Related papers: Elastic field causing noncommutativity
We study the linearized Vlasov equations and the linearized Vlasov-Fokker-Planck equations in the weakly collisional limit in a uniform magnetic field. In both cases, we consider periodic confinement and Maxwellian (or close to Maxwellian)…
The usual methods for formulating and solving the quantum mechanics of a particle moving in a magnetic field respect neither locality nor any global symmetries which happen to be present. For example, Landau's solution for a particle moving…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…
We consider a test particle moving in a random distribution of obstacles in the plane, under the action of a uniform magnetic field, orthogonal to the plane. We show that, in a weak coupling limit, the particle distribution behaves…
Isotropic oscillator on a plane is discussed where both the coordinate and momentum space are considered to be noncommutative. We also discuss the symmetry properties of the oscillator for three separate cases when both the noncommutative…
We show that the uniform motion of a homogeneous distribution of electric charge can be stable or unstable depending on its geometry. When the electrodynamic body is perturbed from a state of rest, it starts to perform fast oscillations,…
We consider a modulated magnetic field, $B(t) = B_0 +\varepsilon f(\omega t)$, perpendicular to a fixed plane, where $B_0$ is constant, $\varepsilon>0$ and $f$ a periodic function on the torus ${\mathbb T}^n$. Our aim is to study classical…
Effect of dc electric field on transport of highly mobile 2D electrons is studied in wide GaAs single quantum wells placed in titled magnetic fields. The study shows that in perpendicular magnetic field resistance oscillates due to electric…
The field dependence of interlayer magnetoresistance of the pressurized (to the normal state) layered organic metal $\alpha $-(BEDT-TTF)$_{2}$KHg(SCN)$_{4}$ is investigated. The high quasi-two-dimensional anisotropy, when the interlayer…
We investigate the two-dimensional motion of relativistic cold electrons in the presence of `strictly' spatially varying magnetic fields satisfying, however, no magnetic monopole condition. We find that the degeneracy of Landau levels,…
The ordinary Landau problem consists of describing a charged particle in time-independent magnetic field. In the present case the problem is generalized onto time-dependent uniform electric fields with time-dependent mass and harmonic…
Free planar electrons in a uniform magnetic field are shown to possess the symmetry of area-preserving diffeomorphisms ($W$-infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on…
Landau theory is used to investigate the behaviour of a metallic magnet driven towards a quantum critical point by the application of pressure. The observed dependence of the transition temperature with pressure is used to show that the…
We construct an effective field theory, a two-dimensional two-component metallic system described by a model with two Fermi surfaces ("pockets"). This model describes a translationally invariant metallic system with two types of fermions,…
Quantum electrodynamics (QED) in a strong constant magnetic field is investigated from the viewpoint of its connection with noncommutative QED. It turns out that within the lowest Landau level (LLL) approximation the 1-loop contribution of…
The Landau problem is discussed in two similar but still different non-commutative frameworks. The ``standard'' one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The ``exotic''…
The linear response of two-dimensional electron gas in a perpendicular magnetic field in the presence of a spatially dependent classically smooth electrostatic potential is studied theoretically, by application of the Kubo formula for…
The problem of diamagnetism, solved by Landau, continues to pose fascinating issues which have relevance even today. These issues relate to inherent quantum nature of the problem, the role of boundary and dissipation, the meaning of…
We investigate the optical response of a conduction electron in a helically twisted mesoscopic medium containing a screw dislocation and a uniform torsional background, in the presence of an axial magnetic field and an Aharonov--Bohm flux.…
An effective Hamiltonian approach is used to study the effect of Landau-level mixing on the energy spectrum of electrons in a smooth but random magnetic field B(r) with a finite uniform component B_0. It is found that, as opposed to…