Quantization of the motion and Cherenkov structure of a Josephson vortex

A generalization of the Sakai-Tateno-Pedersen model is proposed. This model is used to establish the existence of a discrete eigenvalue spectrum of the free-motion velocities of a Josephson vortex, or π kink, produced by the Cherenkov structure of extraordinary vortex-trapped Swihart waves having the spectrum (3.9). The dependence of the current across the Josephson junction on the vortex velocity was obtained, and, at comparatively high velocities, this was characterized by equidistant dips attributable to the Cherenkov resonant interaction of the vortex with Swihart waves.     

Effect of Cherenkov dissipation on vortex velocity in a waveguide-coupled Josephson junction

A motion of slow and fast vortices in a waveguide-coupled Josephson junction induced by a transport current flowing through the entire structure is studied; the coupling is not assumed to be weak. For a fast vortex, conditions are established under which current oscillations due to energy dissipation via Cherenkov radiation of Swihart waves become comparable to the current compensating for ohmic losses in the Josephson junction, waveguide, and adjacent superconductors. For a slow vortex, it is proved that intermediate and strong couplings of the Josephson junction to the waveguide shift current oscillations to the velocity range below the Swihart velocity of the Josephson junction.     

On the velocity of a 4π kink moving under the action of current

The dependence of bias current density through a junction on the velocity of a uniformly moving vortex carrying two magnetic flux quanta is established in the approximation of weakly nonlocal Josephson electrodynamics. It is shown that the velocity quantization of free motion of the vortex, which is induced by the Cherenkov interaction with Swihart waves, leads to the emergence of a discrete family of curves on the velocity-current plane.     

Cherenkov trapping of waves and discreteness of 6 π-kink motion in a long Josephson junction

The phenomenon of Cherenkov trapping of generalized Swihart waves by a moving vortex is established using an analytically solvable model. The quantization of the structure of the field of the trapped waves is manifested as quantization of the values of the velocity of the vortices. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 4, 318–322 (25 February 1999)     

Cherenkov radiation from an Abrikosov-Josephson vortex

The Cherenkov radiation of generalized Swihart waves is investigated in connection with the slow motion of an Abrikosov-Josephson vortex, which corresponds to a 2 π kink in the phase difference of Cooper pairs on opposite sides of a tunnel junction. The radiative friction force acting on such a vortex is determined. An evaluation is made of the steady-state vortex velocity when the accelerating influence of an electric current through the Josephson junction is compensated by radiative slowing of the vortex due to Cherenkov radiation from the Abrikosov-Josephson vortex. Fiz. Tverd. Tela (St. Petersburg) 39, 444–448 (March 1997)     

Emission of radiation from a long Josephson junction in a thin film

Space-time nonlocal electrodynamic equations are derived for nonlinear vortex states of a Josephson junction in a film of thickness much smaller than the London penetration depth. The spectrum and damping of generalized Swihart waves propagating in such a junction are analyzed. The radiation damping constant associated with the possible emission of electromagnetic radiation is determined in the range of Swihart wave phase velocities exceeding the speed of light. The emission of radiation from nonlinear states having dimensions greater than the distance traversed by light in vacuum during the characteristic time of variation of the phase difference is investigated. It is shown that the flux density of radiation emitted by such states is localized in a plane orthogonal to the axis of the tunnel junction and depends weakly on the angle of observation in this plane. Zh. éksp. Teor. Fiz. 115, 1426–1449 (April 1999)     

Some aspects of the nonlocal electrodynamics of infinite Josephson junctions

We derive the basic equations of nonlocal Josephson electrodynamics, valid for any ratios of the characteristic scale of phase-difference variations and junction thickness. The spectrum of generalized Swihart waves is obtained. We also study the effect of finite surface resistance of the superconducting electrodes on the dynamics of vortex structures characteristic of nonlocal electrodynamics. Zh. éksp. Teor. Fiz. 113, 955–966 (March 1998)     

On the current-voltage characteristic of a Josephson junction with a high critical current density

A theory is constructed for the current-voltage characteristic of a Josephson junction with a high critical current density described by nonlocal vortex electrodynamics in the approximation of small dissipation due to the single-particle conductivity of the Josephson junction. The role of the resonant excitation of generalized short-wavelength Swihart waves is determined. New quantitative properties of the current-voltage characteristic, which is an envelope of wave excitation resonances, are established. Zh. éksp. Teor. Fiz. 113, 2148–2161 (June 1998)     

Extended Schwinger-Boson theory of the two-dimensional spin-1/2 anisotropic Heisenberg antiferromagnets

The properties of the possible solitary electromagnetic waves, propagating in two-dimensional SIS Josephson junction without dissipative losses are investigated on the basis of the local theory of the junction. A classification of the waves in the junction with respect to the Swihart velocity is made. It is shown that allowed and forbidden areas for the wave numbers, wave frequency and wave amplitude exist. The cut-off frequency for the solitary waves which velocity is greater than the Swihart velocity can be smaller than the Josephson plasma frequency and moreover these waves can propagate only in a junction that is large in the direction perpendicular to the propagation direction. On the contrary the solitary waves which velocity is smaller than the Swihart velocity request junction size in the above direction to be smaller than a critical one. The investigated two-dimensional solitary waves can be connected with one or two quanta of the magnetic flux.     

