arXiv subjects

R. Dandoloff

Publications and source records attributed to R. Dandoloff.

8 recordsLinked to original sources

arXiv2013

Topological spin excitations induced by an external magnetic field coupled to a surface with rotational symmetry

We study the Heisenberg model in an external magnetic field on curved surfaces with rotational symmetry. The Euler-Lagrange static equations, derived from the Hamiltonian lead to the inhomogeneous double sine-Gordon equation (DSG). However, if the magnetic field is coupled with the metric elements of the surface, and consequently, its curvature, the homogeneous DSG appears and a $2π$-soliton is obtained as a solution for this model. In order to obey the self-dual equations, surface deformations are predicted at the sector where the spins point in the opposite direction to the magnetic field. The model was used to particularize the characteristic lenght of the 2$π$-soliton for three specific rotationally symmetric surfaces: the cylinder, the catenoid and the hyperboloid. Fractional 2$π$-solitons must appear on finite surfaces, as the sphere, torus and barrels, for example.

cond-mat.mes-hall↗

arXiv2011

Quantum anticentrifugal potential in a bent waveguide

We show the existence of an anticentrifugal force for a quantum particle in a bent waveguide. This counterintuitive force due to dimensionality was shown to exist in a flat $R^2$ space but there it needs an additional $δ$-like potential at the origin in order to brake the translational invariance and to exhibit localized states. In the case of the bent waveguide there is no need of any additional potential since here the boundary conditions break the symmetry. The effect may be observed in interference experiments which are sensitive to the additional phase of the wavefunction gained in the bent regions and can find application in distinguishing between straight and bent geometries.

quant-ph↗

arXiv2009

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.

quant-ph↗

arXiv2007

The Manakov system as two moving interacting curves

The two time-dependent Schrodinger equations in a potential V(s,u), $u$ denoting time, can be interpreted geometrically as a moving interacting curves whose Fermi-Walker phase density is given by -dV/ds. The Manakov model appears as two moving interacting curves using extended da Rios system and two Hasimoto transformations.

nlin.SI↗

arXiv2004

Hidden topological structure in the continuous Heisenberg spin chain

In order to study the spin configurations of the classical one-dimensional Heisenberg model, we map the normalized unit vector, representing the spin, to a space curve. We show that the total chirality of the configuration is a conserved quantity. When the space curve forms a knot, this defines a new class of topological spin configurations for the Heisenberg model.

math-ph↗

arXiv2004

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 ξ_0 from the central axis. The twist ωof 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.

math-ph↗

arXiv2002

Geometric phase and quantum potential

We show that the geometric phase of Levy-Leblond arises from a low of parallel transport for wave functions and point out that this phase belongs to a new class of geometric phases due to the presence of a quantum potential.

quant-ph↗

arXiv2001

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 discussed

quant-ph↗