arXiv subjects

Sherwin Kouchekian

Publications and source records attributed to Sherwin Kouchekian.

3 recordsLinked to original sources

arXiv2026

The Lagrangian and symplectic structures of the Kuramoto oscillator model

Despite being under intense scrutiny for 50 years, the Kuramoto oscillator model has remained a quintessential representative of non-equilibrium phase transitions. One of the reasons for its enduring relevance is the apparent lack of an optimization formulation, due to the fact that (superficially), the equations of motion seem to not be compatible with a Lagrangian structure. We show that, as a mean-field classical (twisted) spin model on $S^2$, the Kuramoto model can be described variationaly. Based on this result perturbation analysis around (unstable) Kuramoto equilibria are shown to be equivalent to low-energy fluctuations of mean-field Heisenberg spin models. Intriguingly, off-plane perturbations around these equilibria configurations turn out to be described by a semiclassical Gaudin model, pointing to the fact that oscillator synchronization maps to the spin pairing mechanism investigated by Richardson and subsequently by others.

math-ph↗

arXiv2023

On simultaneous similarity of families of commuting operators

Characterization of simultaneously similarity for commuting $m$-tuples of operators is an open problem even in finite-dimensional spaces; known as ``A wild problem in linear algebra". In this paper we offer a criteria for simultaneously similarity of $m$-tuples of $k$-cyclic commuting operators on an arbitrary Banach space. Moreover, we obtain an additional equivalence condition in the case of finite dimensional Banach spaces, which extends the result found in \cite{BS13} for pairs of cyclic commuting matrices. We also present two applications of our results, one in the case of general multiplication operators on Banach spaces of analytic function, and one for $m$-tuples of commuting square matrices.

math.FA↗

arXiv2017

Poloidal and toroidal plasmons and fields of multilayer nanorings

Composite and janus type metallo-dielectric nanoparticles are increasingly considered as a means to control the spatial and temporal behavior of electromagnetic fields in diverse applications such as coupling to quantum emitters, achieve invisibility cloaks, and obtain quantum correlations between qubits. We investigate the surface modes of a toroidal nano-structure and obtain the canonical plasmon dispersion relations and resonance modes for arbitrarily layered nanorings. Unlike particle plasmon eigenmodes in other geometries, the amplitudes of the eigenmodes of tori exhibit a distinct forward and backward coupling. We present the plasmon dispersion relations for several relevant toroidal configurations in the quasistatic limit and obtain the dominant retarded dispersion relations of a single ring for comparison, discuss mode complementarity and hybridization, and introduce two new types of toroidal particles in the form of janus nanorings. The resonance frequencies for the first few dominant modes of a ring composed of plasmon supporting materials such as gold, silver, and aluminum are provided and compared to those for a silicon ring. A generalized Green's function is obtained for multilayer tori allowing for calculation of the scattering response to interacting fields. Employing the Green's function, the scalar electric potential distribution corresponding to individual poloidal and toroidal modes in response to an arbitrarily polarized external field and the field of electrons is obtained. The results are applied to obtain the local density of states and decay rate of a dipole near the center of the torus.

physics.optics↗