A Solvable N-body Problem of Goldfish Type Featuring N2 Arbitrary Coupling Constants

A N-body problem “of goldfish type” is introduced, the Newtonian (“acceleration equal force”) equations of motion of which describe the motion of N pointlike unit-mass particles moving in the complex z-plane. The model—for arbitrary N—is solvable, namely its configuration (positions and velocities of the N “particles”) at any later time t can be obtained from its configuration at the initial time by algebraic operations. It features specific nonlinear velocity-dependent many-body forces depending on N² arbitrary (complex) coupling constants. Sufficient conditions on these constants are identified which cause the model to be isochronous—so that all its solutions are then periodic with a fixed period independent of the initial data. A variant with twice as many arbitrary coupling constants, or even more, is also identified.     

19—20世纪之交电磁学的发展和影响（Ⅰ）

主要围绕电磁学的“两论两发现”讨论了上一世纪之交电磁学的发展和影响。“两论“是指洛伦兹电子论和爱因斯坦相对论电磁学,“两发现”是指X射线的发现和电子的发现,第一部分着重分析了洛伦兹电子论如何从综合超距电动力学和“无源”电磁场理论中产生的历史背景及其地位、作用和历史局限,第二部分重点讨论了爱因斯坦对经典电磁学的革命性变革、光量子假说、相对论电磁学和质能关系的意义及影响,第三和第四部分,则主要讨论X射线和电子的发现,及其发现后的电磁学的一些重要实验和电子论对一些重要电磁学问题的解释,强调了波粒二象性论争及其积极作用,并阐述了电子论对物质磁性的经典分析,文章的时间范围主要是从洛伦兹电子论到量子力学诞生之前的二三十年,尚水涉及量子电动力学的内容。     

Uplifting the Iwasawa

The Iwasawa manifold is uplifted to seven‐folds of either G₂ holonomy or SU(3) structure, explicit new metrics for the same having been constructed in this work. We uplift the Iwasawa manifold to a G₂ manifold through “size” deformation (of the Iwasawa metric), via Hitchin's Flow equations, showing also the impossibility of the uplift for “shape” and “size” deformations (of the Iwasawa metric). Using results of Dall'Agata and Prezas, Phys. Rev. D 69 , 066004 (2004) [arXiv:hep‐th/0311146] [1], we also uplift the Iwasawa manifold to a 7‐fold with SU(3) structure through “size” and “shape” deformations via generalisation of Hitchin's Flow equations. For seven‐folds with SU(3)‐structure, the result could be interpreted as M5‐branes wrapping two‐cycles embedded in the seven‐fold (as in [1]) ‐ a warped product of either a special hermitian six‐fold or a balanced six‐fold with the unit interval. There can be no uplift to seven‐folds of SU(3) structure involving non‐trivial “size” and “shape” deformations (of the Iwasawa metric) retaining the “standard complex structure” ‐ the uplift generically makes one move in the space of almost complex structures such that one is neither at the standard complex structure point nor at the “edge”. Using the results of Konopelchenko and Landolfi, J. Geom. Phys. 29 , 319 (1999) [arXiv:math.DG/9804144] [2], we show that given two “shape deformation” functions, and the dilaton, one can construct a Riemann surface obtained via Weierstraß representation for the conformal immersion of a surface in R ^l, for a suitable l, with the condition of having conformal immersion being a quadric in CP ^l‐1.     

Meeting Report: Soft-X-ray Photon-in and Photon-out Spectroscopy: New Frontier

Immediately before Johann Wolfgang von Goethe died in 1832, he asked for “more light, open the (window) shutters!” The desire for “more light, open the (beam) shutters!” accompanied me from 1962 on during all my professional life, although the first opening of our beam shutter at the 6 GeV-Synchrotron DESY in Hamburg in 1965 ended in a catastrophe: instead of flooding us with synchrotron light, we were flooding the accelerator completely with air. This was long before 1987, when Synchrotron Radiation News came to life, but a personal view on the development of synchrotron radiation, which the editors of SRN asked me to give, cannot avoid looking back into history, where it all came from.     

On the oscillations of the plasma atmosphere in gamma-ray bursts

One of the possible hypotheses implies that cosmic gamma-ray bursts can arise when two neutron stars or black holes merge together. These bursts sometimes continue for several tens of seconds, but the time dependence of their intensity often exhibits ～10²–10³ almost periodic small peaks with a period of ～10 ms. A model of oscillations in the lower plasma shell, which arises in cosmic gamma-ray bursts and is located near a neutron star, is proposed; the greater part of arising plasma in the form of an “upper” shell continues to expand into the surroundings. Other possible interpretations of periodicity of the “small peaks” are also analyzed.     

