arXiv subjects

Carlo Danieli

Publications and source records attributed to Carlo Danieli.

28 records · Page 2Linked to original sources

arXiv2020

Casting dissipative compact states in coherent perfect absorbers

Coherent perfect absorption (CPA), also known as time-reversed laser, is a wave phenomenon resulting from the reciprocity of destructive interference of transmitted and reflected waves. In this work we consider quasi one-dimensional lattice networks which posses at least one flat band, and show that CPA and lasing can be induced in both linear and nonlinear regimes of this lattice by fine-tuning non-Hermitian defects (dissipative terms localized within one unit-cell). We show that local dissipations that yield CPA simultaneously yield novel dissipative compact solutions of the lattice, whose growth or decay in time can be fine-tuned via the dissipation parameter. The scheme used to numerically visualize the theoretical findings offers a novel platform for the experimental implementation of these phenomena in optical devices.

physics.optics↗

arXiv2019

Observation of quincunx-shaped and dipole-like flatband states in photonic rhombic lattices without band-touching

We demonstrate experimentally the existence of compact localized states (CLSs) in a quasi-one-dimensional photonic rhombic lattice in presence of two distinct refractive-index gradients (i.e., a driven lattice ribbon) acting as external direct current (dc) electric fields. Such a lattice is composed of an array of periodically arranged evanescently coupled waveguides, which hosts a perfect flatband that touches both remaining dispersive bands when it is not driven. The external driving is realized by modulating the relative writing beam intensity of adjacent waveguides. We find that a y-gradient set perpendicularly to the ribbon preserves the flatband while removing the band-touching. The undriven CLS - which occupies two lattices sites over one unit cell - turns into a quincunx-shaped CLS spanned over two unit cells. Instead, an x-gradient acting parallel to the ribbon yields a Stark ladder of CLS whose spatial profile is unchanged with respect to the undriven case. We notably find that their superposition leads to Bloch-like oscillations in momentum space.

physics.optics↗

arXiv2019

Dynamical glass in weakly non-integrable Klein-Gordon chains

Integrable many-body systems are characterized by a complete set of preserved actions. Close to an integrable limit, a {\it nonintegrable} perturbation creates a coupling network in action space which can be short- or long-ranged. We analyze the dynamics of observables which turn into the conserved actions in the integrable limit. We compute distributions of their finite-time averages and obtain the ergodization time scale $T_E$ on which these distributions converge to $δ$-distributions. We relate $T_E \sim (σ_τ^+)^2/μ_τ^+$ to the statistics of fluctuation times of the observables, which acquire fat-tailed distributions with standard deviations $σ_τ^+$ dominating the means $μ_τ^+$. The Lyapunov time $T_Λ$ (the inverse of the largest Lyapunov exponent) is then compared to the above time scales. We use a simple Klein-Gordon chain to emulate long- and short-range coupling networks by tuning its energy density. For long-range coupling networks $T_Λ\approx σ_τ^+$, which indicates that the Lyapunov time sets the ergodization time, with chaos quickly diffusing through the coupling network. For short-range coupling networks we observe a {\it dynamical glass}, where $T_E$ grows dramatically by many orders of magnitude and greatly exceeds the Lyapunov time, which $T_Λ \lesssim μ_τ^+$. This is due to the formation of a highly fragmented inhomogeneous distributions of chaotic groups of actions, separated by growing volumes of non-chaotic regions. These structures persist up to the ergodization time $T_E$.

nlin.CD↗

arXiv2019

Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions

We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the Fermi-Pasta-Ulam-Tsingou (FPUT) chain and the one- and two-dimensional disordered, discrete nonlinear Schrödinger equations (DDNLS). In our analysis we consider methods based on Taylor series expansion, Runge-Kutta discretization and symplectic transformations. The latter have the ability to exactly preserve the symplectic structure of Hamiltonian systems, which results in keeping bounded the error of the system's computed total energy. We perform extensive numerical simulations for several initial conditions of the studied models and compare the numerical efficiency of the used integrators by testing their ability to accurately reproduce characteristics of the systems' dynamics and quantify their chaoticity through the computation of the maximum Lyapunov exponent. We also report the expressions of the implemented symplectic schemes and provide the explicit forms of the used differential operators. Among the tested numerical schemes the symplectic integrators $ABA864$ and $SRKN^a_{14}$ exhibit the best performance, respectively for moderate and high accuracy levels in the case of the FPUT chain, while for the DDNLS models $s9\mathcal{ABC}6$ and $s11\mathcal{ABC}6$ (moderate accuracy), along with $s17\mathcal{ABC}8$ and $s19\mathcal{ABC}8$ (high accuracy) proved to be the most efficient schemes.

