arXiv subjects

Ron Lifshitz

Publications and source records attributed to Ron Lifshitz.

At least 19 recordsLinked to original sources

arXiv2026

Tiling by Near Coincidence

Moir\'e patterns of twisted and scaled bilayers have recently emerged as a fertile source of quasiperiodic order in two-dimensional materials. Inspired by these systems, we introduce the \emph{near-coincidence method} for generating quasiperiodic tilings of the plane. The method is intuitive -- admitting pairs of nearly coincident points from superimposed layers -- yet rigorous, as it maps naturally to the well-established cut-and-project formalism. It reproduces classical tilings, including the Ammann--Beenker, the Niizeki--G\"ahler, and the square and hexagonal Fibonacci tilings, and also reveals new tilings that are unlikely to arise from conventional constructions. The near-coincidence method is algorithmically simple and already realized in a web-based application that generates tilings from specified layer parameters and coincidence conditions. Future extensions include trilayer systems, where preliminary results yield dodecagonal order with square layers, and very small twist angles, where the method may capture the giant moir\'e patterns of bilayer and trilayer graphene.

cond-mat.mtrl-sci↗

arXiv2023

Superconductivity and strong interactions in a tunable moir\'e quasiperiodic crystal

Electronic states in quasiperiodic crystals generally preclude a Bloch description, rendering them simultaneously fascinating and enigmatic. Owing to their complexity and relative scarcity, quasiperiodic crystals are underexplored relative to periodic and amorphous structures. Here, we introduce a new type of highly tunable quasiperiodic crystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two moir\'e patterns with incommensurate moir\'e unit cells. In contrast to many common quasiperiodic structures that are defined on the atomic scale, the quasiperiodicity in our system is defined on moir\'e length scales of several nanometers. This novel "moir\'e quasiperiodic crystal" allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Interestingly, in the quasiperiodic regime we observe superconductivity near a flavor-symmetry-breaking phase transition, the latter indicative of the important role electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems, but it may also provide insights into electronic ordering in related periodic moir\'e crystals. We anticipate that extending this new platform to engineer quasiperiodic crystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasiperiodic crystals.

cond-mat.mes-hall↗

arXiv2022

Hexagonal and trigonal quasiperiodic tilings

Exploring nonminimal-rank quasicrystals, which have symmetries that can be found in both periodic and aperiodic crystals, often provides new insight into the physical nature of aperiodic long-range order in models that are easier to treat. Motivated by the prevalence of experimental systems exhibiting aperiodic long-range order with hexagonal and trigonal symmetry, we introduce a generic two-parameter family of 2-dimensional quasiperiodic tilings with such symmetries. We focus on the special case of trigonal and hexagonal Fibonacci, or golden-mean, tilings, analogous to the well studied square Fibonacci tiling. We first generate the tilings using a generalized version of de Bruijn's dual grid method. We then discuss their interpretation in terms of projections of a hypercubic lattice from six dimensional superspace. We conclude by concentrating on two of the hexagonal members of the family, and examining a few of their properties more closely, while providing a set of substitution rules for their generation.

cond-mat.soft↗

arXiv2021

Emergence of quasiperiodic Bloch wave functions in quasicrystals

We study the emergence of quasiperiodic Bloch wave functions in quasicrystals, employing the one-dimensional Fibonacci model as a test case. We find that despite the fact that Bloch functions are not eigenfunctions themselves, superpositions of relatively small numbers of nearly degenerate eigenfunctions give rise to extended quasiperiodic Bloch functions. These functions possess the structure of earlier ancestors of the underlying Fibonacci potential, and it is often possible to obtain different ancestors as different superpositions around the same energy. There exists an effective crystal momentum that characterizes these ancestors, which is determined by the mean energy of the superimposed eigenfunctions, giving rise to an effective dispersion curve. We also find that quasiperiodic Bloch functions do emerge as eigenfunctions when weak disorder is introduced into the otherwise perfect quasiperiodic potential. These theoretical results may explain a number of experimental observations, and may have practical consequences on emerging theories of band topology and correlated electrons in quasicrystals.

