arXiv subjects

F. K. Diakonos

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

At least 55 records · Page 3Linked to original sources

arXiv2014

Invariant currents and scattering off locally symmetric potential landscapes

We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of spatially invariant nonlocal currents, emerging when the corresponding generalized potential exhibits symmetries in arbitrary spatial domains. These invariants characterize the wave propagation and provide a spatial mapping of the wave function between any symmetry related domains. This generalizes the Bloch and parity theorems for broken reflection and translational symmetries, respectively. Their nonvanishing values indicate the symmetry breaking, whereas a zero value denotes the restoration of the global symmetry where the well-known forms of the two theorems are recovered. These invariants allow for a systematic treatment of systems with any local symmetry combination, providing a tool for the investigation of the scattering properties of aperiodic but locally symmetric systems. To this aim we express the transfer matrix of a locally symmetric potential unit via the corresponding invariants and derive quantities characterizing the complete scattering device which serve as key elements for the investigation of transmission spectra and particularly of perfect transmission resonances.

quant-ph↗

arXiv2014

Invariants of broken discrete symmetries

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

quant-ph↗

arXiv2013

Local symmetries and perfect transmission in aperiodic photonic multilayers

We develop a classification of perfectly transmitting resonances occuring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield piecewise translation-invariant quantities, which are used to distinguish resonances with arbitrary field profile from resonances following the medium symmetries. Focusing on light scattering in aperiodic multilayer structures, we demonstrate this classification for representative setups, providing insight into the origin of perfect transmission. We further show how local symmetries can be utilized for the design of optical devices with perfect transmission at prescribed energies. Providing a link between resonant scattering and local symmetries of the underlying medium, the proposed approach may contribute to the understanding of optical response in complex systems.

physics.optics↗

arXiv2013

Exploring Rigidly Rotating Vortex Configurations and their Bifurcations in Atomic Bose-Einstein Condensates

In the present work, we consider the problem of a system of few vortices $N \leq 5$ as it emerges from its experimental realization in the field of atomic Bose-Einstein condensates. Starting from the corresponding equations of motion, we use a two-pronged approach in order to reveal the configuration space of the system's preferred dynamical states. On the one hand, we use a Monte-Carlo method parametrizing the vortex "particles" by means of hyperspherical coordinates and identifying the minimal energy ground states thereof for $N=2, ..., 5$ and different vortex particle angular momenta. We then complement this picture with a dynamical systems analysis of the possible rigidly rotating states. The latter reveals all the supercritical and subcritical pitchfork, as well as saddle-center bifurcations that arise exposing the full wealth of the problem even at such low dimensional cases. By corroborating the results of the two methods, it becomes fairly transparent which branch the Monte-Carlo approach selects for different values of the angular momentum which is used as a bifurcation parameter.

nlin.PS↗

arXiv2013

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 Schrodinger 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 direct 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 results with the phenomenology of superconductors is discussed.

hep-th↗

arXiv2013

Local symmetry dynamics in one-dimensional aperiodic lattices

A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry possess characteristic distributional and dynamical properties which can be determined for every aperiodic binary lattice. A striking aspect of such a property is given by the return maps of sequential spacings of local symmetry axes, which typically traverse few-point symmetry orbits. This local symmetry dynamics allows for a classification of inherently different aperiodic lattices according to fundamental symmetry principles. Illustrating the local symmetry distributional and dynamical properties for several representative binary lattices, we further show that the renormalized axis spacing sequences follow precisely the particular type of underlying aperiodic order. Our analysis thus reveals that the long-range order of aperiodic lattices is characterized in a compellingly simple way by its local symmetry dynamics.

cond-mat.mes-hall↗

arXiv2013

Nonlinear Schrodinger solitons in massive Yang-Mills theory and partial localization of Dirac matter

We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang-Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.

hep-th↗

arXiv2013

Finite temperature crossover from a crystalline to a cluster phase for a confined finite chain of ions

Employing Monte-Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing temperature. The corresponding transition temperature depends separately on the number of particles N and the box size L, implying non-extensivity due to the long-range character of the interactions. The probability density of the spacing between the particles exhibits at low temperatures an accumulation of discrete peaks with an overall asymmetric shape. In the vicinity of the transition temperature it is of a Gaussian form whereas in the high temperature regime an exponential decay is observed. The high temperature behaviour shows a cluster phase with a mean cluster size that first increases with the temperature and then saturates. The crossover is clearly identifiable also in the non-linear behaviour of the heat capacity with varying temperature. The influence of the trapping potential on the observed results as well as possible experimental realizations are briefly addressed.

