12,534 research outputs found
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
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