Directed chaos in a billiard chain with transversal magnetic field
نویسندگان
چکیده
In generic Hamiltonian systems with a mixed phase space chaotic transport may be directed and ballistic rather than diffusive. We investigate one particular model showing this behaviour, namely a spatially periodic billiard chain in which electrons move under the influence of a perpendicular magnetic field. We analyze the phase-space structure and derive an explicit expression for the chaotic transport velocity. Unlike previous studies of directed chaos our model has a parameter regime in which the dispersion of an ensemble of chaotic trajectories around its moving center of mass is essentially diffusive. We explain how in this limit the deterministic chaos reduces to a biased random walk in a billiard with a rough surface. The diffusion constant for this simplified model is calculated analytically.
منابع مشابه
Directed Transport in classical and quantum chaotic billiards
We construct an autonomous chaotic Hamiltonian ratchet as a channel billiard subdivided by equidistant walls attached perpendicularly to one side of the channel, leaving an opening on the opposite side. A static homogeneous magnetic field penetrating the billiard breaks time-reversal invariance and renders the classical motion partially chaotic. We show that the classical dynamics exhibits dire...
متن کاملSignature of directed chaos in the conductance of a nanowire.
We study the conductance of chaotic or disordered wires in a situation where equilibrium transport decomposes into biased diffusion and a countermoving regular current. A possible realization is a semiconductor nanostructure with a transversal magnetic field and suitably patterned surfaces. We find a nontrivial dependence of the conductance on the wire length. It differs qualitatively from Ohm'...
متن کاملThermal negativity in a two qubit XXX and XX spin chain model in an external magnetic field
In this paper we studied the thermal negativity in a two-qubit XX spin ½ chain model and XXX spin1/2 chain model(isotropic Heisenberg model)spin-1/2 chain subjected to an external magnetic field inz direction. We calculate analytical relation for the thermal negativity for two qubit XX and XXX spinchain models in the external magnetic field. Effects of the magnetic field and temperature on then...
متن کاملEntanglement in the XZ spin chain model in the external magnetic field
The entanglement at zero-temperature is studied in a two-qubit XZ spin-1/2 chain model in anexternal magnetic field which is applied in the z direction. We have obtained an analytical relation forthe effect of the external magnetic field on the concurrence. It is shown that the ground state of thesystem depends on the strength of exchange coupling. We have shown that the analytical relation oft...
متن کاملIntegrability and Ergodicity of Classical Billiards in a Magnetic Field
We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not trivially integrable can be described by a “bouncing map”. We compute a general expression for the Jacobian matrix of this map, which allows to determine stability...
متن کامل