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We show that there is a kind of quantum group symmetry $ sl_{q}(2) $ in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the…
We examine the behaviour of a charged particle in a two-dimensional confining potential, in the presence of a magnetic field. The confinement serves to remove the otherwise infinite degeneracy, but additional ingredients are required to…
Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate…
We numerically study Barrett-Crane models of Riemannian quantum gravity. We have extended the existing numerical techniques to handle q-deformed models and arbitrary space-time triangulations. We present and interpret expectation values of…
The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction…
We study orbital magnetism in a three-dimensional (3D) quantum dot with a parabolic confining potential. We calculate the free energy of the system as a function of the magnetic field and the temperature. By this, we show that the…
We cast the $q$-rotor in the framework of Barnett-Pegg theory for rotation angle, whose underlying algebra is $SU_q(2)$. A new method to fix the deformation parameter from the theory is suggested. We test our ideas by fitting rotational…
By applying a magnetic field perpendicular to GaAs/AlGaAs two-dimensional electron systems, we study the low-field Landau quantization when the thermal damping is reduced with decreasing the temperature. Magneto-oscillations following…
We study a system of spinless electrons moving in a two dimensional noncommutative space subject to a perpendicular magnetic field $\vec B$ and confined by a harmonic potential type ${1\over 2}mw_{0}r^2$. We look for the orbital magnetism…
In this paper we propose a symmetric q-deformed Tamm-Dancoff (S-TD) oscillator algebra and study its representation, coordinate realization, and main properties. In particular, the non-Fibonacci (more exactly, quasi-Fibonacci) nature of…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master…
It is shown that q-deformed quantum mechanics (q-deformed Heisenberg algebra) can be interpreted as quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first-) class constraints. (Saclay, T93/027).
We propose a q-deformed model of the anharmonic vibrations in diatomic molecules. We analyse the applicability of the model to the phenomenological Dunham's expansion by comparing with experimental data. Our methodology involves a global…
We report on the experimental observation of the quantum oscillations in microwave magnetoabsorption of a high-mobility two-dimensional electron gas induced by Landau quantization. Using original resonance-cavity technique, we observe two…
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated to a nonzero minimal uncertainty in position measurements, which is encoded in…
We consider a three-dimensional system where an electron moves under a constant magnetic field (in the z-direction) and a \textit{linear} electric field parallel to the magnetic field above the z=0 plane and anti-parallel below the plane.…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
Within the framework of the q-deformed Heisenberg algebra a dynamical equation of q-deformed quantum mechanics is discussed. The perturbative aspects of the q-deformed Schr\"odinger equation are analyzed. General representations of the…
Due to a special nature of the Landau problem, in which the magnetic field is uniformly spreading over the whole two-dimensional plane, there necessarily exist three conserved quantities, i.e. two conserved momenta and one conserved orbital…
We perturbatively study form factors in the Landau-Lifshitz model and the generalisation originating in the study of the N=4 super-Yang-Mills dilatation generator. In particular we study diagonal form factors which have previously been…