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Galakhov D.,Rutgers University | Melnikov D.,International Institute of Physics | Mironov A.,National Research Nuclear University MEPhI | Morozov A.,National Research Nuclear University MEPhI
Nuclear Physics B | Year: 2015

We remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants. © 2015 The Authors.


Galakhov D.,Rutgers University | Melnikov D.,International Institute of Physics | Mironov A.,National Research Nuclear University MEPhI | Morozov A.,National Research Nuclear University MEPhI | Sleptsov A.,National Research Nuclear University MEPhI
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2015

A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich (g+1)-parametric family of pretzel knots and links. The answer for the Jones and HOMFLY is fully and explicitly expressed through the Racah matrix of Uq(SUN), and looks related to a modular transformation of toric conformal block. © 2015 The Authors.


Hartmann R.R.,De La Salle University - Manila | Portnoi M.E.,University of Exeter | Portnoi M.E.,International Institute of Physics
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2014

We analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that bound states of both positive and negative energies exist in the energy spectrum and that there is a threshold value of the characteristic potential strength for which the first mode appears. Analytical solutions are presented in several limited cases and supercriticality is discussed. © 2014 American Physical Society.


Flayac H.,CNRS Pascal Institute | Pavlovic G.,International Institute of Physics | Kaliteevski M.A.,RAS Ioffe Physical - Technical Institute | Shelykh I.A.,University of Iceland
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

We have theoretically demonstrated the on-demand electric generation of vortices in an exciton-polariton superfluid. Electric pulses applied to a horseshoe-shaped metallic mesa, deposited on top of the microcavity, generate a noncylindrically symmetric solitonic wave in the system. Breakdown of its wave front at focal points leads to the formation of vortex-antivortex pairs, which subsequently propagate in the superfluid. The trajectory of these vortex dipoles can be controlled by applying a voltage to additional electrodes. They can be confined within channels formed by metallic stripes and unbound by a wedged mesa giving birth to grey solitons. Finally, single static vortices can be generated using a single metallic plate configuration. © 2012 American Physical Society.


Savenko I.G.,University of Iceland | Savenko I.G.,Academic University | Shelykh I.A.,University of Iceland | Shelykh I.A.,International Institute of Physics | Kaliteevski M.A.,RAS Ioffe Physical - Technical Institute
Physical Review Letters | Year: 2011

We consider the nonlinear terahertz emission by the system of cavity polaritons in the regime of polariton lasing. To account for the quantum nature of terahertz-polariton coupling, we use the Lindblad master equation approach and demonstrate that quantum microcavities reveal a rich variety of nonlinear phenomena in the terahertz range, including bistability, short terahertz pulse generation, and terahertz switching. © 2011 American Physical Society.


Kyriienko O.,University of Iceland | Shelykh I.A.,University of Iceland | Shelykh I.A.,International Institute of Physics
Physical Review B - Condensed Matter and Materials Physics | Year: 2011

We consider effective interactions in a two-dimensional (2D) hybrid polariton-electron system and calculate dispersion of elementary excitations by accounting for the spin degrees of freedom of the particles. Due to the crucial role played by the exchange term in polariton-electron interactions the dispersions of this system become spin dependent and show unusual behavior. The coupling of the excitations of the condensate with 2D plasmons can result in the appearance of roton minimum in the dispersion and destruction of the condensate for close enough situated quantum wells with electrons and excitons. © 2011 American Physical Society.


Hartmann R.R.,University of Exeter | Shelykh I.A.,University of Iceland | Portnoi M.E.,University of Exeter | Portnoi M.E.,International Institute of Physics
Physical Review B - Condensed Matter and Materials Physics | Year: 2011

We calculate the exciton binding energy in single-walled carbon nanotubes with narrow band gaps, accounting for the quasirelativistic dispersion of electrons and holes. Exact analytical solutions of the quantum relativistic two-body problem are obtained for several limiting cases. We show that the binding energy scales with the band gap, and conclude on the basis of the data available for semiconductor nanotubes that there is no transition to an excitonic insulator in quasimetallic nanotubes and that their THz applications are feasible. © 2011 American Physical Society.


Downing C.A.,University of Exeter | Stone D.A.,University of Exeter | Portnoi M.E.,University of Exeter | Portnoi M.E.,International Institute of Physics
Physical Review B - Condensed Matter and Materials Physics | Year: 2011

We present exact analytical zero-energy solutions for a class of smooth-decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without recourse to magnetic fields. These exact solutions allow us to draw conclusions on the general requirements for the potential to support fully confined states, including a critical value of the potential strength and spatial extent. © 2011 American Physical Society.


Alexeev A.M.,University of Exeter | Portnoi M.E.,University of Exeter | Portnoi M.E.,International Institute of Physics
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

Magneto-oscillations of the electric dipole moment are predicted and analyzed for a single-electron nanoscale ring pierced by a magnetic flux (an Aharonov-Bohm ring) and subjected to an electric field in the ring's plane. These oscillations are accompanied by periodic changes in the selection rules for interlevel optical transitions in the ring allowing control of polarization properties of the associated terahertz radiation. © 2012 American Physical Society.


Stone D.A.,University of Exeter | Downing C.A.,University of Exeter | Portnoi M.E.,International Institute of Physics
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

Using the variable phase method, we reformulate the Dirac equation governing the charge carriers in graphene into a nonlinear first-order differential equation from which we can treat both confined-state problems in electron waveguides and above-barrier scattering problems for arbitrary-shaped potential barriers and wells, decaying at large distances. We show that this method agrees with a known analytic result for a hyperbolic secant potential and go on to investigate the nature of more experimentally realizable electron waveguides, showing that when the Fermi energy is set at the Dirac point, truly confined states are supported in pristine graphene. In contrast to exponentially decaying potentials, we discover that the threshold potential strength at which the first confined state appears is vanishingly small for potentials decaying at large distances as a power law; but nonetheless, further confined states are formed when the strength and spread of the potential reach a certain threshold. © 2012 American Physical Society.

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