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Atti rogati a Gressoney nei secoli XV e XVI. Regesti (dall'Archivio della famiglia di Nicola De La Pierre)
No full textDynamics of mean-field spin models from basic results in abstract differential equations
No full textThe infinite-volume limit of the dynamics of (generalized) mean-field spin models is obtained through a direct analysis of the equations of motion, in a large class of representations of the spin algebra. The resulting dynamics fits into a general framework for systems with long-range interaction: variables at infinity appear in the time evolution of local variables and spontaneous symmetry breaking with an energy gap follows from this mechanism. The independence of the construction of the approximation scheme in finite volume is proven. © 1992 Plenum Publishing Corporation
Quantum Mechanics and Stochastic Mechanics for Compatible Observables at Different Times
Full text linkBohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the
presence of noninteracting subsystems. In both cases, it is shown that correlations at different times of
compatible position observables on stationary states agree with quantum mechanics only in the case
of product wave functions. By appropriate Bell-like inequalities it is shown that no classical theory,
in particular no stochastic process, can reproduce the quantum mechanical correlations of position
variables of noninteracting systems at different times
Infrared and vacuum structure in two-dimensional local quantum field theory models. The massless scalar field
No full textInfrared and vacuum structure in two-dimensional models of local quantum field theory. II. Fermion bosonization
No full textQuantum corrections to the Wigner crystal: A Hartree-Fock expansion
No full textThe quantum corrections to the two-dimensional Wigner crystal, for filling ν≤1/3, are discussed by using a Hartree-Fock expansion based on wave functions which are (i) related to one another by magnetic translations, (ii) orthonormal, and (iii) strongly localized. Such wave functions are constructed in terms of Gaussians that are localized at the sites of a triangular (Wigner) lattice and have a small overlap c. The ground-state energy per particle is calculated by an expansion in ν and in δc1/4, which is rapidly convergent and stable under the thermodynamical limit. In particular, in this limit the cancellation of the infrared divergences occur order by order in the above expansion. The accurate control on the approximations allows a clear-cut comparison with the energy obtained by the Laughlin ansatz on the ground state and the numerical results confirm that the Wigner-crystal picture is energetically favored with respect to the Laughlin state for ν<1/9. © 1993 The American Physical Society
The extension problem for partial Boolean structures in quantum mechanics
No full textAlternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the "number of contexts," classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated. © 2010 American Institute of Physics
Bell inequalities as constraints on unmeasurable correlations
No full textThe interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations 〈Ai〉, 〈B〉, 〈AiB〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation 〈A1A2 〉 associated to different choices for B. The same analysis applies to the Hardy model and to the “perfect correlations ” discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality. 1 a
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