Related papers: The Landau problem and noncommutative quantum mech…
We present a Jordan algebraic formulation of the non-commutative Landau problem coupled to a harmonic potential. To achieve this, an alternative formulation of the Hilbert space version of quantum mechanics is presented. Using this…
In the present contribution we investigate the Landau analog energy quantization for neutral particles, that possesses a nonzero permanent magnetic and electric dipole moments, in the presence of an homogeneous electric and magnetic…
In this work we investigate which radial field configuration yields bound states for neutral particles showing non-zero magnetic and electric dipole moments. The main result is that, in contrast with previous works, the Landau analog levels…
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''…
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 study the quantum mechanics of a charged particle on a constant curvature noncommutative Riemann surface in the presence of a constant magnetic field. We formulate the problem by considering quantum mechanics on the noncommutative AdS_2…
We point out the connection between the problem of formulating quantum mechanics in phase space and projecting the motion of a quantum mechanical particle onto a particular Landau level. In particular, we show that lowest Landau level wave…
Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and…
The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen-Olesen vortices are established. Firstly we show that the Landau problem with non-homogeneous…
Landau levels have represented a very rich field of research, which has gained widespread attention after their application to quantum Hall effect. In a particular gauge, the holomorphic gauge, they give a physical implementation of…
We consider quantum mechanics on the noncommutative spaces characterized by the commutation relations $$ [x_a, x_b] \ =\ i\theta f_{abc} x_c\,, $$ where $f_{abc}$ are the structure constants of a Lie algebra. We note that this problem can…
In this paper we discuss a Landau levels problem within the framework of noncommutative configuration space and phase space. We show that the associated energy levels are being shifted in terms of the noncommutative parameter and can be…
We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for…
It has been argued, that in noncommutative field theories sizes of physical objects cannot be taken smaller than an elementary length related to noncommutativity parameters. By gauge-covariantly extending field equations of noncommutative…
The quantum mechanical bound states of the $-{\alpha}/x^2$ potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
The comparison of the Hamiltonians of the noncommutative isotropic harmonic oscillator and Landau problem are analysed to study the specific conditions under which these two models are indistinguishable. The energy eigenvalues and…
The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their…
Triviality and Landau poles are often greeted as harbingers of new physics at 1 TeV. After briefly reviewing the ideas behind this, a model of singular quantum mechanics is introduced. Its ultraviolet structure, as well as some features of…
This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in…