Related papers: On an integrable magnetic geodesic flow on the two…
In this paper we study the energy spectrum of a two dimensional electron gas (2DEG) in a two dimensional periodic magnetic field. Both a square magnetic lattice and a triangular one are considered. We consider the general case where the…
This paper shows that the left-invariant geodesic flow on the symplectic group relative to the Frobenius metric is an integrable system that is not contained in the Mishchenko-Fomenko class of rigid body metrics. This system may be…
The conjecture is verified that the optimum, energy minimizing magnetic flux for a half-filled band of electrons hopping on a planar, bipartite graph is $\pi$ per square plaquette. We require {\it only} that the graph has periodicity in one…
A three-dimensional numerical computation of magnetohydrodynamic dynamo behavior is described. The dynamo is mechanically forced with a driving term of the Taylor-Green type. The magnetic field development is followed from negligibly small…
Let $M$ be a closed surface and let $\{g_s \ | \ s \in (-\epsilon, \epsilon)\}$ be a smooth one-parameter family of Riemannian metrics on $M$. Also let $\{\kappa_s : M \rightarrow \mathbb{R} \ | \ s \in (-\epsilon, \epsilon)\}$ be a smooth…
We present fractional flux periodicity in the ground state of planar systems made of a square lattice whose boundary is compacted into a torus. The ground-state energy shows a fractional period of the fundamental unit of magnetic flux…
An example of a real-analytic metric on a compact manifold whose geodesic flow is Liouville integrable by $C^\infty$ functions and has positive topological entropy is constructed.
We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a…
In this paper we study quasi-linear system of partial differential equations which describes the existence of the polynomial in momenta first integral of the integrable geodesic flow on 2-torus. We proved in [3] that this is a…
Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first…
We establish that, for every hyperbolic orbifold of type (2, q, $\infty$) and for every orbifold of type (2, 3, 4g+2), the geodesic flow on the unit tangent bundle is left-handed. This implies that the link formed by every collection of…
We construct symbolic dynamics on sets of full measure (w.r.t. an ergodic measure of positive entropy) for $C^{1+\epsilon}$ flows on compact smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent…
Starting with a static, spherically symmetric spacetime incorporating critical (unstable) closed null geodesics, a family of models for equilibrium states of non-isolated compact objects is obtained by solving the Einstein equations for an…
We develop the in-out formalism for one-loop effective actions in electromagnetic fields in the space-dependent gauge. We further advance a method using the inverse scattering matrix to calculate the effective actions in pure magnetic…
This paper develops new links between contact geometry, magnetic dynamics, and symmetry in exact magnetic systems. First, we establish an interpolation property for Killing magnetic systems on contact manifolds under an additional…
It is shown that in the case of free electron in a spatially periodic magnetic field the concept of magnetic translations operators is still valid and, moreover, these operators can be defined in the same way as for a Bloch electron in a…
The energy spectra of spin-1/2 electrons under two-dimensional magnetic field modulations are calculated beyond the one-band approximation. Our formulation is generally applicable to a modulation field with a rectangular lattice symmetry.…
The present study is a continuation of a previous one on "hyperelliptic" axisymmetric equilibria started in [Tasso and Throumoulopoulos, Phys. Plasmas 5, 2378 (1998)]. Specifically, some equilibria with incompressible flow nonaligned with…
While there are no known analytic solutions for force-free fields in toroidal coordinates, with a reasonable boundary condition it is possible to find a solution for the surface field and, with a restriction on the form of the field, to the…
We provide a unified treatment of electric-magnetic duality, at the action level and with manifest Lorentz invariance, for massive, massless as well as partially-massless gravitons propagating in maximally symmetric spacetimes of any…