Calculations of the Overtone Transitions Of Sh− Pairs In KCl

In this work all vibration transitions up to the second overtone of pair SH^? molecules in KCl were calculated. The interaction of the identical molecules, which are characterized by “exact” resonance (equal pairs “SH^?—”SH^?, n = 32,33,34,36) were researched. The unequal molecular ions—“inexact” interaction (unequal pairs, “SH^?—^kSH^?, n≠ k, n, k = 32,33,34,36) were also considered. In both cases the problem was to find the eigenvalues of the matrix of dipole—dipole interaction that conforms to the solution of a secular equation. The elements of the dipole—dipole matrix were calculated in terms of the mechanical anharmonicity. It was supposed that the function of the dipole moment has linear dependence on the vibrational coordinate. The conditions of “exact” resonance and the conditions of “inexact” resonance diverged considerably. In the case of the “exact” resonance we used the orthogonal transformation of the dipole-dipole matrix and obtained a precise solution. In case of the “inexact” resonance we used the method of successive diagonalization. The intensities of the pair lines were calculated as well.     

Mössbauer studies of hemoglobin in high altitude polycythemia

The Mössbauer spectra have been measured in erythrocytes from normal adults and the patients with high altitude polycythemia (HAPC). The results indicated that two subspectra “a” and “b”, corresponding to oxy- and deoxyhemoglobin respectively, were present in all blood samples, and a third subspectrum “c” was found to exist in almost all samples from the patients. The parameters of the third subspectra “cl” in most samples from the patients were similar to those of carbon monoxyhemoglobin. The components were considered to be the denatured hemoglobin in RBCs (red blood cells). Together with clinical analysis, a possible mechanism of HAPC has been discussed.     

Voraussetzungen für die Isotopen-Forschung: Grundlegende Entdeckungen in der Physik vor hundert Jahren

Abstract

Reviewed is the transition period in the history of physics between 1895 and 1905, a decade which began 100 years ago and which is characterized by high scientific activity and creativity with significant results for the further development of natural science. A great number of outstanding scientists, especially physicists, worked in this period. Their important discoveries manifest the beginning of the history of isotopic research.     

Solvable and/or Integrable and/or Linearizable N-Body Problems in Ordinary (Three-Dimensional) Space. I

Abstract

Several N -body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (“acceleration equal force;” in most cases, the forces are velocity-dependent) and are amenable to exact treatment (“solvable” and/or “integrable” and/or “linearizable”). These equations of motion are always rotation-invariant, and sometimes translation-invariant as well. In many cases they are Hamiltonian, but the discussion of this aspect is postponed to a subsequent paper. We consider “few-body problems” (with, say, N =1,2,3,4,6,8,12,16,...) as well as “many-body problems” (N an arbitrary positive integer). The main focus of this paper is on various techniques to uncover such N -body problems. We do not discuss the detailed behavior of the solutions of all these problems, but we do identify several models whose motions are completely periodic or multiply periodic, and we exhibit in rather explicit form the solutions in some cases.     

Duality Covariant Formulation of Extended Supergravity: Central Charges,BPS States and Black-Hole Entropy

In these lectures we give a geometrical formulation of N-extrended supergravities which generalizes N = 2 special geometry of N = 2 theories. In all these theories duality symmetries are related to the notion of “flat symplectic bundles” and central charges may be defined as “sections” over these bundles. Attractor points giving rise to “fixed scalars” of the horizon geometry and Bekenstein-Hawking entropy formula for extremal black-holes are discussed in some details.     

Quantum bit threads of MERA tensor network in large c limit

The Ryu-Takayanagi (RT) formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena. The recent reinterpretation of this formula in terms of a set of “bit threads” is an interesting effort in understanding holography. In this study, we investigate a quantum generalization of the “bit threads” based on a tensor network, with particular focus on the multi-scale entanglement renormalization ansatz (MERA). We demonstrate that, in the large c limit, isometries of the MERA can be regarded as “sources” (or “sinks”) of the information flow, which extensively modifies the original picture of bit threads by introducing a new variable ρ: density of the isometries. In this modified picture of information flow, the isometries can be viewed as generators of the flow. The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture. The large c limit implies that classical gravity can emerge from the information flow.     

