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 $q$ couples to a term linear in $qA^3M$, where $A^3$ is the transverse component of the electromagnetic vector potential and $M$ 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 $\alpha$ 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 $\alpha$. Especially the electron transportation varies periodically versus the arc angle $\theta_{w}$. 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