Improved model for the topological soliton-potential interaction in Phi^4 Model

An improved model for the soliton-potential interaction is presented. This model is constructed with a better approximation for adding the potential to the lagrangian through a space-time metric. The results of the model are compared with other models and the differences are discussed.Comment: 8 pages, 11 figure

Why not a di-NUT? or Gravitational duality and rotating solutions

We study how gravitational duality acts on rotating solutions, using the Kerr-NUT black hole as an example. After properly reconsidering how to take into account both electric (i.e. mass-like) and magnetic (i.e. NUT-like) sources in the equations of general relativity, we propose a set of definitions for the dual Lorentz charges. We then show that the Kerr-NUT solution has non-trivial such charges. Further, we clarify in which respect Kerr's source can be seen as a mass M with a dipole of NUT charges.Comment: 20 pages. v2: minor clarifications in section 4, version to appear in PR

Interaction of topological solitons with defects: using a nontrivial metric

By including potential into the flat metric, we study interaction of sine-Gordon soliton with potentials. We will show numerically that while the soliton-barrier system shows fully classical behaviour, the soliton-well system demonstrates non-classical behaviour. In particular, solitons with low velocities are trapped in the well and emit energy radiation.Comment: 10 pages, 11 figure

Analytical formulation for soliton-potential dynamics

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the soliton is like a point particle living under the influence of a complicated potential which is a function of soliton velocity and the potential parameters. The analytic model does not have a clear prediction for the islands of initial velocities in which the soliton may reflect back or escape over the potential well.Comment: 12 pages, 10 figure

Electromagnetic Casimir piston in higher dimensional spacetimes

We consider the Casimir effect of the electromagnetic field in a higher dimensional spacetime of the form $M\times \mathcal{N}$, where $M$ is the 4-dimensional Minkowski spacetime and $\mathcal{N}$ is an $n$-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder with the same cross section is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in $M$ is large. It is found that if the separation between the plates is much smaller than the size of $\mathcal{N}$, the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the $(4+n)$-dimensional Minkowski spacetime. However, if the size of $\mathcal{N}$ is much smaller than the separation between the plates, the leading term of the Casimir force is $1+h/2$ times the Casimir force on a pair of large parallel plates in the 4-dimensional Minkowski spacetime, where $h$ is the first Betti number of $\mathcal{N}$. In the limit the manifold $\mathcal{N}$ vanishes, one does not obtain the Casimir force in the 4-dimensional Minkowski spacetime if $h$ is nonzero.Comment: 22 pages, 4 figure

Bose-Einstein condensates in strong electric fields -- effective gauge potentials and rotating states

Magnetically-trapped atoms in Bose-Einstein condensates are spin polarized. Since the magnetic field is inhomogeneous, the atoms aquire Berry phases of the Aharonov-Bohm type during adiabatic motion. In the presence of an eletric field there is an additional Aharonov-Casher effect. Taking into account the limitations on the strength of the electric fields due to the polarizability of the atoms, we investigate the extent to which these effects can be used to induce rotation in a Bose-Einstein condensate.Comment: 5 pages, 2 ps figures, RevTe

Nonlocal Phases of Local Quantum Mechanical Wavefunctions in Static and Time-Dependent Aharonov-Bohm Experiments

We show that the standard Dirac phase factor is not the only solution of the gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials), apart from Dirac phases also contains terms of classical fields that act nonlocally (in spacetime) on the local solutions of the time-dependent Schr\"odinger equation: the phases of wavefunctions in the Schr\"odinger picture are affected nonlocally by spatially and temporally remote magnetic and electric fields, in ways that are fully explored. These contributions go beyond the usual Aharonov-Bohm effects (magnetic or electric). (i) Application to cases of particles passing through static magnetic or electric fields leads to cancellations of Aharonov-Bohm phases at the observation point; these are linked to behaviors at the semiclassical level (to the old Werner & Brill experimental observations, or their "electric analogs" - or to recent reports of Batelaan & Tonomura) but are shown to be far more general (true not only for narrow wavepackets but also for completely delocalized quantum states). By using these cancellations, certain previously unnoticed sign-errors in the literature are corrected. (ii) Application to time-dependent situations provides a remedy for erroneous results in the literature (on improper uses of Dirac phase factors) and leads to phases that contain an Aharonov-Bohm part and a field-nonlocal part: their competition is shown to recover Relativistic Causality in earlier "paradoxes" (such as the van Kampen thought-experiment), while a more general consideration indicates that the temporal nonlocalities found here demonstrate in part a causal propagation of phases of quantum mechanical wavefunctions in the Schr\"odinger picture. This may open a direct way to address time-dependent double-slit experiments and the associated causal issuesComment: 49 pages, 1 figure, presented in Conferences "50 years of the Aharonov-Bohm effect and 25 years of the Berry's phase" (Tel Aviv and Bristol), published in Journ. Phys. A. Compared to the published paper, this version has 17 additional lines after eqn.(14) for maximum clarity, and the Abstract has been slightly modified and reduced from the published 2035 characters to the required 1920 character

Classical electromagnetic field theory in the presence of magnetic sources

Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a consistent Lagrangian for the theory. Then from the action principle we get both Maxwell's equation and the equation of motion of a dyon moving in the electro-magnetic field.Comment: 10 pages, no figure

Topological quenching of the tunnel splitting for a particle in a double-well potential on a planar loop

The motion of a particle along a one-dimensional closed curve in a plane is considered. The only restriction on the shape of the loop is that it must be invariant under a twofold rotation about an axis perpendicular to the plane of motion. Along the curve a symmetric double-well potential is present leading to a twofold degeneracy of the classical ground state. In quantum mechanics, this degeneracy is lifted: the energies of the ground state and the first excited state are separated from each other by a slight difference ¿E, the tunnel splitting. Although a magnetic field perpendicular to the plane of the loop does not influence the classical motion of the charged particle, the quantum-mechanical separation of levels turns out to be a function of its strength B. The dependence of ¿E on the field B is oscillatory: for specific discrete values Bn the splitting drops to zero, indicating a twofold degeneracy of the ground state. This result is obtained within the path-integral formulation of quantum mechanics; in particular, the semiclassical instanton method is used. The origin of the quenched splitting is intuitively obvious: it is due to the fact that the configuration space of the system is not simply connected, thus allowing for destructive interference of quantum-mechanical amplitudes. From an abstract point of view this phenomenon can be traced back to the existence of a topological term in the Lagrangian and a nonsimply connected configuration space. In principle, it should be possible to observe the splitting in appropriately fabricated mesoscopic rings consisting of normally conducting metal

Bogomol'nyi Decomposition for Vesicles of Arbitrary Genus

We apply the Bogomol'nyi technique, which is usually invoked in the study of solitons or models with topological invariants, to the case of elastic energy of vesicles. We show that spontaneous bending contribution caused by any deformation from metastable bending shapes falls in two distinct topological sets: shapes of spherical topology and shapes of non-spherical topology experience respectively a deviatoric bending contribution a la Fischer and a mean curvature bending contribution a la Helfrich. In other words, topology may be considered to describe bending phenomena. Besides, we calculate the bending energy per genus and the bending closure energy regardless of the shape of the vesicle. As an illustration we briefly consider geometrical frustration phenomena experienced by magnetically coated vesicles.Comment: 8 pages, 1 figure; LaTeX2e + IOPar