physics.comp-ph↗

arXiv2019

Dynamical Glass and Ergodization Times in Classical Josephson Junction Chains

Models of classical Josephson junction chains turn integrable in the limit of large energy densities or small Josephson energies. Close to these limits the Josephson coupling between the superconducting grains induces a short range nonintegrable network. We compute distributions of finite time averages of grain charges and extract the ergodization time $T_E$ which controls their convergence to ergodic $δ$-distributions. We relate $T_E$ to the statistics of fluctuation times of the charges, which are dominated by fat tails. $T_E$ is growing anomalously fast upon approaching the integrable limit, as compared to the Lyapunov time $T_Λ$ - the inverse of the largest Lyapunov exponent - reaching astonishing ratios $T_E/T_Λ \geq 10^8$. The microscopic reason for the observed dynamical glass is routed in a growing number of grains evolving over long times in a regular almost integrable fashion due to the low probability of resonant interactions with the nearest neighbors. We conjecture that the observed dynamical glass is a generic property of Josephson junction networks irrespective of their space dimensionality.

cond-mat.stat-mech↗

arXiv2018

Weakly nonergodic dynamics in the Gross--Pitaevskii lattice

The microcanonical Gross--Pitaevskii (aka semiclassical Bose-Hubbard) lattice model dynamics is characterized by a pair of energy and norm densities. The grand canonical Gibbs distribution fails to describe a part of the density space, due to the boundedness of its kinetic energy spectrum. We define Poincare equilibrium manifolds and compute the statistics of microcanonical excursion times off them. The tails of the distribution functions quantify the proximity of the many-body dynamics to a weakly-nonergodic phase, which occurs when the average excursion time is infinite. We find that a crossover to weakly-nonergodic dynamics takes place inside the nonGibbs phase, being unnoticed by the largest Lyapunov exponent. In the ergodic part of the non-Gibbs phase, the Gibbs distribution should be replaced by an unknown modified one. We relate our findings to the corresponding integrable limit, close to which the actions are interacting through a short range coupling network.

nlin.CD↗

arXiv2018

Fano Resonances in Flat Band Networks

Linear wave equations on Hamiltonian lattices with translational invariance are characterized by an eigenvalue band structure in reciprocal space. Flat band lattices have at least one of the bands completely dispersionless. Such bands are coined flat bands. Flat bands occur in fine-tuned networks, and can be protected by (e.g. chiral) symmetries. Recently a number of such systems were realized in structured optical systems, exciton-polariton condensates, and ultracold atomic gases. Flat band networks support compact localized modes. Local defects couple these compact modes to dispersive states and generate Fano resonances in the wave propagation. Disorder (i.e. a finite density of defects) leads to a dense set of Fano defects, and to novel scaling laws in the localization length of disordered dispersive states. Nonlinearities can preserve the compactness of flat band modes, along with renormalizing (tuning) their frequencies. These strictly compact nonlinear excitations induce tunable Fano resonances in the wave propagation of a nonlinear flat band lattice.

cond-mat.dis-nn↗

arXiv2015

Flatband Engineering of Mobility Edges

Properly modulated flatband lattices have a divergent density of states at the flatband energy. Quasiperiodic modulations are known to host a metal insulator transition already in one space dimension. Their embedding into flatband geometries consequently allows for a precise engineering and fine tuning of mobility edges. We obtain analytic expressions for singular mobility edges for two flatband lattice examples. In particular, we engineer cases with arbitrarily small energy separations of mobility edge, zeroes, and divergencies.

cond-mat.str-el↗

arXiv2014

Flat Bands Under Correlated Perturbations

Flat band networks are characterized by coexistence of dispersive and flat bands. Flat bands (FB) are generated by compact localized eigenstates (CLS) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLS without additional renormalization, yet with surprising consequencies: (i) states are expelled from the FB energy $E_{FB}$, (ii) the localization length of eigenstates vanishes as $ξ\sim 1 / \ln (E- E_{FB})$, (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), (iv) mobility edge curves show algebraic singularities at $E_{FB}$. Our analytical results are based on perturbative expansions of the CLS, and supported by numerical data in one and two lattice dimensions.

cond-mat.dis-nn↗

arXiv2014

Comment on "Metal-Insulator Transition in an Aperiodic Ladder Network: An Exact Result"

Sil, Maiti, and Chakrabarti (SMC) (Phys. Rev. Lett. 101, 076803 (2008), arXiv:0801.2670) introduce an aperiodic two-leg ladder network composed of atomic sites with on-site potentials distributed according to a quasiperiodic Aubry-Andre potential. SMC claim the existence of multiple mobility edges, i.e. metal-insulator transitions at multiple values of the Fermi energy. SMC use numerical calculations of the conductance and den- sity of states, and an analytical result in a limiting case. In the following, we restate in the real space the change of basis done by SMC. This change of basis reduces their model to two decoupled chains, each with its own Aubry- Andre potential. Each of the chains has its own critical point, where all states change from metallic to insulat- ing, without any notion of a mobility edge. Since the two chains are not interacting, their spectra may overlap such that localized states (from one chain) and delocal- ized states (from the other chain) coexist at the same en- ergy. Consequently, the analysis of the density of states and the conductance alone is misleading, and that is due to the choice of the symmetric quasiperiodic potential. We briefly outline the possibility to obtain true mobility edges.

cond-mat.dis-nn↗