We derive a class of time-dependent Bell inequalities in Wigner form under the assumption of locality in the framework of Kolmogorov's probability theory. We consider violation of the obtained inequalities for three cases: spin correlations in an external magnetic field, oscillations of neutral pseudoscalar mesons, and decays of a pseudoscalar into a fermion-antifermion pair.

arXiv:1408.6023Physical Review AOct 31, 20148 citations

On the quantum mechanical scattering from a potential step

Victor F. Los, Andrei V. Los

Journal of Physics A Mathematical and TheoreticalJan 14, 201012 citations

arXiv:hep-th/0302042 · Physics Letters A

Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional spacetime

Antonio S. de Castro

Published Mar 1, 2003• 19 citations

arXiv HTML PDF

DOI: 10.1016/s0375-9601(03)00294-9

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The problem of finding the exact spacetime particle's propagator in the presence of a potential step (interface between different materials) is revisited. In contrast to the conventional Feynman path-integral approach, integration over all energy values of the particle's spectral density matrix (discontinuity of the energy-dependent Green's function across the real energy axis) is suggested for obtaining the exact spacetime propagator. The energy-dependent Green's functions are found in the framework of the multiple scattering theory (MST). The problem of finding the step-localized energy-dependent potentials responsible for the particle's reflection from and transmission through a potential step, which are needed for MST application, is solved. The obtained exact result for the particle's propagator is expressed in terms of integrals of elementary functions and has a significantly simpler form than that reported earlier. The obtained expressions allow easy evaluation of all limiting cases, including the case of the infinitely large potential step, as well as simple numerical visualization. The square of the absolute value of the propagator, which represents the relative transition probability density between two spacetime points, is plotted and discussed in detail for the cases of particle reflection and transmission.The problem of finding the exact spacetime particle's propagator in the presence of a potential step (interface between different materials) is revisited. In contrast to the conventional Feynman path-integral approach, integration over all energy values of the particle's spectral density matrix (discontinuity of the energy-dependent Green's function across the real energy axis) is suggested for obtaining the exact spacetime propagator. The energy-dependent Green's functions are found in the framework of the multiple scattering theory (MST). The problem of finding the step-localized energy-dependent potentials responsible for the particle's reflection from and transmission through a potential step, which are needed for MST application, is solved. The obtained exact result for the particle's propagator is expressed in terms of integrals of elementary functions and has a significantly simpler form than that reported earlier. The obtained expressions allow easy evaluation of all limiting cases, including the case of the infinitely large potential step, as well as simple numerical visualization. The square of the absolute value of the propagator, which represents the relative transition probability density between two spacetime points, is plotted and discussed in detail for the cases of particle reflection and transmission.

Journal of Physics A Mathematical and TheoreticalJan 14, 201012 citations

N_x=54

lattice sites and up to

20

time steps. Spacetime correlation functions were computed on IBM's quantum computers, using

109

qubits with

10,806

CZ gates applied, reaching a two-qubit gate depth of

246

. We demonstrate how to study bound states and extract scattering amplitudes from these correlation functions.