arXiv subjects

P. A. Kalozoumis

Publications and source records attributed to P. A. Kalozoumis.

At least 19 recordsLinked to original sources

arXiv2022

Topological edge-states of the PT-symmetric Su-Schrieffer-Heeger model: An effective two-state description

We consider the non-Hermitian, parity-time (PT) symmetric extensions of the one-dimensional Su-Schrieffer-Heeger (SSH) model in the topological non-trivial configuration. We study the properties of the topologically protected edge states, and develop an effective two-state analytical description of the system that accurately predicts the PT-symmetry breaking point for the edge states. We verify our analytical results by exact numerical calculations.

quant-ph↗

arXiv2021

Generalized Continuity Equations for Schrödinger and Dirac Equations

The concept of the generalized continuity equation (GCE) was recently introduced in [J. Phys. A: Math. and Theor. {\bf 52}, 1552034 (2019)], and was derived in the context of $N$ independent Schrödinger systems. The GCE is induced by a symmetry transformation which mixes the states of these systems, even though the $N$-system Lagrangian does not. As the $N$-system Schrödinger Lagrangian is not invariant under such a transformation, the GCE will involve source terms which, under certain conditions vanish and lead to conserved currents. These conditions may hold globally or locally in a finite domain, leading to globally or locally conserved currents, respectively. In this work, we extend this idea to the case of arbitrary $SU(N)$-transformations and we show that a similar GCE emerges for $N$ systems in the Dirac dynamics framework. The emerging GCEs and the conditions which lead to the attendant conservation laws provide a rich phenomenology and potential use for the preparation and control of fermionic states.

quant-ph↗

arXiv2020

Coherent population oscillations and an effective spin-exchange interaction in a $\mathcal{PT}$ symmetric polariton mixture

We study a two-species mixture of exciton-polaritons with self- and cross-interaction nonlinearities in a double well structure, in the presence of relaxation and continuous pumping. We identify the conditions that render the system parity-time ($\mathcal{PT}$) symmetric, and investigate its dynamic and static properties. We show that the system can exhibit long-term coherent oscillations of populations of the two polaritonic components between the two potential wells, and can simulate the dynamics of a pair of spin-1/2 particles (qubits) in the presence of exchange interaction.

quant-ph↗

arXiv2018

Open and closed spin chains as multiprocessor wires: optimal engineering and reachability

We consider the perfect transfer of a state between arbitrary nodes of one-dimensional spin-1/2 chain with optimally engineered couplings. Motivated by the fact that such a system could be used as a data bus for connecting multiple quantum processors, we derive two necessary and sufficient conditions that have to be met in order to perfectly transfer a state between any two nodes and we employ them to examine both open and closed geometries. Analytical calculations and numerical optimizations are performed for both cases in order to determine the reachability of certain target states and to provide optimal values for the couplings which ensure perfect fidelity. An important finding is that even-sized closed chains allow for perfect transfer between any pair of sites and therefore are a promising platform for the implementation of data bus protocols.

quant-ph↗

arXiv2018

Time-dependent transport through a T-coupled quantum dot

We are considering the time-dependent transport through a discrete system, consiting of a quantum dot T-coupled to an infinite tight-binding chain. The periodic driving that is induced on the coupling between the dot and the chain, leads to the emergence of a characteristic multiple Fano resonant profile in the transmission spectrum. We focus on investigating the underlying physical mechanisms that give rise to the quantum resonances. To this end, we use Floquet theory for calculating the transmission spectrum and in addition employ the Geometric Phase Propagator (GPP) approach [Ann. Phys. 375, 351 (2016)] to calculate the transition amplitudes of the time-resolved virtual processes, in terms of which we describe the resonant behavior. This two fold approach, allows us to give a rigorous definition of a quantum resonance in the context of driven systems and explains the emergence of the characteristic Fano profile in the transmission spectrum.

quant-ph↗

arXiv2018

Duality of bounded and scattering wave systems with local symmetries

We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domain-wise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard wall boundaries leads to extrema of the eigenenergies. The underlying wavefunction becomes then an eigenstate of the local symmetry transform in each of the domains of local symmetry. These extrema accumulate towards eigenenergies which do not depend on the position of the potentials inside the walls. They correspond to perfect transmission resonances of the associated scattering setup, obtained by removing the hard walls. We argue that this property characterizes the duality between scattering and bounded systems in the presence of local symmetries. Our findings are illustrated at hand of a numerical example with a potential consisting of two domains of local symmetry, each one comprised of Dirac ? barriers.

cond-mat.other↗

arXiv2017

Finite size effects on topological interface states in one-dimensional scattering systems

One-dimensional topological edge modes are usually studied considering the interface between two different semi infinite periodic crystals (PCs) with inverted band structure around the Dirac point. Here we consider the case where the two PCs are finite, constituting an open scattering system, and we study the influence of the size of this finite structure on the interface mode by inspecting the complex resonances. First we show the complex resonance distribution corresponding to the band inversion around the Dirac point. Perturbations from the Dirac point display the emergence of the localized interface mode. We also report on a remarkable robustness of the interface mode as the system size varies which persists even for the smallest possible size.

physics.optics↗

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

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

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

${\mathcal{PT}}$ 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

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

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↗

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↗

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

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↗