Related papers: On the relation between the anyon and Calogero mod…
We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD) symmetry generators, with special emphasis on complex…
In the framework of a geometrical model, in which the affine connection of a space is expressed in terms of the electromagnetic field, a possibility of the momentum non-conservation is shown. A toy device with an object moving in a magnetic…
We study Galileon scalar field model by considering the lowest order Galileon term in the lagrangian, $(\partial_{\mu} \phi)^2 \Box\phi$ by invoking a field potential. We use Statefinder hierarchy to distinguish the light mass galileon…
The $l_2$ flattening lemma of Johnson and Lindenstrauss [JL84] is a powerful tool for dimension reduction. It has been conjectured that the target dimension bounds can be refined and bounded in terms of the intrinsic dimensionality of the…
Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the…
We prove variationally that at weak coupling in one, two, and three dimensions there exist correlated electron-phonon states below the approximate ground states characteristically found by adiabatic polaron theory. Besides differing…
We study the dimensional crossover of weak localization in strongly anisotropic systems. This crossover from three-dimensional behavior to an effective lower dimensional system is triggered by increasing temperature if the phase coherence…
We investigated some influences of unconventional physics, such Lorentz-symmetry violation, for quantum mechanical systems. In this context, we calculated a important contribution for Standard Model Extension. In the non-relativistic limit,…
The Landau-Lifshitz-Gilbert (LLG) equation that describes the dynamics of a macroscopic magnetic moment finds its limit of validity at very short times. The reason for this limit is well understood in terms of separation of the…
In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…
To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level…
This thesis is a theoretical analysis of sample two- and one-dimensional systems. The two-dimensional examples are the quantum Hall liquid and anomalous paired states. The most widely accepted effective theory of the quantum Hall liquid is…
We review a growing theoretical motivation and evidence that the number of dimensions actually reduces at high energies. This reduction can happen near the Planck scale, or much before, the dimensions that are reduced can be effective,…
The divergence in the interaction term of the Calogero model can be prevented introducing a cutoff length parameter, this modification leads to a quasi-exactly solvable model whose eigenfunctions can be written in terms of Heun's…
We consider Coulomb drag between two layers of two-dimensional electron gases subject to a strong magnetic field, with the Landau level filling factor in each layer being 1/2. We find $\rho_D$ to be very large, as compared to the zero…
We present a simple discussion of the appearance of light-front partons in local field theory.The description in terms of partons provides a dimensional reduction which relates a 2+1 with a 3+1 dimensional theory for example. The…
A Green's-function theory of antiferromagnetic short-range and long-range order (LRO) in the $S=1/2$ quasi-two-dimensional easy-plane XXZ model is presented. As the main new result, {\it two} phase transitions due to the combined influence…
Two-dimensional abelian anyons are, in the magnetic gauge picture, represented as fermions coupled to magnetic flux tubes. For the ground state of such a system in a trapping potential, we theoretically and numerically investigate a Hartree…
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes…
In the traditional Kaluza-Klein theory, the cylinder condition and the constancy of the extra-dimensional radius (scalar field) imply that timelike geodesics on the 5-dimensional bundle project to solutions of the Lorentz force equation on…