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In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, the consistent deformed bosonic algebra at the non-perturbation level described by the deformed annihilation and creation…
This is my PhD thesis. In this thesis we study the gauge theories on noncommutative Moyal space. We find new static solitons and instantons in terms of the so called generalized Bose operators. Generalized Bose operators are constructed to…
We consider a charged particle moving in a two dimensional plane in the presence of a background magnetic field perpendicular to the plane, i.e. the Landau system in a phase-space where the coordinates and momenta both follow canonical…
We elaborate an approach to quantum fluctuations of angular momentum based on the diagonalization of the covariance matrix in two versions: real symmetric and complex Hermitian. At difference with previous approaches this is SU(2) invariant…
Inspired by a recent work that proposes using coherent states to evaluate the Feynman kernel in noncommutative space, we provide an independent formulation of the path-integral approach for quantum mechanics on the Moyal plane, with the…
As is well known, an external magnetic field in configuration space coupled to a quantum dynamics induces noncommutativity in its velocity momentum space. By phase space duality, an external vector potential in the conjugate momentum sector…
Equal-time commutators of different components of the energy-momentum tensor at spatially separated points are calculated for a relativistic quantum Fermi gas at finite temperature and density. Different definitions of such components, also…
We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus…
We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this…
The solution of the problem of describing the Friedmann observables (the Hubble law, the red shift, etc.) in quantum cosmology is proposed on the basis of the method of gaugeless Hamiltonian reduction in which the gravitational part of the…
A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $\theta $, we find an explicit…
Universality is a powerful concept that arises from the divergence of a characteristic length scale. For condensed matter systems, this length scale is typically the correlation length, which diverges at critical points separating two…
Molecular dynamics simulations are used to investigate the atomic mobility and diffusivity of a generalized Frenkel-Kontorova model which takes into account anharmonic (exponential) interaction of atoms subjected to a three-dimensional…
We generalize the Moyal equation, which describes the dynamics of quantum observables in phase space, to quantum systems coupled to a reservoir. It is shown that phase space observables become functionals of fluctuating noise forces…
We study random products of matrices in SL_2(C) from the point of view of holomorphic dynamics. For non-elementary measures with finite first moment we obtain the exponential convergence towards the stationary measure in Sobolev norm. As a…
We study partial derivatives on the product of two metric measure structures, in particular in connection with calculus via modules as proposed by the first named author. Our main results are 1) The extension to this non-smooth framework of…
We consider a quantum probe $P$ undergoing pure dephasing due to its interaction with a quantum system $S$. The dynamics of $P$ is then described by a well-defined sub-algebra of operators of $S,$ i.e. the "accessible" algebra on $S$ from…
We investigate the collective behavior of orbital angular momentum in the spin ferromagnetic state of a Mott insulator with $t_{2g}$ orbital degeneracy. The frustrated nature of the interactions leads to an infinite degeneracy of classical…
The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, with paying attention to the natural domains of these unbounded operators. The results are…
We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo-Riemannian manifolds enabled with…