Quantum systems as classical systems

A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in a random way with a statistical character. What kind of statistical theory is obtainable in this way? It is possible, for example, to obtain exactly the statistical previsions of quantum mechanics? Or, in other words, can a physical system showing a classical behaviour appear to be a quantum system to a confusing observer? We show that from a mathematical viewpoint it is not difficult to produce a theory with hidden variables having this property. We don't even try to justify in physical terms the artificial construction we propose; what we do is to give a general and rigorous argument showing how the interplay between the classical and quantum mechanics we offer is interpretable as the difference between an imaginary very expert observer and another nonexpert observer. This proves also that besides the well known theorems concerning the impossibility of hidden variables (cfr. Von Neumann [Neu] and Jauch-Piron [J-P]) there is also room for a result in favor of the possibility.Comment: late

Kinetic study of styrene/maleic anhydride copolymers using succine anhydride as the model compound

The reaction of aniline with succinic anhydride, a low molecular weight poly[styrene-co-(maleic anhydride)], and a high molecular weight poly[styreneco-( maleic anhydride)] were used to determine if these polymer reactions are diffusion- or reaction-controlled. Kinetic study protocols were developed to determine the rate constants for the succinic anhydride/aniline model reaction and for the 50/50 and 86/14 copolymers. These protocols were then used to gather kinetic data. The succinic anhydride/aniline reaction was determined to be exothermic and to have an induction period. The succinic anhydride/aniline reaction was also determined to have an experimental rate constant of 13 L/molmin 25% at 67 +/- 1.5 degrees Celsius. For the copolymer/aniline reactions, the experimental rate constants at 67 +/- 1.5 degrees Celsius were determined to be .051 L/molmin 15% for the 50/50 polymer and .008 L/molmin 18% for the 86/14 polymer. The model reaction was found to be 250 times faster than the 50/50 polymer/aniline reaction and 1600 times faster than the 86/14 polymer/aniline reaction. The 50/50 polymer/aniline reaction was determined to be 6 times faster than the 86/14 polymer/aniline reaction. At 20 1.5 degrees Celsius, the theoretical diffusion-controlled rate constant for the succinic anhydride/aniline reaction was determined to be 7.09 x 10^11 L/molmin and the experimental rate of reaction was determined to be 0.72 L/molmin 25%. Thus, these reactions were determined to be reaction-controlled

Electron density distribution in paramagnetic chromium A gamma ray diffraction study

High accuracy single crystal structure factors, complete up to sin amp; 61553; amp; 61548; amp; 61472; amp; 61501; amp; 61472; amp; 61489; amp; 61486; amp; 61495; amp; 61496; amp; 61472; amp; 61485; amp; 61489; amp; 61484; amp; 61472; have been measured from paramagnetic chromium at 333 K using 316.5 keV gamma radiation. A detailed description of the electron density distribution is derived in terms of a multipolar atomic deformation model. There is pronounced charge asphericity in the valence region arising from preferential occupancy of the t2g subshell. The 3d charge distribution is contracted by 12.6 relative to the free atom, in accordance with magnetic synchrotron x ray and neutron measurements. By contrast, the atomic crystal scattering factor deduced from experiment is found to be in contradiction with earlier experimental and theoretical work. Achievement of a reliable Debye Waller factor is of vital importance in this context. There is no evidence for an anharmonic term in the atomic potential. Real space and energetic features of the charge density topology are used to characterize the directed metallic bonds. Special attention is paid to the form factor approximation in diffraction data analysis

Reassessment of the electron density in Cu2O using gamma ray diffraction

The electron density distribution in Cu2O has been critically reexamined to test controversial conclusions from earlier experimental and theoretical studies. The electron density is derived via multipole refinement of high quality single crystal diffraction data, collected at room temperature with 316.5 keV gamma radiation. Four gamma lines in the energy range 200 600 keV have been used to extrapolate extinction free low order structure factors. The remaining extinction corrections refine to a crystal mosaicity identical to the observed one. There is no support for anharmonic contributions to the thermal parameters. Important features of the derived electron density are i a partially filled dz2 orbital, ii an incomplete ionization of Cu and O, iii no interstitial Cu Cu charge pileup, thereby refuting the covalent bonding hypothesi

