arXiv subjects
Publications and source records attributed to K. Toms.
In the framework of non-relativistic quantum mechanics we present a proposal for a gedunken experimental setup of a quantum system allowing information exchange. We discuss the compatibility of the procedure with a few no-go theorems.
In the framework of the Standard Model we present predictions for partial widths, double and single differential distributions, and forward--backward lepton asymmetries for four-leptonic decays $B^- \to μ^+μ^- {\bar ν}_e\, e^-$, $B^- \to e^+ e^- {\bar ν}_μ\,μ^-$, $B^- \to μ^+ μ^-{\bar ν}_μ\,μ^-$, and $B^- \to e^+ e^- {\bar ν}_e\, e^-$. We consider the contributions of virtual photon emission from the light and heavy quarks of the $B^-$--meson, and we include bremsstrahlung of a virtual photon from the charged lepton in the final state. We use the model of vector meson dominance for calculation of virtual photon emission by the light quark of the $B^-$--meson and take into account the isotopic correction.
We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for test of realism not only in quantum mechanical systems, but also in quantum field systems. Also we propose a mathematically consistent derivation of the Leggett--Garg inequality in Wigner form, which was recently presented in the literature, for three and $n$ distinct moments of time. Contrary to these works, our rigor derivation uses Kolmogorov axiomatics of probability theory. We pay special attention to the construction and studies of the spaces of elementary outcomes. Basing on the the Leggett--Garg inequality in Wigner form for $n$ distinct moments of time we prove that any unitary evolution of a quantum system contradicts the concept of macroscopic realism. We show that application of the concept of macroscopic realism to any quantum system leads to ``freezing'' of the system in the initial state. It is shown that for a particle with an infinite number of observables the probability to find a pair of the observables in some defined state is zero, even if the operators of these observables commute. This fact might serve as an additional logical argument for the contradiction between quantum theory and classical realism.
In this paper we propose a time-independent \textit{equality} and time-dependent \textit{inequality}, suitable for an experimental test of the hypothesis of realism. The derivation of these relations is based on the concept of conditional probability and on Bayes' theorem in the framework of Kolmogorov's axiomatics of probability theory. The equality obtained is intrinsically different from the well known GHZ-equality and its variants, because violation of the new equality might be tested in experiments with only two microsystems in a maximally entangled Bell state $\big\vert\, Ψ^-\,\big\rangle$, while a test of the GHZ-equality requires at least three quantum systems in a special state $\big\vert\, Ψ^{\textrm{GHZ}}\,\big\rangle$. The obtained inequality differs from Bell's, Wigner's, and Leggett-Garg inequalities, because it deals with spin $s=1/2$ projections onto only two non-parallel directions at two different moments of time, while a test of the Bell and Wigner inequalities requires at least three non-parallel directions, and a test of the Leggett-Garg inequalities -- at least three distinct moments of time. Hence, the proposed inequality seems to allow one to avoid the "contextuality loophole". Violation of the proposed equality and inequality is illustrated with the behaviour of a pair of anti-correlated spins in an external magnetic field and also with the oscillations of flavour-entangled pairs of neutral pseudoscalar mesons.
Recently a new class of time-dependent Bell inequalities in Wigner form was introduced. The structure of the inequalities allows experimental studies of quantum and open quantum systems in external fields. In this paper we study the properties of the time dependent Wigner inequalities using the time evolution of neutral pseudoscalar mesons. It is shown that it is always possible to find a range of parameters to test for violation in an experimentally accessible area. The effect of the relaxation of the inequalities for large time scales is demonstrated.
We derive a new 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.