The mystery of relationship of mechanics and field in the many-body quantum world

We have revealed three fatal errors incurred from a blind transferring of quantum field methods into the quantum mechanics. This had tragic consequences because it produced crippled model Hamiltonians, unfortunately considered sufficient for a description of solids including superconductors. From there, of course, Fr\"ohlich derived wrong effective Hamiltonian, from which incorrect BCS theory arose. 1) Mechanical and field patterns cannot be mixed. Instead of field methods applied to the mechanical Born-Oppenheimer approximation we have entirely to avoid it and construct an independent and standalone field pattern. This leads to a new form of the Bohr's complementarity on the level of composite systems. 2) We have correctly to deal with the center of gravity, which is under the field pattern "materialized" in the form of new quasipartiles - rotons and translons. This leads to a new type of relativity of internal and external degrees of freedom and one-particle way of bypassing degeneracies (gap formation). 3) The possible symmetry cannot be apriori loaded but has to be aposteriori obtained as a solution of field equations, formulated in a general form without translational or any other symmetry. This leads to an utterly revised view of symmetry breaking in non-adiabatic systems, namely Jahn-Teller effect and superconductivity. These two phenomena are synonyms and share a unique symmetry breaking.Comment: 24 pages, 9 sections; remake of abstract, introduction and conclusion; more physics, less philosoph

The Hypothesis of Locality and its Limitations

The hypothesis of locality, its origin and consequences are discussed. This supposition is necessary for establishing the local spacetime frame of accelerated observers; in this connection, the measurement of length in a rotating system is considered in detail. Various limitations of the hypothesis of locality are examined.Comment: LaTeX file, no figures, 14 pages, to appear in: "Relativity in Rotating Frames", edited by G. Rizzi and M.L. Ruggiero (Kluwer Academic Publishers, Dordrecht, 2003

Translational outcomes in a full gene deletion of ubiquitin protein ligase E3A rat model of Angelman syndrome.

Angelman syndrome (AS) is a rare neurodevelopmental disorder characterized by developmental delay, impaired communication, motor deficits and ataxia, intellectual disabilities, microcephaly, and seizures. The genetic cause of AS is the loss of expression of UBE3A (ubiquitin protein ligase E6-AP) in the brain, typically due to a deletion of the maternal 15q11-q13 region. Previous studies have been performed using a mouse model with a deletion of a single exon of Ube3a. Since three splice variants of Ube3a exist, this has led to a lack of consistent reports and the theory that perhaps not all mouse studies were assessing the effects of an absence of all functional UBE3A. Herein, we report the generation and functional characterization of a novel model of Angelman syndrome by deleting the entire Ube3a gene in the rat. We validated that this resulted in the first comprehensive gene deletion rodent model. Ultrasonic vocalizations from newborn Ube3am-/p+ were reduced in the maternal inherited deletion group with no observable change in the Ube3am+/p- paternal transmission cohort. We also discovered Ube3am-/p+ exhibited delayed reflex development, motor deficits in rearing and fine motor skills, aberrant social communication, and impaired touchscreen learning and memory in young adults. These behavioral deficits were large in effect size and easily apparent in the larger rodent species. Low social communication was detected using a playback task that is unique to rats. Structural imaging illustrated decreased brain volume in Ube3am-/p+ and a variety of intriguing neuroanatomical phenotypes while Ube3am+/p- did not exhibit altered neuroanatomy. Our report identifies, for the first time, unique AS relevant functional phenotypes and anatomical markers as preclinical outcomes to test various strategies for gene and molecular therapies in AS

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Centre-of-mass separation in quantum mechanics: Implications for the many-body treatment in quantum chemistry and solid state physics

