arXiv subjects

F. Palmero

Publications and source records attributed to F. Palmero.

At least 19 recordsLinked to original sources

arXiv2026

Topologically Protected Spatially Localized Modes: An Easy Experimental Realization of the Su--Schrieffer--Heeger Model

In this paper, we review the basic concepts of topologically protected edge modes using the Su Schrieffer Heeger (SSH) model, originally introduced to describe electrical conductivity in doped polyacetylene polymer chains. We then propose an electrical circuit that emulates this model, provide its mathematical description, and present its experimental realization. The experimental setup is described in detail, with explanations designed to be broadly accessible without much prior familiarity with lattice theory, thus offering an introduction to this active area of research. Both theoretical predictions and experimental results confirm the presence of these modes, showing very good overall agreement. Using this concrete experimental system as a motivating example, we highlight the key aspects of topological protection.

cond-mat.mes-hall↗

arXiv2022

Scattering-induced splitting of solitons in the discrete NLS equation with saturable nonlinearity

We study systematically the scattering of solitons on localized impurities in the discrete nonlinear Schrödinger (DNLS) equation with a saturable nonlinearity. We show that, apart from the generic scenario of the outcome of the scattering process, namely the emergence of a reflected and a transmitted soliton, other effects can occur. In particular, it is found that, in the case of an attractive impurity, a soliton trapped at the impurity can coexist with the reflected and transmitted ones. This effect, which resembles the behaviour of a quantum particle interacting with a narrow impurity, has not previously reported for discrete setting. Parameter regimes are explored for determining soliton splitting on the impurity with special attention to equal soliton splitting.

nlin.PS↗

arXiv2020

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and inside the band of linear modes. We identify a number of discrete breathers both existing in the bulk and also (predominantly) ones arising at the domain boundaries, localized either along the arm-chair or along the zig-zag edges. The types of edge-localized breathers observed and computed emerge in distinct frequency bands near the Dirac-point frequency of the dispersion surface while driving the lattice subharmonically (in a spatially homogeneous manner). These observations/computations can represent a starting point towards the exploration of the interplay of nonlinearity and topology in an experimentally tractable system such as the honeycomb electrical lattice.

nlin.PS↗

arXiv2018

Experimental and numerical observation of dark and bright discrete solitons in the band-gap of a diatomic-like electrical lattice

We observe dark and bright intrinsic localized modes (ILMs) or discrete breathers (DB) experimentally and numerically in a diatomic-like electrical lattice. The generation of dark ILMs by driving a dissipative lattice with spatially-homogenous amplitude is, to our knowledge, unprecedented. In addition, the experimental manifestation of bright breathers within the bandgap is also novel in this system. In experimental measurements the dark modes appear just below the bottom of the top branch in frequency. As the frequency is then lowered further into the band-gap, the dark DBs persist, until the nonlinear localization pattern reverses and bright DBs appear on top of the finite background. Deep into the bandgap, only a single bright structure survives in a lattice of 32 nodes. The vicinity of the bottom band also features bright and dark self-localized excitations. These results pave the way for a more systematic study of dark breathers and their bifurcations in diatomic-like chains.

nlin.PS↗

arXiv2018

Impulse-induced localized nonlinear modes in an electrical lattice

Intrinsic localized modes, also called discrete breathers, can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external harmonic excitations. In this work, we have studied experimentally the efectiveness of generic periodic excitations of variable waveform at generating discrete breathers in such lattices. We have found that this generation phenomenon is optimally controlled by the impulse transmitted by the external excitation (time integral over two consecutive zeros

nlin.PS↗

arXiv2016

Impulse-induced generation of stationary and moving discrete breathers in nonlinear oscillator networks

We study discrete breathers in prototypical nonlinear oscillator networks subjected to non-harmonic zero-mean periodic excitations. We show how the generation of stationary and moving discrete breathers are optimally controlled by solely varying the impulse transmitted by the periodic excitations, while keeping constant the excitation's amplitude and period. Our theoretical and numerical results show that the enhancer effect of increasing values of the excitation's impulse, in the sense of facilitating the generation of stationary and moving breathers, is due to a correlative increase of the breather's action and energy.

nlin.PS↗

arXiv2015

Multifrequency and edge breathers in the discrete sine-Gordon system via subharmonic driving: theory, computation and experiment

We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes, also known as discrete breathers, can exist. Recently, the existence of multifrequency breathers via subharmonic driving has been theoretically proposed and numerically illustrated by Xu {\em et al.} in Phys. Rev. E {\bf 90}, 042921 (2014). In this paper, we verify this prediction experimentally. Comparison of the experimental results to numerical simulations with realistic system parameters (including a Floquet stability analysis), and wherever possible to analytical results (e.g. for the subharmonic response of the single driven-damped pendulum), yields good agreement. Finally, we report on period-1 and multifrequency edge breathers which are localized at the open boundaries of the chain, for which we have again found good agreement between experiments and numerical computations

nlin.PS↗

arXiv2013

From Nodeless Clouds and Vortices to Gray Rings and Symmetry-Broken States in Two-Dimensional Polariton Condensates

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrastedto the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of {\em stable} nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, {\it stable} stationary gray rings (that can be thought of as radial forms of a Nozaki-Bekki hole) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry.

