Related papers: A General Criterion of Quantum Integrability Accom…
Integrable structures arise in general relativity when the spacetime possesses a pair of commuting Killing vectors admitting 2-spaces orthogonal to the group orbits. The physical interpretation of such spacetimes depends on the norm of the…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen…
We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as introduced by Morales-Ruiz and Ramis. The…
Full set of autonomous completely solvable differential systems of equations in total differentials is built by basis of infinitesimal operators, universal invariant, and structure constants of admited multiparametric Lie group (abelian and…
Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n-1 symmetries polynomial in the canonical momenta, so that they are in…
Several recent studies have suggested that incompatible variables, which play an essential role in quantum mechanics (QM), are, somewhat surprisingly, not necessarily unique to QM. To investigate this possibility and obtain a better…
We re-examine results of the Liouville theory and provide arguments that a {\it negative} bare cosmological constant is essential to define two-dimensional quantum gravity. From this we are naturally led to a regularization of quantum…
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry…
It was generally believed throughout the 20-th century that irreversibility is a purely classical event without operator counterpart. However, a classical irreversible system cannot be consistently decomposed into a finite number of…
In ordinary Quantum Mechanics only ideally instantaneous observations of a quantity or a set of compatible quantities are usually considered. In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of…
We propose Bell inequalities for discrete or continuous quantum systems which test the compatibility of quantum physics with an interpretation in terms of deterministic hidden-variable theories. The wave function collapse that occurs in a…
A general and computable criterion for k-(in)separability in continuous multipartite quantum systems is presented. The criterion can be experimentally implemented with a finite and comparatively low number of local observables. We discuss…
A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum computers by using states preserved by evolution is presented. The concept of the dynamical symmetry is generalized from the level of classical Lie…
A basic principle of physics is the freedom to locally choose any unit system when describing physical quantities. Its implementation amounts to treating Weyl invariance as a fundamental symmetry of all physical theories. In this thesis, we…
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…
Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for…
We consider the quantum version of Arnold's generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any…
An exact invariant operator of time-dependent coupled oscillators is derived using the Liouville-von Neumann equation. The unitary relation between this invariant and the invariant of two uncoupled simple harmonic oscillators is…
Quantum entanglement is a foundational resource in quantum information science, underpinning applications across physics. However, detecting and quantifying entanglement remains a significant challenge. In this article, we introduce a…