Observation of Filamentary Structures on the Boundary Region of the LHD Stellarator

Large Helical Device (LHD) high β regime discharges are observed with a fast camera, with 〈β 〉 values up to almost 5%. High frequency sequences (20 µs between shots) of the density fluctuations in the edge region are obtained. Macroscopic coherent scructures, in the shape of “comet”‐like filaments can be seen in these sequences, propagating from the external ergodic region to the wall. These structures are analyzed and their radial and parallel transport is discussed. Strong relation between the generation of low frequency particle ejections and m/n= 2/3 edge mode is found. In the strike point region, “reflected” structures are observed as a response to ejected filaments. These are discussed in terms of plasma wall interaction phenomena (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Hausdorff dimension of some fractals and attractors of overlapping construction

We introduce a method to show that the Hausdorff dimension of certain fractals of overlapping construction is “almost always” what would be observed if no overlapping occurred. The method is also used to examine the dimension of attractors in some noninjective, piecewise linear, “baker's”-type transformations.     

Those Wonderful Pioneer Years of SSRL: A Personal Reflection

It is a rare moment in the history of science when a new capability is born that transforms our ability to “see” what is happening in the world in which we live. The use of the light emitted from accelerating electrons as they are bent by magnetic fields that was pioneered at SSRL in the 1970s is not just another example of this, but arguably is the most important development in the history of science in enabling us to “see” the world of electrons and atoms. There is, in addition, a special feature of the new capability enabled by synchrotron radiation: it is likely to remain, in the future, the best way to see the microscopic world forever. This is because the light used to “see” does not only have all the intensity one needs, but also because all its properties can be adjusted so as to provide the ideal illumination for the particular thing one wants to “see.” Thus, literally what was born at SSRL, which has since then been and will be continually improved, will forever provide our species the ability to “see” and understand the microscopic world in which we live.     

Revisiting the Darmois and Lichnerowicz junction conditions

What have become known as the “Darmois” and “Lichnerowicz” junction conditions are often stated to be equivalent, “essentially” equivalent, in a “sense” equivalent, and so on. One even sees not infrequent reference to the “Darmois–Lichnerowicz” conditions. Whereas the equivalence of these conditions is manifest in Gaussian-normal coordinates, a fact that has been known for close to a century, this equivalence does not extend to a loose definition of “admissible” coordinates (coordinates in which the metric and its first order derivatives are continuous). We show this here by way of a simple, but physically relevant, example. In general, a loose definition of the “Lichnerowicz” conditions gives additional restrictions, some of which simply amount to a convenient choice of gauge, and some of which amount to real physical restrictions, away from strict “admissible” coordinates. The situation was totally confused by a very influential, and now frequently misquoted, paper by Bonnor and Vickers, that erroneously claimed a proof of the equivalence of the “Darmois” and “Lichnerowicz” conditions within this loose definition of “admissible” coordinates. A correct proof, based on a strict definition of “admissible” coordinates, was given years previous by Israel. It is that proof, generally unrecognized, that we must refer to. Attention here is given to a clarification of the subject, and to the history of the subject, which, it turns out, is rather fascinating in itself.     

A new interpretation of the Ψ-resonances

Recent experimental discoveries favor speculations that there may be several new “flavors” of tricolored quarks. We interpret the Ψ(3095) and Ψ′(3684) resonances as bound states composed of the two new quark flavors of electric charge 2/3 required by the minimal vectorlike theory of the weak interactions. Implications for e⁺e^?-annihilation and neutrino production are discussed.     

Is Seeing Believing?: Observation in Physics

In 2016 the LIGO-Virgo collaboration announced “the first direct detection of gravitational waves.” This was to distinguish their result from the indirect observation of Russell Hulse, Joel Weisberg, and Joseph Taylor, which used the decrease in the period of a binary pulsar to “establish, with a high degree of confidence the existence of gravitational radiation as predicted by general relativity.” This raises several interesting questions. One might ask how one can distinguish between direct and indirect observation and whether that distinction is exemplified in the practice of science. One might also ask whether a direct observation has more epistemic weight than an indirect observation. In this essay, I briefly discuss several episodes from the history of modern physics in an attempt to answer those questions. These episodes include Galileo and falling bodies, the discovery of the neutrino, the Higgs boson, and gravitational radiation.     

The photoelectron spectra of anti- and syn-[2.2](2,6)-azulenophanes

The He(Iα) photoelectron spectra of the title compounds are almost superposable, as predicted on the basis of a simple LCMO model which takes account of the “through-space” and “through-bond” interactions between the two azulene moieties. This observation, i.e., that the interaction of the two “layers” (decks) of the azulenophane molecule is independent of their relative orientation, may seem surprising in view of the fact that azulene is a polar molecule. However, the observed result indicates once more that azulene is essentially a perturbed [10]annulene rather than a “strongly” non-alternant hydrocarbon, a conclusion which had already been reached by the analysis of other spectroscopic properties of this molecule.