nlin.PS↗

arXiv2013

Nonlinear localized modes in two-dimensional electrical lattices

We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and traveling self-localized modes were generated experimentally and theoretically in a family of two-dimensional square, as well as hon- eycomb lattices composed of 6x6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILM), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introduc- ing additional capacitors into the unit cell, these lattices can controllably induce traveling discrete breathers. When more than one such ILMs are experimentally generated in the lattice, the interplay of nonlinearity, discreteness and wave interactions generate a complex dynamics wherein the ILMs attempt to maintain a minimum distance between one another. Numerical simulations show good agreement with experimental results, and confirm that these phenomena qualitatively carry over to larger lattice sizes.

nlin.PS↗

arXiv2011

Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where $n$-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of $n$-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary $n$-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.

nlin.PS↗

arXiv2009

Lower and upper estimates on the excitation threshold for breathers in DNLS lattices

We propose analytical lower and upper estimates on the excitation threshold for breathers (in the form of spatially localized and time periodic solutions) in DNLS lattices with power nonlinearity. The estimation depending explicitly on the lattice parameters, is derived by a combination of a comparison argument on appropriate lower bounds depending on the frequency of each solution with a simple and justified heuristic argument. The numerical studies verify that the analytical estimates can be of particular usefulness, as a simple analytical detection of the activation energy for breathers in DNLS lattices.

nlin.PS↗

arXiv2007

Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity

In this paper we analyze the existence, stability, dynamical formation and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schrödinger equation with a linear point defect. We consider both attractive and repulsive defects in a focusing lattice. Among our main findings are: a) the destabilization of the on--site mode centered at the defect in the repulsive case; b) the disappearance of localized modes in the vicinity of the defect due to saddle-node bifurcations for sufficiently strong defects of either type; c) the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects; and d) the detailed elucidation as a function of initial speed and defect strength of the different regimes (trapping, trapping and reflection, pure reflection and pure transmission) of interaction of a moving localized mode with the defect.

nlin.PS↗

arXiv2005

Aharonov-Bohm effect for an exciton in a finite width nano-ring

We study the Aharonov-Bohm effect for an exciton on a nano-ring using a 2D attractive fermionic Hubbard model. We extend previous results obtained for a 1D ring in which only azimuthal motion is considered, to a more general case of 2D annular lattices. In general, we show that the existence of the localization effect, increased by the nonlinearity, makes the phenomenon in the 2D system similar to the 1D case. However, the introduction of radial motion introduces extra frequencies, different from the original isolated frequency corresponding to the excitonic Aharonov-Bohm oscillations. If the circumference of the system becomes large enough, the Aharonov-Bohm effect is suppressed.

cond-mat.str-el↗

arXiv2005

Classical and quantum nonlinear localized excitations in discrete systems

Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of discrete breather that exist at the atomic scale in a magnetic solid. Other observations of breathers refer to systems such as Josephson--junction arrays, photonic crystals and optical-switching waveguide arrays. All these observations underscore their importance in physical phenomena at all scales. The authors review some of their latest theoretical contributions in the field of classical and quantum breathers, with possible applications to these widely different physical systems and to many other such as DNA, proteins, quantum dots, quantum computing, etc.

nlin.PS↗

arXiv2003

Effect of base-pair inhomogeneities on charge transport along DNA mediated by twist and radial polarons

Some recent results for a three--dimensional, semi--classical, tight--binding model for DNA show that there are two types of polarons, named radial and twist polarons, that can transport charge along the DNA molecule. However, the existence of two types of base pairs in real DNA, makes it crucial to find out if charge transport also exist in DNA chains with different base pairs. In this paper we address this problem in its simple case, an homogeneous chain except for a single different base pair, what we call a base-pair inhomogeneity, and its effect on charge transport. Radial polarons experience either reflection or trapping. However, twist polarons are good candidates for charge transport along real DNA. This transport is also very robust with respect to weak parametric and diagonal disorder.

nlin.PS↗

arXiv2003

Quantum breathers in an attractive fermionic Hubbard model

In one-dimensional translationally invariant anharmonic lattices, an extended Bloch state with two or more strongly correlated particles is usually called a quantum breather. Here we study an attractive fermionic Hubbard model with two kind of particles of opposite spin. We discuss the existence of breathers, and several effects that break the translational symmetry of the system and localize the breather in the lattice.

nlin.PS↗

arXiv2003

Trapping in quantum chains

A quantum breather on a translationally invariant one-dimensional anharmonic lattice is an extended Bloch state with two or more particles in a strongly correlated state. We discuss several effects that break the lattice symmetry and lead to spatial localization of the breather.

nlin.PS↗

arXiv2003

Nonlinear charge transport in DNA mediated by twist modes

Recent works on localized charge transport along DNA, based on a three--dimensional, tight--binding model (Eur. Phys. J. B 30:211, 2002; Phys. D 180:256, 2003), suggest that charge transport is mediated by the coupling of the radial and electron variables. However, these works are based on a linear approximation of the distances among nucleotides, which forces for consistency the assumption that the parameter $α$, that describes the coupling between the transfer integral and the distance between nucleotides is fairly small. In the present letter we perform an improvement of the model which allows larger values of $α$, showing that there exist two very different regimes. Particulary, for large $α$, the conclusions of the previous works are reversed and charge transport can be produced only by the coupling with the twisting modes.

nlin.PS↗