相关论文: Causality and Localization Operators

The physical meaning and the geometrical interpretation of causality implementation in classical field theories are discussed. Local causality are kinematical constraints dynamically implemented via solutions of the field equations, but in…

We study the $H$-convergence of nonlocal linear operators in fractional divergence form, where the oscillations of the matrices are prescribed outside the reference domain. Our compactness argument bypasses the failure of the classical…

We propose and develop a new calculus for local variational differential operators. The main difference of the new formalism with the canonical differential calculus is that the image of higher order operators on local functionals does not…

We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of…

In their constructions of system of quantum stochastic differential equations, mathematicians and/or several physicists interpret that the function of random force operator is to preserve the canonical commutation relation in time, i.e., to…

We show that non-locality in the conservation of both the order parameter and a noncritical density (model D dynamics) leads to new fixed points for critical dynamics. Depending upon the parameters characterizing the non-locality in the two…

We investigate the solution to the logistic equation involving non-local operators in time. In the linear case such operators lead to the well-known theory of time changes. We provide the probabilistic representation for the non-linear…

The fluctuation theorem characterizes the distribution of the dissipation in nonequilibrium systems and proves that the average dissipation will be positive. For a large system with no external source of fluctuation, fluctuations in…

We consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…

We consider the reversible processes between two one-to-one correlated measurement outcomes which underly both problem-solving and quantum nonlocality. In the former case the two outcomes are the setting and the solution of the problem, in…

Although quantum mechanics is a very successful theory, its foundations are still a subject of intense debate. One of the main problems is the fact that quantum mechanics is based on abstract mathematical axioms, rather than on physical…

Exchangeability -- in which the distribution of an infinite sequence is invariant to reorderings of its elements -- implies the existence of a simple conditional independence structure that may be leveraged in the design of statistical…

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…

In the study of the Doppler Effect, non-locality is not taken into account. We present two cases in which a continuous change in the receiver's speed and in the angle at which the successive wavecrests are received takes place. In each case…

We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. Our construction is an improvement over the so-called phase…

It is always stated that the position operator for massless particles has non-comutting components. It is shown that the reason is that the commutation relations between coordinates and momenta differs for massive and massless particles.…

If a physical system contains a single particle, and if two distant detectors test the presence of linear superpositions of one-particle and vacuum states, a violation of classical locality can occur. It is due to the creation of a…

We investigate whether commutativity is necessary to represent relativistic locality for localization observables of relativistic quantum systems in Minkowski spacetime. A well known no-go theorem by Halvorson and Clifton shows that…

We are concerned with solvability of a non-potential system involving two relativistic operators, subject to boundary conditions expressed in terms of maximal monotone operators. The approach makes use of a fixed point formulation and…

The controversy between relativistic causality and quantum non-locality can be resolved by establishing the general relativistic background of quantum non-locality.