cond-mat.mtrl-sci↗

arXiv2020

Quantum limit-cycles and the Rayleigh and van der Pol oscillators

Self-oscillating systems, described in classical dynamics as limit cycles, are emerging as canonical models for driven dissipative nonequilibrium open quantum systems, and as key elements in quantum technology. We consider a family of models that interpolates between the classical textbook examples of the Rayleigh and the van der Pol oscillators, and follow their transition from the classical to the quantum domain, while properly formulating their corresponding quantum descriptions. We derive an exact analytical solution for the steady-state quantum dynamics of the simplest of these models, applicable to any bosonic system---whether mechanical, optical, or otherwise---that is coupled to its environment via single-boson and double-boson emission and absorption. Our solution is a generalization to arbitrary temperature of existing solutions for very-low, or zero, temperature, often misattributed to the quantum van der Pol oscillator. We closely explore the classical to quantum transition of the bifurcation to self-oscillations of this oscillator, while noting changes in the dynamics and identifying features that are uniquely quantum.

quant-ph↗

arXiv2018

Multiple-scale structures: from Faraday waves to soft-matter quasicrystals

For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids. Much effort is being invested in understanding the thermodynamic properties of these soft-matter quasicrystals in order to predict and possibly control the structures that form, and hopefully to shed light on the broader yet unresolved general questions of quasicrystal formation and stability. Moreover, the ability to control the self-assembly of soft quasicrystals may contribute to the development of novel photonic or other applications based on self-assembled metamaterials. Here a path is followed, leading to quantitative stability predictions, that starts with a model developed two decades ago to treat the formation of multiple-scale quasiperiodic Faraday waves (standing wave patterns in vibrated fluid surfaces) and which was later mapped onto systems of soft particles, interacting via multiple-scale pair potentials. The article reviews, and substantially expands, the quantitative predictions of these models, while correcting a few discrepancies in earlier calculations, and presents new analytical methods for treating the models. In so doing, a number of new stable quasicrystalline structures with octagonal, octadecagonal and higher-order symmetries, some of which may, it is hoped, be observed in future experiments.

cond-mat.soft↗

arXiv2014

Controlled self-assembly of periodic and aperiodic cluster crystals

Soft particles are known to overlap and form stable clusters that self-assemble into periodic crystalline phases with density-independent lattice constants. We use molecular dynamics simulations in two dimensions to demonstrate that, through a judicious design of an isotropic pair potential, one can control the ordering of the clusters and generate a variety of phases, including decagonal and dodecagonal quasicrystals. Our results confirm analytical predictions based on a mean-field approximation, providing insight into the stabilization of quasicrystals in soft macromolecular systems, and suggesting a practical approach for their controlled self-assembly in laboratory realizations using synthesized soft-matter particles.

cond-mat.soft↗

arXiv2013

Comment on "Quantum Quasicrystals of Spin-Orbit-Coupled Dipolar Bosons"

In a recent Letter, Gopalakrishnan, Martin, and Demler [Phys. Rev. Lett. 111 (2013) 185304] show that quasi-two-dimensional dipolar Bose gases, subject to a Rashba spin-orbit coupling, exhibit a variety of spatially ordered, or crystalline, ground states, including a pentagonal quasicrystal. Indeed, as the authors say, realizing quasicrystalline condensates would provide new ways to explore the physics of quasicrystals, and in particular to study the quantum dynamics of their unique collective phason modes. Yet, the authors conclude that "there are typically additional phasons in quantum-mechanical quasicrystals, when compared with their classical equivalents." In this Comment I review the notion of phason modes in quasicrystals, and explain why their number does not depend on whether they are classical or quantum.

cond-mat.stat-mech↗

arXiv2013

Phonon-mediated damping of mechanical vibrations in a finite atomic chain coupled to an outer environment

