arXiv subjects

Alexey Osipov

Publications and source records attributed to Alexey Osipov.

5 recordsLinked to original sources

arXiv2023

Observation of Zitterbewegung in photonic microcavities

We present and experimentally study the effects of the photonic spin-orbit coupling on real space propagetion of polariton wavepackets in planar semiconductor microcavities and polaritonic analogs of graphene. In particular, we demonstrate the appearance of an analog Zitterbewegung effect, a term which translates as 'trembling motion' in english, which was originally proposed for relativistic Dirac electrons and consists of the oscillations of the center of mass of a wavepacket in the direction perpendicular to its propagation. For a planar microcavity we observe regular Zitterbewegung oscillations whose amplitude and period depend on the wavevector of the polaritons. We then extend these results to a honeycomb lattice of coupled microcavity resonators. Compared to the planar cavity such lattices are inherently more tuneable and versatile, allowing simulation of the Hamilitonians of a wide range of important physical systems. We observe an oscillation pattern related to the presence of the spin-split Dirac cones in the dispersion. In both cases the experimentally observed oscillations are in good agreement with theoretical modelling and independently measured bandstructure parameters, providing strong evidence for the observation of Zitterbewegung.

physics.optics↗

arXiv2014

Shadowing for differential equations with grow-up

We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of shadowing lemma. Besides, we prove a theorem about weighted shadowing for flows. We compactify the system (using Poincare compactification, for example), apply the results about nonuniform or weighted shadowing to the compactified system, and then transfer the results back to the initial system using the decompactification procedure.

math.DS↗

arXiv2013

Shadowing for actions of some finitely generated groups

We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpotent groups. We construct an example of a faithful linear action of a solvable Baumslag-Solitar group and show that the shadowing property depends on quantitative characteristics of hyperbolicity. Finally we show that any linear action of a non-abelian free group does not have the shadowing property.

math.DS↗

arXiv2010

Periodic shadowing and $Ω$-stability

We show that the following three properties of a diffeomorphism $f$ of a smooth closed manifold are equivalent: (i) $f$ belongs to the $C^1$-interior of the set of diffeomorphisms having periodic shadowing property; (ii) $f$ has Lipschitz periodic shadowing property; (iii) $f$ is $Ω$-stable.

math.DS↗

arXiv2006

Magneto-Dielectric Substrates in Antenna Miniaturization: Potential and Limitations

In the present paper we discuss antenna miniaturization using magneto-dielectric substrates. Recent results found in the literature reveal that advantages over conventional dielectric substrates can only be achieved if natural magnetic inclusions are embedded into the substrate. This observation is revised and the physical background is clarified. We present a detailed discussion concerning magnetic materials available in the microwave regime and containing natural magnetic constituents. The effects of magnetic dispersion and loss are studied: constraints on the microwave permeability are used to estimate the effect of magnetic substrates on the achievable impedance bandwidth. Microwave composites filled with thin ferromagnetic films are considered as a prospective antenna substrate. We calculate the impedance bandwidth for a $λ/2$-patch antenna loaded with the proposed substrate, and challenge the results against those obtained with conventional dielectric substrates. It is shown that the radiation quality factor is strongly minimized with the proposed substrate even in the presence of realistic losses. Estimates for the radiation efficiency are given as a function of the magnetic loss factor.

physics.class-ph↗