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In this work, we study the existence of various classes of standing waves for a nonlinear Schr\"odinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state…

We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides a direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function…

The significance of the de Broglie-Bohm hidden-particle position in the relativistic regime is addressed, seeking connection to the (orthodox) single-particle Newton-Wigner position. The effect of non-positive excursions of the ensemble…

Formulas for calculating the joint probability of outcomes of measurements performed on mutually non-interacting component systems of a combined system prepared in an entangled state are presented. The formulas are based on non-relativistic…

We study local activity and its opposite, local passivity, for linear systems and show that generically an eigenvalue of the system matrix with positive real part implies local activity. If all state variables are port variables we prove…

A model for measurement in collapse-free nonrelativistic fermionic quantum field theory is presented. In addition to local propagation and effectively-local interactions, the model incorporates explicit representations of localized…

We explain how the so-called Einstein locality is to be understood in the Schr\"odinger picture of quantum mechanics. This notion is perfectly compatible with the Bell non-locality exhibited by entangled states. Contrary to some beliefs…

Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy…

Schr\"odinger-Pauli equation (SP-eq) derived from weakly relativistic approximation (WRA) of Dirac eq, combined with Electromagnetic (EM) field Lagrangian for variational principle, is expected to give a new level of EM response theory. A…

Error estimates are rigorously derived for a semi-discrete version of a conservative spectral method for approximating the space-homogeneous Fokker-Planck-Landau (FPL) equation associated to hard potentials. The analysis included shows that…

Based on total variance of a pair of Einstein-Podolsky-Rosen (EPR) type operators, the generalized EPR entangled states in continuous variable systems are defined. We show that such entangled states must correspond with two-mode squeezing…

Choosing four entangled stets to form an orthogonal and complete basis for a two-particle system, we argue that a local hidden variable model should give the probability of each entangled state if the two-particle system is described by a…

In the first part of this presentation (sections 2 to 6), I show that Bell's Inequalities provide a quantitative criterion to test "reasonable" Supplementary Parameters Theories versus Quantum Mechanics. Following Bell, I first explain the…

This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by W.Schmid in [Sch]. A corresponding problem in the compact group setting was solved by…

We analyse notion of independence in the EPR-Bohm framework by using comparative analysis of independence in conventional and frequency probability theories. Such an analysis is important to demonstrate that Bell's inequality was obtained…

Kallenberg (2005) provided a necessary and sufficient condition for the local finiteness of a jointly exchangeable random measure on $\R_+^2$. Here we note an additional condition that was missing in Kallenberg's theorem, but was implicitly…

While entanglement and violation of Bell inequalities were initially thought to be equivalent quantum phenomena, we now have different examples of entangled states whose correlations can be described by local hidden--variable models and,…

Construed as an argument against hidden variable theories, Bell's Theorem assumes that hidden variables would be independent of future measurement settings. This Independence Assumption (IA) is rarely questioned. Bell considered relaxing it…

EPR paper contains an error. Its correction leads to a conclusion that position and momentum of a particle can be defined precisely simultaneously, EPR paradox does not exist and uncertainty relations have nothing to do with quantum…

Starting from the late 60's many experiments have been performed to verify the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell's inequality is a consequence…