Wave-induced bed flows by a Lagrangian vortex scheme

Nominally 2-dimensional viscous flow induced by gravity waves over a spatially periodic bed is simulated by a Lagrangian vortex scheme. A vortex sheet is introduced on the surface at each time step to satisfy the zero velocity conditions. The sheet is discretised; the vortex-in-cell method is used to convect vorticity and random walks are added to effect viscous diffusion. Good agreement with analytical theory is obtained for velocity profiles in uniform sinusoidal flow and for mass transport due to linear waves. Mass transport for finite amplitude waves is also obtained. For separated flow over rippled beds, which is still liminar, a vortex decay factor is required to produce agreement with experiment and is thought to compensate for large scale 3-dimensional effects.     

Induced motion of a fast Josephson vortex

A relation is established between the transport current flowing through the entire S ₁ IS ₂ WS ₃ layered structure and the velocity of a fast vortex. The fast vortex exists when the Swihart velocity in the waveguide is significantly higher than that in the Josephson junction. It is demonstrated that the main contribution to the Lorentz force that induces the vortex motion is due to the current flowing through the waveguide and skin layers of the adjacent superconductors.

     

Spatially periodic structures of an atomic Bose-Einstein condensate

The conditions providing the formation of periodic vortex lattices of an interference nature in an atomic Bose-Einstein condensate (i.e., in the absence of rotation of the condensate) are determined. Spatially periodic exact solutions of the nonlocal nonlinear Schrödinger equation (the generalized Gross-Pitaevskii equation) that describes the Bose-Einstein condensate of a dilute gas of alkali metal atoms with due regard for the nonlocality of interatomic interactions are obtained in the form of a set of two or three plane waves. It is shown that periodic vortex lattices can be produced in interference experiments with a Bose-Einstein condensate of a dilute gas of alkali metal atoms.     

On the decay of generalized Swihart waves

For Josephson junctions in sandwich geometry and in thin-film geometry we formulate the equations of nonlocal electrodynamics which take account of the influence of normal electrons in superconductors. On the basis of these equations we examine the spectrum and decay of generalized Swihart waves. We find that the decay of these waves by normal electrons becomes especially prominent in the short-wavelength region. Comparison of various dissipation mechanisms has revealed the conditions for efficient emission of electromagnetic waves from Josephson structures with finite dimensions. Fiz. Tverd. Tela (St. Petersburg) 41, 1160–1167 (July 1999)     

Using Josephson vortex lattices to control terahertz radiation: tunable transparency and terahertz photonic crystals

The Josephson vortex (JV) lattice is a periodic array that scatters electromagnetic waves in the THz-frequency range. We show that JV lattices can produce a photonic band-gap structure (THz photonic crystal) with easily tunable forbidden zones controlled by the in-plane magnetic field. The scattering of electromagnetic waves by JVs results in a strong magnetic-field dependence of the reflection and transparency. Fully transparent or fully reflected frequency windows can be conveniently tuned by the in-plane magnetic field. These proposals are potentially useful for controllable THz filters.     

Topological defects in incommensurate magnetic and crystal structures and quasi-periodic solutions of the elliptic sine-Gordon equation

Vortex-type singular solutions with a topological charge of the elliptic sine-Gordon equation have been studied. One- and two-dimensional vortex lattices on a homogeneous and periodic background are constructed in the explicit form using the Bäcklund transformation. The interaction of vortices is investigated and finite energy configurations are found. On the basis of the obtained results new topological defects in incommensurate magnetic and crystal structures are predicted and described. The interaction of vortex magnetic structures with nonlinear spin waves is considered.     

Low frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling

A long-standing problem of the low-energy dynamics of a disordered XY spin chain is reexamined. The case of a rigid chain is studied, where the quantum effects can be treated quasiclassically. It is shown that, as the frequency decreases, the relevant excitations change from localized spin waves to two-level systems to soliton-antisoliton pairs. The linear-response correlation functions are calculated. The results apply to other periodic glassy systems such as pinned density waves, planar vortex lattices, stripes, and disordered Luttinger liquids.