We study phonon-mediated damping of mechanical vibrations in a finite quantum-mechanical atomic-chain model. Our study is motivated by the quest to understand the quality factors (Q) of nanomechanical resonators and nanoelectromechanical systems (NEMS), as well as actual experiments with suspended atomic chains and molecular junctions. We consider a finite atomic chain which is coupled to a zero-temperature outer environment, modeled as two additional semi-infinite chains, thus inducing "clamping-losses". Weak coupling to the outer environment ensures that the clamping losses are small, and that the initially discrete nature of the phonon spectrum is approximately maintained. We then consider a phonon damping process known as "Landau-Rumer damping", where phonons in the excited mode of vibration decay into other modes through anharmonic phonon-phonon interaction. The approximately discrete nature of the phonon spectrum leads to sharp nonmonotonic changes in Q as parameters are varied, and to the appearance of resonances in the damping. The latter correspond to the existence of decay processes where the participating phonons approximately conserve energy. We explore means to control the damping by changing either the number of atoms in the chains or the ratio between the longitudinal and transverse speeds of sound, thereby suggesting future experiments to observe this resonance-like behavior.

cond-mat.mes-hall↗

arXiv2012

Analysis of dislocations in quasicrystals composed of self-assembled nanoparticles

We analyze transmission electron microscopy (TEM) images of self-assembled quasicrystals, composed of binary systems of nanoparticles. We use an automated procedure that identifies the positions of dislocations and determines their topological character. To achieve this we decompose the quasicrystal into its individual density modes, or Fourier components, and identify their topological winding numbers for every dislocation. This procedure associates a Burgers function with each dislocation, from which we extract the components of the Burgers vector after choosing a basis. The Burgers vectors that we see in the experimental images are all of lowest order, containing only 0's and 1's as their components. We argue that the density of the different types of Burgers vectors depends on their energetic cost.

cond-mat.mtrl-sci↗

arXiv2012

Optimal operating points of oscillators using nonlinear resonators

We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.

cond-mat.other↗

arXiv2012

Damping of mechanical vibrations by free electrons in metallic nanoresonators

We investigate the effect of free electrons on the quality factor (Q) of a metallic nanomechanical resonator in the form of a thin elastic beam. The flexural and longitudinal modes of the beam are modeled using thin beam elasticity theory, and simple perturbation theory is used to calculate the rate at which an externally excited vibration mode decays due to its interaction with free electrons. We find that electron-phonon interaction significantly affects the Q of longitudinal modes, and may also be of significance to the damping of flexural modes in otherwise high-Q beams. The finite geometry of the beam is manifested in two important ways. Its finite length breaks translation invariance along the beam and introduces an imperfect momentum conservation law in place of the exact law. Its finite width imposes a quantization of the electronic states that introduces a temperature scale for which there exists a crossover from a high-temperature macroscopic regime, where electron-phonon damping behaves as if the electrons were in the bulk, to a low-temperature mesoscopic regime, where damping is dominated by just a few dissipation channels and exhibits sharp non-monotonic changes as parameters are varied. This suggests a novel scheme for probing the electronic spectrum of a nanoscale device by measuring the Q of its mechanical vibrations.

cond-mat.mes-hall↗

arXiv2012

A Passive Phase Noise Cancellation Element

We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the output of a conventional oscillator at a frequency close to the sum of the linear mode frequencies. Above the threshold for parametric response, the coupled resonators exhibit self-oscillation at an inherent frequency. We find operating points of the device for which this periodic signal is immune to frequency noise in the driving oscillator, providing a way to clean its phase noise. We present results for the effect of thermal noise to advance a broader understanding of the overall noise sensitivity and the fundamental operating limits.

cond-mat.mes-hall↗

arXiv2011

Symmetry Breaking and Order in the Age of Quasicrystals

The discovery of quasicrystals has changed our view of some of the most basic notions related to the condensed state of matter. Before the age of quasicrystals, it was believed that crystals break the continuous translation and rotation symmetries of the liquid-phase into a discrete lattice of translations, and a finite group of rotations. Quasicrystals, on the other hand, possess no such symmetries-there are no translations, nor, in general, are there any rotations, leaving them invariant. Does this imply that no symmetry is left, or that the meaning of symmetry should be revised? We review this and other questions related to the liquid-to-crystal symmetry-breaking transition using the notion of indistinguishability. We characterize the order-parameter space, describe the different elementary excitations, phonons and phasons, and discuss the nature of dislocations-keeping in mind that we are now living in the age of quasicrystals.

