Searcharxiv⌕ Search

arXiv subjects

Ron Lifshitz

Publications and source records attributed to Ron Lifshitz.

51 records · Page 3Linked to original sources
arXiv2004

Photonic quasicrystals for general purpose nonlinear optical frequency conversion

We present a general method for the design of 2-dimensional nonlinear photonic quasicrystals that can be utilized for the simultaneous phase-matching of arbitrary optical frequency-conversion processes. The proposed scheme--based on the generalized dual-grid method that is used for constructing tiling models of quasicrystals--gives complete design flexibility, removing any constraints imposed by previous approaches. As an example we demonstrate the design of a color fan--a nonlinear photonic quasicrystal whose input is a single wave at frequency $ω$ and whose output consists of the second, third, and fourth harmonics of $ω$, each in a different spatial direction.

cond-mat.mtrl-sci↗
arXiv2004

Synchronization by Nonlinear Frequency Pulling

We analyze a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling motivated by the physics of arrays of nanoscale oscillators. We study the model for the mean field case of all-to-all coupling, deriving results for the onset of synchronization as the coupling or nonlinearity increase, and the fully locked state when all the oscillators evolve with the same frequency.

cond-mat.other↗
arXiv2003

Electrons and Phonons on the Square Fibonacci Tiling

We study the Schroedinger equation for an off-diagonal tight-binding hamiltonian, as well as the equations of motion for out-of-plane vibrations, on the separable square Fibonacci quasicrystal. We discuss the nature of the spectra and wave functions of the solutions.

cond-mat↗
arXiv2003

Magnetically-ordered quasicrystals: Enumeration of spin groups and calculation of magnetic selection rules

We provide the details of the theory of magnetic symmetry in quasicrystals, which has previously only been outlined. We develop a practical formalism for the enumeration of spin point groups and spin space groups, and for the calculation of selection rules for neutron scattering experiments. We demonstrate the formalism using the simple, yet non-trivial, example of magnetically-ordered octagonal quasicrystals in two dimensions. In a companion paper we shall provide complete results for octagonal quasicrystals in three dimensions.

cond-mat.mtrl-sci↗
arXiv2003

Quasicrystals: A matter of definition

It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.

cond-mat.mtrl-sci↗
arXiv2002

Response of parametrically-driven nonlinear coupled oscillators with application to micro- and nanomechanical resonator arrays

The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of the numerical integration of the model equations of motion for large arrays. The results provide a qualitative explanation for a recent experiment [Buks and Roukes, cond-mat/0008211, to appear in J. MEMS (2002)] involving a parametrically-excited micromechanical resonator array. Future experiments are suggested that could provide quantitative tests of the theoretical predictions.

cond-mat.mes-hall↗
arXiv2000

Elastic Wave Transmission at an Abrupt Junction in a Thin Plate, with Application to Heat Transport and Vibrations in Mesoscopic Systems

The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in mesoscopic systems and the Q for vibrations in mesoscopic oscillators. Complete results are calculated in a simple scalar model of the elastic waves, and results for long wavelength modes are calculated using the full elasticity theory calculation. We suggest that thin plate elasticty theory provide a useful and tractable approximation to the full three dimensional geometry.

cond-mat.mes-hall↗
arXiv2000

The definition of quasicrystals

It is argued that the definition of quasicrystals should not include the requirement that they possess an axis of symmetry that is forbidden in periodic crystals. The term "quasicrystal" should simply be regarded as an abbreviation for "quasiperiodic crystal," possibly with two provisos, as discussed below. The argument is supported by theoretical as well as experimental examples of quasicrystals without any forbidden symmetry.

cond-mat.mtrl-sci↗
arXiv1999

Magnetic quasicrystals: What can we expect to see in their neutron diffraction data?

The theory of magnetic symmetry in quasicrystals is used to characterize the nature of magnetic peaks, expected in elastic neutron diffraction experiments. It is established that there is no symmetry-based argument which forbids the existence of quasiperiodic long-range magnetic order. Suggestions are offered as to where one should look for the simplest kinds of antiferromagnetic quasicrystals.

cond-mat.mtrl-sci↗
arXiv1999

Thermoelastic Damping in Micro- and Nano-Mechanical Systems

The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electro-mechanical systems (MEMS and NEMS). The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener's well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.

cond-mat.mes-hall↗
arXiv1999

Spin Injection in a Ballistic Two-Dimensional Electron Gas

We explore electrically injected, spin polarized transport in a ballistic two-dimensional electron gas. We augment the Buettiker-Landauer picture with a simple, but realistic model for spin-selective contacts to describe multimode reservoir-to-reservoir transport of ballistic spin 1/2 particles. Clear and unambiguous signatures of spin transport are established in this regime, for the simplest measurement configuration that demonstrates them directly. These new effects originate from spin precession of ballistic carriers; they exhibit strong dependence upon device geometry and vanish in the diffusive limit. Our results have important implications for prospective ``spin transistor'' devices.

cond-mat.mes-hall↗
arXiv1998

Lattice Color Groups of Quasicrystals

Lattice color groups are introduced and used to study the partitioning of a periodically- or quasiperiodically-ordered set of points into N symmetry-related subsets. Applications range from magnetic structure to superlattice ordering in periodic and quasiperiodic crystals.

cond-mat↗
arXiv1998

Theoretical Model for Faraday Waves with Multiple-Frequency Forcing

A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a fluid driven by a linear combination of two frequencies. The model exhibits steady-state solutions with two-, four-, six-, and twelve-fold symmetric patterns, similar to the periodic and quasiperiodic patterns observed in recent experiments.

cond-mat.soft↗
arXiv1998

Symmetry of Magnetically Ordered Quasicrystals

The notion of magnetic symmetry is reexamined in light of the recent observation of long range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a magnetically-ordered (periodic or quasiperiodic) crystal, given in terms of a ``spin space group,'' and its neutron diffraction diagram is established. In doing so, an outline of a symmetry classification scheme for magnetically ordered quasiperiodic crystals is provided. Predictions are given for the expected diffraction patterns of magnetically ordered icosahedral crystals, provided their symmetry is well described by icosahedral spin space groups.

cond-mat.mtrl-sci↗