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In this paper we present exact solutions of the Dirac equation on the non-commutative plane in the presence of crossed electric and magnetic fields. In the standard commutative plane such a system is known to exhibit contraction of Landau levels when the electric field approaches a critical value. In the present case we find exact solutions in terms of the non-commutative parameters $eta$ (momentum non-commutativity) and $theta$ (coordinate non-commutativity) and provide an explicit expression for the Landau levels. We show that non-commutativity preserves the collapse of the spectrum. We provide a dual description of the system: (i) one in which at a given electric field the magnetic field is varied and the other (ii) in which at a given magnetic field the electric field is varied. In the former case we find that momentum non-commutativity ($eta$) splits the critical magnetic field into two critical fields while coordinates non-commutativity ($theta$) gives rise to two additional critical points not at all present in the commutative scenario.
We obtain solutions of the (2 + 1) dimensional k deformed Dirac equation in the presence of crossed magnetic and electric fields. It is shown that the k deformed Landau levels are modified in the presence of the electric field. Contraction of Landau
Quantum oscillations of nonlinear resistance are investigated in response to electric current and magnetic field applied perpendicular to single GaAs quantum wells with two populated subbands. At small magnetic fields current-induced oscillations app
The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed fields, which su
The longitudinal resistivity of two dimensional (2D) electrons placed in strong magnetic field is significantly reduced by applied electric field, an effect which is studied in a broad range of magnetic fields and temperatures in GaAs quantum wells w
Oscillations of dissipative resistance of two-dimensional electrons in GaAs quantum wells are observed in response to an electric current I and a strong magnetic field applied perpendicular to the two-dimensional systems. Period of the current-induce