cond-mat.stat-mech↗

arXiv2013

Local symmetries in one-dimensional quantum scattering

We introduce the concept of parity symmetry in restricted spatial domains -- local parity -- and explore its impact on the stationary transport properties of generic, one-dimensional aperiodic potentials of compact support. It is shown that, in each domain of local parity symmetry of the potential, there exists an invariant quantity in the form of a non-local current, in addition to the globally invariant probability current. For symmetrically incoming states, both invariant currents vanish if weak commutation of the total local parity operator with the Hamiltonian is established, leading to local parity eigenstates. For asymmetrically incoming states which resonate within locally symmetric potential units, the complete local parity symmetry of the probability density is shown to be necessary and sufficient for the occurrence of perfect transmission. We connect the presence of local parity symmetries on different spatial scales to the occurrence of multiple perfectly transmitting resonances and propose a construction scheme for the design of resonant transparent aperiodic potentials. Our findings are illustrated through application to the analytically tractable case of piecewise constant potentials.

quant-ph↗

arXiv2012

Coupled $\ell$-wave confinement-induced resonances in cylindrically symmetric waveguides

A semi-analytical approach to atomic waveguide scattering for harmonic confinement is developed taking into account all partial waves. As a consequence $\ell$-wave confinement-induced resonances are formed being coupled to each other due to the confinement. The corresponding resonance condition is obtained analytically using the $K$-matrix formalism. Atomic scattering is described by transition diagrams which depict all relevant processes the atoms undergo during the collision. Our analytical results are compared to corresponding numerical data and show very good agreement.

cond-mat.quant-gas↗

arXiv2012

Quantum versus Classical Dynamics in a driven barrier: the role of kinematic effects

We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. Moreover, in the frequency region of optimal agreement between classical and quantum transmission coefficient, the transmission threshold, i.e. the energy above which the transmission coefficient becomes larger than a specific small threshold value, is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well separated coherent pulses, a phenomenon which can admit purely classical kinematic interpretation.

nlin.CD↗

arXiv2012

A consistent approach for the treatment of Fermi acceleration in time-dependent billiards

The standard description of Fermi acceleration, developing in a class of time-dependent billiards, is given in terms of a diffusion process taking place in momentum space. Within this framework the evolution of the probability density function (PDF) of the magnitude of particle velocities as a function of the number of collisions $n$ is determined by the Fokker-Planck equation (FPE). In the literature the FPE is constructed by identifying the transport coefficients with the ensemble averages of the change of the magnitude of particle velocity and its square in the course of one collision. Although this treatment leads to the correct solution after a sufficiently large number of collisions has been reached, the transient part of the evolution of the PDF is not described. Moreover, in the case of the Fermi-Ulam model (FUM), if a stadanrd simplification is employed, the solution of the FPE is even inconsistent with the values of the transport coefficients used for its derivation. The goal of our work is to provide a self-consistent methodology for the treatment of Fermi acceleration in time-dependent billiards. The proposed approach obviates any assumptions for the continuity of the random process and the existence of the limits formally defining the transport coefficients of the FPE. Specifically, we suggest, instead of the calculation of ensemble averages, the derivation of the one-step transition probability function and the use of the Chapman-Kolmogorov forward equation. This approach is generic and can be applied to any time-dependent billiard for the treatment of Fermi-acceleration. As a first step, we apply this methodology to the FUM, being the archetype of time-dependent billiards to exhibit Fermi acceleration.

nlin.CD↗

arXiv2011

A multi-scale perturbative approach to SU(2)-Higgs classical dynamics: stability of nonlinear plane waves and bounds of the Higgs field mass

We study the classical dynamics of SU(2)-Higgs field theory using multiple scale perturbation theory. In the spontaneously broken phase, assuming small perturbations of the Higgs field around its vacuum expectation value, we derive a nonlinear Schroedinger equation and study the stability of its nonlinear plane wave solutions. The latter, turn out to be stable only if the Higgs amplitude is an order of magnitude smaller than that of the gauge field. In this case, the Higgs field mass possesses some bounds which may be relevant to the search for the Higgs particle at ongoing experiments.

