相关论文: Variations on the Planar Landau Problem: Canonical…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…
In the present paper the linearized problem of half-space plasma oscillations in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the plasma…
Landau levels are the eigenstates of a charged particle in two dimensions under a magnetic field, and are at the heart of the integer and fractional quantum Hall effects, which are two prototypical phenomena showing topological features.…
The problem of a single electron in a magnetic field is revisited from first principles. It is shown that the standard quantization, used by Landau, is inconsistent for this problem, whence Landau's wave functions spontaneously break the…
At even-denominator Landau level filling fractions, such as $\nu=1/2$, the ground state, in most cases, has no energy gap, and there is no quantized plateau in the Hall conductance. Nevertheless, the states exhibit non-trivial low-energy…
Here we prove that the classical (respectively, quantum) system, consisting of a particle moving in a static electromagnetic field, is canonically (respectively, unitarily) equivalent to a harmonic oscillator perturbed by a spatially…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
In this contribution we study the Landau levels arising within the relativistic quantum dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field. We consider the…
This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the…
A canonical transformation of a new type is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum…
We show that the Landau quantum systems (or integer quantum Hall effect systems) in a plane, sphere or a hyperboloid, can be explained in a complete meaningful way from group-theoretical considerations concerning the symmetry group of the…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and…
The conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories is explored. If the potential in noncommutative quantum mechanics is chosen as $V= \Omega \aleph$ with $\aleph$ defined in the text,…
The quest for universal signatures of topological phases is fundamentally important since these properties are robust to variations in system-specific details. Here we present general results for the response of quantum Hall states to…
Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the…
In this paper we study the Landau levels in the non-relativistic dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field in the curved spacetime background with the…
We discuss a novel form of the variational approach in Quantum Field Theory in which the trial quantum configuration is represented directly in terms of relevant expectation values rather than, e.g., increasingly complicated structure from…
We study a regularized version of the Landau equation, which was recently introduced in~\cite{CHWW20} to numerically approximate the Landau equation with good accuracy at reasonable computational cost. We develop the existence and…