38 research outputs found
Quantum mechanics of a constrained electrically charged particle in the presence of electric currents
We discuss the dynamics of a classical spinless quantum particle carrying
electric charge and constrained to move on a non singular static surface in
ordinary three dimensional space in the presence of arbitrary configurations of
time independent electric currents. Starting from the canonical action in the
embedding space we show that a charged particle with charge couples to a
term linear in , where is the transverse component of the
electromagnetic vector potential and is the mean curvature in the surface.
This term cancels exactly a curvature contribution to the orbital magnetic
moment of the particle. It is shown that particles, independently of the value
of the charge, in addition to the known couplings to the geometry also couple
to the mean curvature in the surface when a Neumann type of constraint is
applied on the transverse fluctuations of the wave function. In contrast to a
Dirrichlet constraint on the transverse fluctuations a Neumann type of
constraint on these degrees of freedom will in general make the equations of
motion non separable. The exceptions are the equations of motion for
electrically neutral particles on surfaces with constant mean curvature. In the
presence of electric currents the equation of motion of a charged particle is
generally non separable independently of the coupling to the geometry and the
boundary constraints.Comment: to appear in Phys.Rev.
Quantum Hall-like effect on strips due to geometry
In this Letter we present an exact calculation of the effective potential
which appears on a helicoidal strip. This potential leads to the appearance of
lcalized states at a distance \xi_0 from the central axis. The twist \omega of
the strip plays the role of a magnetic field and is responsable for the
appearance of these localized states and an effective transverse electric field
thus this is reminiscent of the quantum Hall effect. At very low temperatures
the twisted configuration of the strip may be stalilized by the electronic
states.Comment: 3 page
Geometry of entangled states, Bloch spheres and Hopf fibrations
We discuss a generalization to 2 qubits of the standard Bloch sphere
representation for a single qubit, in the framework of Hopf fibrations of high
dimensional spheres by lower dimensional spheres. The single qubit Hilbert
space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented
S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres
represent the qubit overall phase degree of freedom. For the two qubits case,
the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf
fibration, with S3 fibres and a S4 base. A main striking result is that
suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation
with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.
Diluted planar ferromagnets: nonlinear excitations on a non-simply connected manifold
We study the behavior of magnetic vortices on a two-dimensional support
manifold being not simply connected. It is done by considering the continuum
approach of the XY-model on a plane with two disks removed from it. We argue
that an effective attractive interaction between the two disks may exist due to
the presence of a vortex. The results can be applied to diluted planar
ferromagnets with easy-plane anisotropy, where the disks can be seen as
nonmagnetic impurities. Simulations are also used to test the predictions of
the continuum limit.Comment: 5 pages, 6 figure
Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve
We develop a new interpretation of the geometric phase in evolution with a
non-Hermitian real value Hamiltonian by relating it to the angle developed
during the parallel transport along a closed curve by a unit vector triad in
the 3D-Minkovsky space. We also show that this geometric phase is responsible
for the anholonomy effects in stochastic processes considered in [N. A.
Sinitsyn and I. Nemenman, EPL {\bf 77}, 58001 (2007)], and use it to derive the
stochastic system response to periodic parameter variations.Comment: 10 pages 2 figure
Quantum transport in a curved one-dimensional quantum wire with spin-orbit interactions
The one-dimensional effective Hamiltonian for a planar curvilinear quantum
wire with arbitrary shape is proposed in the presence of the Rashba spin-orbit
interaction. Single electron propagation through a device of two straight lines
conjugated with an arc has been investigated and the analytic expressions of
the reflection and transmission probabilities have been derived. The effects of
the device geometry and the spin-orbit coupling strength on the
reflection and transmission probabilities and the conductance are investigated
in the case of spin polarized electron incidence. We find that no spin-flip
exists in the reflection of the first junction. The reflection probabilities
are mainly influenced by the arc angle and the radius, while the transmission
probabilities are affected by both spin-orbit coupling and the device geometry.
The probabilities and the conductance take the general behavior of oscillation
versus the device geometry parameters and . Especially the electron
transportation varies periodically versus the arc angle . We also
investigate the relationship between the conductance and the electron energy,
and find that electron resonant transmission occurs for certain energy.
Finally, the electron transmission for the incoming electron with arbitrary
state is considered. For the outgoing electron, the polarization ratio is
obtained and the effects of the incoming electron state are discussed. We find
that the outgoing electron state can be spin polarization and reveal the
polarized conditions.Comment: 7 pages, 8 figure