arXiv subjects
Publications and source records attributed to G. Auberson.
An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states.
We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e. depending on a (complete) commuting set of $N$ variables, are considered. A diagrammatic or graph theoretic formulation of the problem is developed. We then exactly determine the set of ``admissible'' data, i.e. those types of data for which the problem always admits solutions. This is done in the case where the joint distributions originate from quantum mechanics as well as in the case where this constraint is not imposed. In particular, it is shown that a necessary (but not sufficient) condition for the existence of solutions is $n\leq N+1$. When the data are admissible and the quantum constraint is not imposed, the general solution for the phase space density is determined explicitly. For admissible data of a quantum origin, the general solution is given in certain (but not all) cases. In the remaining cases, only a subset of solutions is obtained.
We address the classical and quantum marginal problems, namely the question of simultaneous realizability through a common probability density in phase space of a given set of compatible probability distributions. We consider only distributions authorized by quantum mechanics, i.e. those corresponding to complete commuting sets of observables. For four-dimensional phase space with position variables qi and momentum variables pj, we establish the two following points: i) given four compatible probabilities for (q1,q2), (q1,p2), (p1,q2) and (p1,p2), there does not always exist a positive phase space density rho({qi},{pj}) reproducing them as marginals; this settles a long standing conjecture; it is achieved by first deriving Bell-like inequalities in phase space which have their own theoretical and experimental interest. ii) given instead at most three compatible probabilities, there always exist an associated phase space density rho({qi},{pj}); the solution is not unique and its general form is worked out. These two points constitute our ``three marginal theorem''.
We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $ρ(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there exist quantum states for which more than three of the quantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and $(p_1,q_2)$ cannot be reproduced as marginals of a positive $ρ(\overrightarrow{q},\overrightarrow{p})$''. We also construct the most general positive $ρ(\overrightarrow{q},\overrightarrow{p})$ which reproduces any three of the above quantum probability densities for arbitrary quantum states. This is crucial for the construction of a maximally realistic quantum theory.
We prove that there is off-diagonal long-range order in the symmetrised version of the one-dimensional many-body problem presented by Jain and Khare (Phys. Lett. A262 (1999)35). This model is related to the short-range Dyson model employed to study intermediate statistics in systems like the Anderson model in three dimensions at the metal-insulator transition point and pseudointegrable billiards. To the best of our knowledge, this is the only example showing quantum phases and possibility of Bose-Einstein condensation in one-dimensional statistical mechanics.
Integrated forms of the one-loop evolution equations are given for the Yukawa couplings in the MSSM, valid for any value of $\tan β$, generalizable to virtually any number of Yukawa fermions, and including all gauge couplings. These forms turn out to have nice mathematical convergence properties which we prove, and we determine the ensuing convergence criteria. Furthermore, they allow to write down general sufficient and necessary conditions to avoid singularities in the evolution of the Yukawa couplings over physically relevant energy ranges. We also comment briefly on the possible use of these features for physics issues and give a short numerical illustration.