92 citations · 269 across the 28 of their papers we have counts for
6 papers · 2 filters
Highlights of Symmetry Groups
Giampiero Esposito, Giuseppe Marmo
The concepts of symmetry and symmetry groups are at the heart of several developments in modern theoretical and mathematical physics. The present paper is devoted to a number of se…
Geometry of quantum systems: density states and entanglement
Janusz Grabowski, Marek Kuś, Giuseppe Marmo
Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Ri…
Quantum Bi-Hamiltonian systems, alternative Hermitian structures and Bi-Unitary transformations
G. Marmo, G. Scolarici, A. Simoni +1
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space.…
Classical and Quantum Systems: Alternative Hamiltonian Descriptions
G. Marmo, G. Scolarici, A. Simoni +1
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible He…
Reduction and Unfolding for Quantum Systems: the Hydrogen Atom
A. D'Avanzo, G. Marmo, A. Valentino
In this paper we propose a ``quantum reduction procedure'' based on the reduction of algebras of differential operators on a manifold. We use these techniques to show, in a systema…
Alternative structures and bi-Hamiltonian systems on a Hilbert space
G. Marmo, G. Scolarici, A. Simoni +1
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional compl…