arXiv subjects

F. K. Diakonos

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

At least 19 recordsLinked to original sources

arXiv2026

Lévy-like flights and fractal geometry of finite point sets

We study Lévy-like and truncated Lévy-like flights with step probability distribution of the form $r^{-1+ν}$ for negative, positive, and zero $ν$, focusing on the appearance of fractal geometry characteristics in the generated point sets. Forming ensembles of such point sets with fixed multiplicity, we develop simulation techniques leading to the desired value of correlation dimension in a vast continuous interval of scales. In particular, we demonstrate the possibility to produce ensembles of data sets with a low number of points with the needed properties. Furthermore, we show that the positive $ν$ distributions, apart from a region near the upper scale limit, show fractal behaviour that extends to infinitesimally low scales. As an example, we apply our findings to producing simulations relevant to the search for critical fluctuations, related to QCD critical endpoint, in heavy-ion collision experiments.

cond-mat.stat-mech↗

arXiv2026

Mechanisms of localization in a finite harmonically confined optical superlattice

We investigate the impact of harmonic confinement in a finite optical superlattice and reveal the different mechanisms that can lead to the emergence of localized states. The optical superlattice, with odd or even number of unit cells, can exhibit either a trivial or a non-trivial underlying topology, characterized by the corresponding Zak phase. We focus on a distinct localization mechanism in the intermediate harmonic trapping frequency regime. Specifically, the four lowest-lying eigenstates in this regime form an effective four-level system in the topologically non-trivial configuration. Larger trapping frequency values drive the system into a harmonic trap dominated regime, featuring classical pairing and localization of all states of the lower band, as in a usual optical lattice. For the lower trapping frequency regime, the fate of topological edge states is discussed. Our results are based on exact diagonalization and on a tight-binding approximation that maps the continuous to a discrete system. We address several aspects relevant to the experimental implementation of optical superlattices and provide a brief illustration of the dynamics, highlighting direct ways to observe and distinguish between the different localization mechanisms.

physics.optics↗

arXiv2025

Long-Range Interacting Particles on a Helix: A Statistical and Correlation Analysis of Equilibrium Configurations

We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional helical manifold. The two-body system has been demonstrated to yield an oscillatory effective potential, thus providing stable equilibrium configurations despite the repulsive Coulomb interactions. As the system size grows, the number of equilibria increases, approximately following a power-law. This can be attributed to the increasing complexity in the highly non-linear oscillatory behavior of the potential energy surface. This property is reflected in a crossover from a spatially regular distribution of equilibria for the two-body system to a heightened degree of disorder upon the addition of particles. However, in accordance with the repulsion within a helical winding, the observed interparticle distances in equilibrium configurations cluster around values of odd multiples of half a helical winding, thus maintaining an underlying regularity. Furthermore, an energetic hierarchy exists based on the spatial location of the local equilibria, which is subject to increasing fluctuations as the system size grows.

physics.atom-ph↗

arXiv2024

Chiral QCD phase in equilibrium with Hadron Gas and the location of the critical point

We develop a description of the equation of state of QCD matter with restored chiral symmetry, which is in thermal and chemical equilibrium with the hadronic phase. The hadron gas is described with thermodynamically consistent volume corrections. The chiral phase is composed of a set of few quark condensates, each of which corresponds to a family of hadrons with specific quark content. On the boundary between the two phases we apply the requirement of conservation of particle numbers per family. We use lattice calculations for temperatures below the transition curve to determine hadronic volumes. We find that the pion system plays decisive role in the shift of the transition from higher order (crossover) to first order. For four volume models we calculate the location of the critical point as function of critical temperature $T_c$ at vanishing baryon density. Particularly, if we additionally impose the equality between the densities of quarks contained in mesons and baryons, we find a critical point residing in the interval of baryon chemical potential $μ_B \simeq$ 233-267 MeV and of temperature $T \simeq$ 153-158 MeV.

nucl-th↗

arXiv2024

Restoring the topological edge states in a finite optical superlattice

We consider the emergence of edge states in a finite optical lattice and show that the boundaries of the lattice play a decisive role for their location in the corresponding energy spectrum. We introduce a simple parametrisation of the boundaries of the optical lattice and demonstrate the existence of an optimal choice of the values of the parameters which lead to an approximate restoration of chiral symmetry. A crucial property of this optimization is the suppression of tunneling between next-nearest neighboring wells of the lattice. This in turn allows the mapping of the optical lattice set-up to a finite SSH model. The topological character of the emerging edge states is discussed.

quant-ph↗

arXiv2024

Existence and characterization of edge states in an acoustic trimer Su-Schrieffer-Heeger model

We report on a direct mapping of acoustic slender waveguides to the one dimensional trimer Su- Schrieffer-Heeger model, with neither chiral nor mirror symmetry. Importantly, we can choose to perform this mapping for either the acoustic velocity or pressure. We demonstrate that, for finite systems, this choice is necessarily linked to the boundary conditions. It allows for the unveiling of the edge states of the acoustic system through an edge state phase diagram. An experimental realization of our setup in the audible regime corroborates our theoretical predictions.

physics.app-ph↗

arXiv2023

Latent symmetry induced degeneracies

Degeneracies in the energy spectra of physical systems are commonly considered to be either of accidental character or induced by symmetries of the Hamiltonian. We develop an approach to explain degeneracies by tracing them back to symmetries of an isospectral effective Hamiltonian derived by subsystem partitioning. We provide an intuitive interpretation of such latent symmetries by relating them to corresponding local symmetries in the powers of the underlying Hamiltonian matrix. As an application, we relate the degeneracies induced by the rotation symmetry of a real Hamiltonian to a non-abelian latent symmetry group. It is demonstrated that the rotational symmetries can be broken in a controlled manner while maintaining the underlying more fundamental latent symmetry. This opens up the perspective of investigating accidental degeneracies in terms of latent symmetries.