hep-ph↗

arXiv2011

Stationary states of a nonlinear Schrödinger lattice with a harmonic trap

We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that - in the discrete regime - all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only inside the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed.

cond-mat.quant-gas↗

arXiv2011

Resonant Population Transfer in the Time-Dependent Quantum Elliptical Billiard

We analyze the quantum dynamics of the time-dependent elliptical billiard using the example of a certain breathing mode. A numerical method for the time-propagation of an arbitrary initial state is developed, based on a series of transformations thereby removing the time-dependence of the boundary conditions. The time-evolution of the energies of different initial states is studied. The maximal and minimal energy that is reached during the time-evolution shows a series of resonances as a function of the applied driving frequency. At these resonances, higher (or lower) lying states are periodically populated, leading to the observed change in energy. The resonances occur when the driving frequency or a multiple of it matches exactly the mean energetic difference between the two involved states. This picture is confirmed by a few-level Rabi-like model with periodic couplings, reproducing the key results of our numerical study.

quant-ph↗

arXiv2011

The simplified stochastic Fermi-Ulam model revisited

The description of Fermi acceleration developing in the phase-randomized simplified Fermi-Ulam model (SFUM) can be achieved in terms of a random walk taking place in momentum space. Within this framework the evolution of the probability density function of particle velocities is determined by the Fokker-Planck equation (FPE). However, the standard treatment in the literature leads to a result, which even though is in agreement with the numerical results, it is inconsistent with the transport coefficients used for the construction of the FPE. In this work we present a consistent scheme for the description of Fermi acceleration, resolving this contradiction.

nlin.CD↗

arXiv2010

MIT bag model inspired partonic transverse momentum distribution for prompt photon production in pp collisions

We consider the prompt photon production in pp collisions using, within the framework of perturbative QCD, a non-Gaussian distribution for the transverse momentum distribution of the partons inside the proton. Our description adopts the widely used in the literature factorization of the partonic momentum distribution into longitudinal and transverse components. It is argued that the non-Gaussian distribution of the intrinsic transverse momenta of the partons is dictated by the asymptotic freedom as well as the 3D confinement of the partons in the proton. To make this association more transparent we use the MIT bag model, which plainly incorporates both properties (asymptotic freedom, confinement), in order to determine in a simplified way the partonic transverse momentum distribution. A large set of data from six different experiments have been fitted with this simple description using as a single free parameter the mean partonic transverse momentum . Surprisingly enough, a perfect fit of the experimental data turns out to require values which are compatible with Heisenberg's uncertainty relation for the proton and decrease almost smoothly as a function of the scaled variable z=pT/\sqrt{s}, where pT is the transverse momentum of the final photon and \sqrt{s} is the beam energy in the center of mass frame. Our analysis indicates that asymptotic freedom and 3D confinement may influence significantly the form of the partonic transverse momentum distribution leaving an imprint on the pp\toγ+X cross section.

hep-ph↗

arXiv2010

Partonic transverse momenta in non-relativistic hyper-central quark potential models

We investigate the impact of three-body forces on the transverse-momentum distribution of partons inside the proton. This is achieved by considering the three-body problem in a class of hyper-central quark potential models. Solving the corresponding Schrödinger equation, we determine the quark wave function in the proton and with appropriate transformations and projections we find the transverse-momentum distribution of a single quark. In each case the parameters of the quark potentials are adjusted in order to sufficiently describe observable properties of the proton. Using a factorization ansatz, we incorporate the obtained transverse-momentum distribution in a perturbative QCD scheme for the calculation of the cross-section for prompt photon production in pp collisions. A large set of experimental data is fitted using as a single free parameter the mean partonic transverse momentum. The dependence of on the collision characteristics (initial energy and transverse momentum of the final photon) is much smoother when compared with similar results found in the literature using a Gaussian distribution for the partonic transverse momenta. Within the considered class of hyper-central quark potentials the one with the weaker dependence on the hyper-radius is preferred for the description of the data since it leads to the smoothest mean partonic transverse-momentum profile. We have repeated all the calculations using a two-body potential of the same form as the optimal (within the considered class) hyper-central potential in order to check if the presence of three-body forces is supported by the experimental data. Our analysis indicates that three-body forces influence significantly the form of the parton transverse-momentum distribution and consequently lead to an improved description of the considered data.

hep-ph↗