cond-mat.mtrl-sci↗

arXiv2011

Collective Dynamics in Arrays of Coupled Nonlinear Resonators

The study of collective nonlinear dynamics of coupled mechanical resonators is regaining attention in recent years thanks to rapid developments in the fields of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). We review a wide range of collective dynamical phenomena, while highlighting the common concepts and theoretical tools that we have developed for treating them. We provide detailed derivations of amplitude equations, which allow us to obtain reduced descriptions for the relevant dynamics of our complex systems. We apply these amplitude equations to study (a) resonant response to parametric excitation; (b) pattern selection, or the nonlinear competition between extended modes in situations of multistability; (c) formation and dynamics of intrinsically localized modes (ILM); and (d) spontaneous synchronization of oscillators with differing frequencies. All the predictions obtained from analyzing the different amplitude equations are in excellent agreement with numerical solutions of the underlying equations of motion, suggesting that the predicted effects can be observed in arrays of real micromechanical or nanomechanical resonators, thus motivating new experiments in these systems.

nlin.PS↗

arXiv2011

Possibility of Electron Pairing in Small Metallic Nanoparticles

We investigate the possibility of electron pairing in small metallic nanoparticles at zero temperature. In these particles both electrons and phonons are mesoscopic, i.e. modified by the nanoparticle's finite size. The electrons, the phonons, and their interaction are described within the framework of a simplified model. The effective electron-electron interaction is derived from the underlying electron-phonon interaction. The effect of both effective interaction and Coulomb interaction on the electronic spectrum is evaluated. Results are presented for aluminum, zinc and potassium nanoparticles containing a few hundred atoms. We find that a large portion of the aluminum and zinc particles exhibit modifications in their electronic spectrum due to pairing correlations, while pairing correlations are not present in the potassium particles.

cond-mat.supr-con↗

arXiv2011

Stability of Quasicrystals Composed of Soft Isotropic Particles

Quasicrystals whose building blocks are of mesoscopic rather than atomic scale have recently been discovered in several soft-matter systems. Contrary to metallurgic quasicrystals whose source of stability remains a question of great debate to this day, we argue that the stability of certain soft-matter quasicrystals can be directly explained by examining a coarse-grained free energy for a system of soft isotropic particles. We show, both theoretically and numerically, that the stability can be attributed to the existence of two natural length scales in the pair potential, combined with effective three-body interactions arising from entropy. Our newly gained understanding of the stability of soft quasicrystals allows us to point at their region of stability in the phase diagram, and thereby may help control the self-assembly of quasicrystals and a variety of other desired structures in future experimental realizations.

cond-mat.soft↗

arXiv2010

Homoclinic orbits and chaos in a pair of parametrically-driven coupled nonlinear resonators

We study the dynamics of a pair of parametrically-driven coupled nonlinear mechanical resonators of the kind that is typically encountered in applications involving microelectromechanical and nanoelectromechanical systems (MEMS & NEMS). We take advantage of the weak damping that characterizes these systems to perform a multiple-scales analysis and obtain amplitude equations, describing the slow dynamics of the system. This picture allows us to expose the existence of homoclinic orbits in the dynamics of the integrable part of the slow equations of motion. Using a version of the high-dimensional Melnikov approach, developed by Kovacic and Wiggins [Physica D, 57, 185 (1992)], we are able to obtain explicit parameter values for which these orbits persist in the full system, consisting of both Hamiltonian and non-Hamiltonian perturbations, to form so-called Shilnikov orbits, indicating a loss of integrability and the existence of chaos. Our analytical calculations of Shilnikov orbits are confirmed numerically.

nlin.CD↗