We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the electron-vibrational Hamiltonian is fundamentally inconsistent with the Born-Handy ansatz so that such a treatment can never respect the COM problem. Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case where the degrees of freedom can be treated in a classical way. Beyond the B-O approximation they are inseparable in principle. The unique covariant description of all equations with respect to individual degrees of freedom leads to new types of interaction: besides the known vibronic (electron-phonon) one the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that due to the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is justified only in the adiabatic systems. This fact calls for the total revision of our contemporary knowledge of all non-adiabatic effects, especially the Jahn-Teller effect and superconductivity. The vibronic coupling is responsible only for removing of electron (quasi)degeneracies but for the explanation of symmetry breaking and forming of structure the rotonic and translonic coupling is necessary.Comment: 39 pages, 11 sections, 3 appendice

Voltage-programmable liquid optical interface

Recently, there has been intense interest in photonic devices based on microfluidics, including displays and refractive tunable microlenses and optical beamsteerers, that work using the principle of electrowetting. Here, we report a novel approach to optical devices in which static wrinkles are produced at the surface of a thin film of oil as a result of dielectrophoretic forces. We have demonstrated this voltage-programmable surface wrinkling effect in periodic devices with pitch lengths of between 20 and 240 µm and with response times of less than 40 µs. By a careful choice of oils, it is possible to optimize either for high-amplitude sinusoidal wrinkles at micrometre-scale pitches or more complex non-sinusoidal profiles with higher Fourier components at longer pitches. This opens up the possibility of developing rapidly responsive voltage-programmable, polarization-insensitive transmission and reflection diffraction devices and arbitrary surface profile optical devices

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...Comment: 51 single column pages, 19 postscript figures, 2 tables, GRG tex style; minor corrections added; final version appearing in General Relativity and Gravitatio

The Potential Energy Surface in Molecular Quantum Mechanics

The idea of a Potential Energy Surface (PES) forms the basis of almost all accounts of the mechanisms of chemical reactions, and much of theoretical molecular spectroscopy. It is assumed that, in principle, the PES can be calculated by means of clamped-nuclei electronic structure calculations based upon the Schr\"{o}dinger Coulomb Hamiltonian. This article is devoted to a discussion of the origin of the idea, its development in the context of the Old Quantum Theory, and its present status in the quantum mechanics of molecules. It is argued that its present status must be regarded as uncertain.Comment: 18 pages, Proceedings of QSCP-XVII, Turku, Finland 201

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Coulomb Interactions between Cytoplasmic Electric Fields and Phosphorylated Messenger Proteins Optimize Information Flow in Cells

Normal cell function requires timely and accurate transmission of information from receptors on the cell membrane (CM) to the nucleus. Movement of messenger proteins in the cytoplasm is thought to be dependent on random walk. However, Brownian motion will disperse messenger proteins throughout the cytosol resulting in slow and highly variable transit times. We propose that a critical component of information transfer is an intracellular electric field generated by distribution of charge on the nuclear membrane (NM). While the latter has been demonstrated experimentally for decades, the role of the consequent electric field has been assumed to be minimal due to a Debye length of about 1 nanometer that results from screening by intracellular Cl- and K+. We propose inclusion of these inorganic ions in the Debye-Huckel equation is incorrect because nuclear pores allow transit through the membrane at a rate far faster than the time to thermodynamic equilibrium. In our model, only the charged, mobile messenger proteins contribute to the Debye length.Using this revised model and published data, we estimate the NM possesses a Debye-Huckel length of a few microns and find this is consistent with recent measurement using intracellular nano-voltmeters. We demonstrate the field will accelerate isolated messenger proteins toward the nucleus through Coulomb interactions with negative charges added by phosphorylation. We calculate transit times as short as 0.01 sec. When large numbers of phosphorylated messenger proteins are generated by increasing concentrations of extracellular ligands, we demonstrate they generate a self-screening environment that regionally attenuates the cytoplasmic field, slowing movement but permitting greater cross talk among pathways. Preliminary experimental results with phosphorylated RAF are consistent with model predictions.This work demonstrates that previously unrecognized Coulomb interactions between phosphorylated messenger proteins and intracellular electric fields will optimize information transfer from the CM to the NM in cells