gauge and the Higgs field, are long lived. Furthermore plane waves and oscillating kinks are shown to decay into oscillon- like patterns, due to the modulation instability mechanism.

hep-th↗