quant-ph↗

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↗

arXiv2022

Correlation Integral vs. second order Factorial Moments and an efficient computational technique

We develop a mapping between the factorial moments of the second order $F_2$ and the correlation integral $C$. We formulate a fast computation technique for the evaluation of both, which is more efficient, compared to conventional methods, for data containing number of pairs per event which is lower than the estimation points. We find the effectiveness of the technique to be more prominent as the dimension of the embedding space increases. We are able to analyse large amount of data in short computation time and access very low scales in $C$ or extremely high partitions in $F_2$. The technique is an indispensable tool for detecting a very weak signal hidden in strong noise.

hep-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

Fast and robust quantum state transfer via a topological chain

We propose a fast and robust quantum state transfer protocol employing a Su-Schrieffer-Heeger chain, where the interchain couplings vary in time. Based on simple considerations around the terms involved in the definition of the adiabatic invariant, we construct an exponential time-driving function that successfully takes advantage of resonant effects to speed up the transfer process. Using optimal control theory, we confirm that the proposed time-driving function is close to optimal. To unravel the crucial aspects of our construction, we proceed to a comparison with two other protocols. One where the underlying Su-Schrieffer-Heeger chain is adiabatically time-driven and another where the underlying chain is topologically trivial and resonant effects are at work. By numerically investigating the resilience of each protocol to static noise, we highlight the robustness of the exponential driving.

quant-ph↗

arXiv2020

Transfer efficiency enhancement and eigenstate properties in locally symmetric disordered finite chains

The impact of local reflection symmetry on wave localization and transport within finite disordered chains is investigated. Local symmetries thereby play the role of a spatial correlation of variable range in the finite system. We find that, on ensemble average, the chain eigenstates become more fragmented spatially for intermediate average symmetry domain sizes, depending on the degree of disorder. This is caused by the partial formation of states with approximate local parity confined within fictitious, disorder-induced double wells and perturbed by the coupling to adjacent domains. The dynamical evolution of wave-packets shows that the average site-resolved transfer efficiency is enhanced between regions connected by local symmetry. The transfer may further be drastically amplified in the presence of spatial overlap between the symmetry domains, and in particular when global and local symmetry coexist. Applicable to generic discrete models for matter and light waves, our work provides a perspective to understand and exploit the impact of local order at multiple scales in complex systems.

cond-mat.dis-nn↗

arXiv2020

Fast, robust and amplified transfer of topological edge modes on time-varying mechanical chain

We show that it is possible to successfully, rapidly and robustly transfer a topological vibrational edge mode across a time-varying mechanical chain. The stiffness values of the springs of the chain are arranged in an alternating staggered way, such that we obtain a mechanical analog of the quantum Su-Schrieffer-Heeger model which exhibits a non trivial topological phase. Using optimal control methods, we are able to design control schemes for driving the stiffness parameters, such that the transfer is done with high fidelity, speed and robustness against disorder as well as energy amplification of the target edge mode.

physics.class-ph↗

arXiv2019

Designing pretty good state transfer via isospectral reductions

We present an algorithm to design networks that feature pretty good state transfer (PGST), which is of interest for high-fidelity transfer of information in quantum computing. Realizations of PGST networks have so far mostly relied either on very special network geometries or imposed conditions such as transcendental on-site potentials. However, it was recently shown [Eisenberg et al., arXiv:1804.01645] that PGST generally arises when a network's eigenvectors and the factors $P_{\pm}$ of its characteristic polynomial $P$ fulfill certain conditions, where $P_{\pm}$ correspond to eigenvectors which have $\pm 1$ parity on the input and target sites. We combine this result with the so-called isospectral reduction of a network to obtain $P_{\pm}$ from a dimensionally reduced form of the Hamiltonian. Equipped with the knowledge of the factors $P_{\pm}$, we show how a variety of setups can be equipped with PGST by proper tuning of $P_{\pm}$. Having demonstrated a method of designing networks featuring pretty good state transfer of single site excitations, we further show how the obtained networks can be manipulated such that they allow for robust storage of qubits. We hereby rely on the concept of compact localized states, which are eigenstates of a Hamiltonian localized on a small subdomain, and whose amplitudes completely vanish outside of this domain. Such states are natural candidates for the storage of quantum information, and we show how certain Hamiltonians featuring pretty good state transfer of single site excitation can be equipped with compact localized states such that their transfer is made possible.

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

Quantum network transfer and storage with compact localized states induced by local symmetries

We propose modulation protocols designed to generate, store and transfer compact localized states in a quantum network. Induced by parameter tuning or local reflection symmetries, such states vanish outside selected domains of the complete system and are therefore ideal for information storage. Their creation and transfer is here achieved either via amplitude phase flips or via optimal temporal control of inter-site couplings. We apply the concept to a decorated, locally symmetric Lieb lattice where one sublattice is dimerized, and also demonstrate it for more complex setups. The approach allows for a flexible storage and transfer of states along independent paths in lattices supporting flat energetic bands. The generic network and protocols proposed can be utilized in various physical setups such as atomic or molecular spin lattices, photonic waveguide arrays, and acoustic setups.

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↗