Related papers: Motion in an Asymmetric Double Well
Quantum tunneling between two potential wells in a magnetic field can be strongly increased when the potential barrier varies in the direction perpendicular to the line connecting the two wells and remains constant along this line. An…
Exact solutions are found for Euler's equations of rigid body motion for general asymmetrical bodies under the influence of torque by using Jacobi elliptic functions. Differential equations are determined for the amplitudes and the…
We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two…
We explore the helical quantum two-body problem i.e. two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb…
The dynamics of non-spherical rigid particles immersed in an axisymmetric random flow is studied analytically. The motion of the particles is described by Jeffery's equation; the random flow is Gaussian and has short correlation time.The…
For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger…
We investigate the behaviour of a two-component Fermi superfluid in a double-well potential. We numerically solve the time dependent Bogoliubov-de Gennes equations and characterize the regimes of Josephson oscillations and self-trapping for…
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\chi_2$ type nonlinearity as well as two mode…
The representations of position and momentum operators of a planar phase space having both position and momentum noncommutativity are obtained. Using these representations the dynamics of a particle in a gravitational quantum well is…
In the present paper a description of a problem of point vortices on a plane and a sphere in the "internal" variables is discussed. The hamiltonian equations of motion of vortices on a plane are built on the Lie-Poisson algebras, and in the…
In this methodological paper we consider geodesic motion of particles in a spherically symmetric black hole space-times. We develop an approach based on splitting the velocity of a freely falling particle to the flow velocity, which depends…
In this paper, we study the geodesic motion in spherically symmetric electro-vacuum Euclidean solutions of the Einstein equation. There are two kinds of such solutions: the Euclidean Reissner-Nordstr\"{o}m (ERN) metrics, and the…
We investigate a non-interacting many-particle bosonic system, placed in an asymmetric double-well potential. We first consider the dynamics of a single particle and determine its time-dependent probabilities to be in the left or the right…
The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does…
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
We consider travelling periodical and quasiperiodical waves in single mode fibres, with weak birefringence and under the action of cross-phase modulation. The problem is reduced to the ``1:2:1" integrable case of the two-particle quartic…
Large-scale collective oscillation is discovered in the two-dimensional Euler equations. For initial conditions far from a base stationary flow, the system does not relax to the base stationary flow, but instead shows pairs of coherent…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We use the Rayleigh-Schr\"odinger perturbation theory to calculate the corrections to the adiabatic geometric phase due to a perturbation of the Hamiltonian. We show that these corrections are at least of second order in the perturbation…
Rotating black holes are algebraically special solutions to the vacuum Einstein equation. Using properties of the algebraically special solutions we construct the dual fluid, which flows on black hole horizon. An explicit form of the Kerr…