Scalar differential invariants of symplectic Monge–Ampère equations

All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère PDEs with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. A series of invariant differential forms and vector fields are also introduced: they allow one to construct numerous scalar differential invariants of higher order. The introduced invariants give a solution to the symplectic equivalence problem for Monge-Ampère equations

Second Order Inductive Logic and Wilmers' Principle

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity

On convergence-sensitive bisimulation and the embedding of CCS in timed CCS

We propose a notion of convergence-sensitive bisimulation that is built just over the notions of (internal) reduction and of (static) context. In the framework of timed CCS, we characterise this notion of `contextual' bisimulation via the usual labelled transition system. We also remark that it provides a suitable semantic framework for a fully abstract embedding of untimed processes into timed ones. Finally, we show that the notion can be refined to include sensitivity to divergence

Maximum-likelihood method in quantum estimation

The maximum-likelihood method for quantum estimation is reviewed and applied to the reconstruction of density matrix of spin and radiation as well as to the determination of several parameters of interest in quantum optics.Comment: 12 pages, 4 figure

Non-divisibility vs backflow of information in understanding revivals of quantum correlations for continuous-variable systems interacting with fluctuating environments

We address the dynamics of quantum correlations for a bipartite continuous-variable quantum system interacting with its fluctuating environment. In particular, we consider two independent quantum oscillators initially prepared in a Gaussian state, e.g. a squeezed thermal state, and compare the dynamics resulting from local noise, i.e. oscillators coupled to two independent external fields, to that originating from common noise, i.e. oscillators interacting with a single common field. We prove non-Markovianity (non-divisibility) of the dynamics in both regimes and analyze the connections between non-divisibility, backflow of information and revivals of quantum correlations. Our main results may be summarized as follows: (i) revivals of quantumness are present in both scenarios, however, the interaction with a common environment better preserves the quantum features of the system; (ii) the dynamics is always non-divisible but revivals of quantum correlations are present only when backflow of information is present as well. We conclude that non-divisibility in its own is not a resource to preserve quantum correlations in our system, i.e. it is not sufficient to observe recoherence phenomena. Rather, it represents a necessary prerequisite to obtain backflow of information, which is the true ingredient to obtain revivals of quantumness