arXiv subjects

El Hassan El Kinani

Publications and source records attributed to El Hassan El Kinani.

4 recordsLinked to original sources

arXiv2022

Virtual excitations and quantum correlations in ultra-strongly coupled harmonic oscillators under intrinsic decoherence

We study the intrinsic decoherence of coupled harmonic oscillators. The Milburn master equation is solved exactly, and the dynamics of virtual ground state excitations are investigated. The interaction of quantum correlations and virtual excitation was then studied. The following is a summary of our major findings. (i) The damped oscillatory profile of all three quantities is the same. (ii) Ultra-strong coupling combined with huge anisotropy values results in the reemergence of entanglement and steering. (iii) To sustain entanglement and steering, virtual excitations are required. (iv) The quantum correlations are amplified in the quantum synchronous regime. (v) Ultra-strong couplings cause inherent decoherence to be avoided.

quant-ph↗

arXiv2012

Existence and Uniqueness of Solution to a Functional Integro-differential Fractional Equation

We prove, using a fixed point theorem in a Banach algebra, an existence result for a fractional functional differential equation in the Riemann-Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result are also derived.

math.CA↗

arXiv2003

Two Coupled Harmonic Oscillators on Non-commutative Plane

We investigate a system of two coupled harmonic oscillators on the non-commutative plane \RR^2_θ by requiring that the spatial coordinates do not commute. We show that the system can be diagonalized by a suitable transformation, i.e. a rotation with a mixing angle α. The obtained eigenstates as well as the eigenvalues depend on the non-commutativity parameter θ. Focusing on the ground state wave function before the transformation, we calculate the density matrix ρ_0(θ) and find that its traces {\rm Tr}(ρ_{0}(θ)) and {\rm Tr}(ρ_0^2(θ)) are not affected by the non-commutativity. Evaluating the Wigner function on \RR^2_θ confirms this. The uncertainty relation is explicitly determined and found to depend on θ. For small values of θ, the relation is shifted by a θ^2 term, which can be interpreted as a quantum correction. The calculated entropy does not change with respect to the normal case. We consider the limits α=1 and α={π\over 2}. In first case, by identifying θto the squared magnetic length, one can recover basic features of the Hall system.

hep-th↗

arXiv2000

Graded q-pseudo-differential Operators and Supersymmetric Algebras

We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra. With this scheme we also get a quantum superalgebra $U_{t}(sl(2/1)$.

hep-th↗