Electron density distribution in paramagnetic chromium A gamma ray diffraction study

High accuracy single crystal structure factors, complete up to sin amp; 61553; amp; 61548; amp; 61472; amp; 61501; amp; 61472; amp; 61489; amp; 61486; amp; 61495; amp; 61496; amp; 61472; amp; 61485; amp; 61489; amp; 61484; amp; 61472; have been measured from paramagnetic chromium at 333 K using 316.5 keV gamma radiation. A detailed description of the electron density distribution is derived in terms of a multipolar atomic deformation model. There is pronounced charge asphericity in the valence region arising from preferential occupancy of the t2g subshell. The 3d charge distribution is contracted by 12.6 relative to the free atom, in accordance with magnetic synchrotron x ray and neutron measurements. By contrast, the atomic crystal scattering factor deduced from experiment is found to be in contradiction with earlier experimental and theoretical work. Achievement of a reliable Debye Waller factor is of vital importance in this context. There is no evidence for an anharmonic term in the atomic potential. Real space and energetic features of the charge density topology are used to characterize the directed metallic bonds. Special attention is paid to the form factor approximation in diffraction data analysis

Comment on `On the Quantum Theory of Molecules' [J. Chem.Phys. {\bf 137}, 22A544 (2012)]

In our previous paper [J. Chem.Phys. {\bf 137}, 22A544 (2012)] we argued that the Born-Oppenheimer approximation could not be based on an exact transformation of the molecular Schr\"{o}dinger equation. In this Comment we suggest that the fundamental reason for the approximate nature of the Born-Oppenheimer model is the lack of a complete set of functions for the electronic space, and the need to describe the continuous spectrum using spectral projection.Comment: 2 page

Construction of a Complete Set of States in Relativistic Scattering Theory

The space of physical states in relativistic scattering theory is constructed, using a rigorous version of the Dirac formalism, where the Hilbert space structure is extended to a Gel'fand triple. This extension enables the construction of ``a complete set of states'', the basic concept of the original Dirac formalism, also in the cases of unbounded operators and continuous spectra. We construct explicitly the Gel'fand triple and a complete set of ``plane waves'' -- momentum eigenstates -- using the group of space-time symmetries. This construction is used (in a separate article) to prove a generalization of the Coleman-Mandula theorem to higher dimension.Comment: 30 pages, Late

Probabilities from envariance?

Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's derivation it is argued that this claim is exaggerated if not wholly unjustified. In order to demonstrate that Born's rule arises noncircularly from deterministically evolving quantum states, it is not sufficient to assume that quantum states are somehow associated with probabilities and then prove that these probabilities are given by Born's rule. One has to show how irreducible probabilities can arise in the context of an ontological no-collapse interpretation of quantum states. It is argued that the reason why all attempts to do this have so far failed is that quantum states are fundamentally algorithms for computing correlations between possible measurement outcomes, rather than evolving ontological states.Comment: To appear in IJQI; 9 pages, LaTe

Triple Compton effect: A photon splitting into three upon collision with a free electron

The process in which a photon splits into three after the collision with a free electron (triple Compton effect) is the most basic process for the generation of a high-energy multi-particle entangled state composed out of elementary quanta. The cross section of the process is evaluated in two experimentally realizable situations, one employing gamma photons and stationary electrons, and the other using keV photons and GeV electrons of an x-ray free electron laser. For the first case, our calculation is in agreement with the only available measurement of the differential cross section for the process under study. Our estimates indicate that the process should be readily measurable also in the second case. We quantify the polarization entanglement in the final state by a recently proposed multi-particle entanglement measure.Comment: 5 pages; RevTeX; to be published in Phys.Rev.Let