Related papers: Manifestly covariant classical correlation dynamic…
We consider a classical spinning particle in the frame of the relativistic physics by means of a covariant Hamiltonian and of a generalization of Poisson brackets which take into account the gauge fields. We obtain different equations of…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
We present the full diagonalization of a non-quadratic bosonic Liouvillian with a two-body loss term. The Liouvillian is shown to be exactly diagonalizable in terms of left and right confluent hypergeometric functions, whose distinction…
The invariance for the equation of fast diffusion in the 2D coordinate space has been proved, and its reduction to the 1D (with respect to the spatial variable) analog is demonstrated. On the basis of these results, new exact…
A fundamental theorem of Liouville asserts that positive entire harmonic functions in Euclidean spaces must be constant. A remarkable Liouville-type theorem of Caffarelli-Gidas-Spruck states that positive entire solutions of $-\Delta u=u^{…
We prove a generalization of the classical Poincar\'e--Birkhoff theorem for Liouville domains, in arbitrary even dimensions. This is inspired by the existence of global hypersurfaces of section for the spatial case of the restricted…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational…
We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, $D_{ab}=| \Phi_a…
The classical two-body system with Lorentz-invariant Coulomb interaction V=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stueckelberg. Particular solutions for the reduced motion are obtained…
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
Difficulties in founding microscopically the Vlasov equation for Coulomb-interacting particles are recalled for both the statistical approach (BBGKY hierarchy and Liouville equation on phase space) and the dynamical approach (single…
A possibility to represent the standard model of fundamental particles covariant derivatives by means of approximate generalized fractional Riemann-Liouville derivatives of multifractal time and space model is shown.
I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by…
The Liouville theorem states that classical time evolution is an incompressible flow in phase space. We investigate two formulations of classical mechanics in which this property is manifested. First, the traditional Hamilton-Jacobi theory…
The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common…
We rigorously show that the probability to have a specific trajectory of an externally perturbed classical open system satisfies a universal symmetry for Liouvillian reversible dynamics. It connects the ratio between the probabilities of…