September 16th, 2020


Классическая теория рассеяния и дифракции в электромагнетизме: учебное

Все очень хорошо, много полезного, в т.ч. оптическая теорема. При выводе формул даже показано зачеркиванием. какие члены сокращаются, как на доске:) В конце обсуждается рассеяние нейтронов в ферромагнетике.
Недостаток: система СИ, похоже, от нее уже никуда не скрыться:((

A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction:
Masud Mansuripur
Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium's optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.
Comments: 44 pages, 9 figures, 122 equations, 32 references, 13 appendices
лошадь, диаграмма, Фейнман

Геометрический подход к обобщению теоремы Нётер

Еще не читал, но интересно. Введение, во всяком случае, содержательное:)

A geometric approach to the generalized Noether theorem:
Alessandro Bravetti, Angel Garcia-Chung
We provide a geometric extension of the generalized Noether theorem for scaling symmetries recently presented in \cite{zhang2020generalized}. Our version of the generalized Noether theorem has several positive features: it is constructed in the most natural extension of the phase space, allowing for the symmetries to be vector fields on such manifold and for the associated invariants to be first integrals of motion; it has a direct geometrical proof, paralleling the proof of the standard phase space version of Noether's theorem; it automatically yields an inverse Noether theorem; it applies also to a large class of dissipative systems; and finally, it allows for a much larger class of symmetries than just scaling transformations which form a Lie algebra, and are thus amenable to algebraic treatments.
лошадь, диаграмма, Фейнман

Две заметки, связанные со статфизикой

What Is the Temperature? Modern Outlook on the Concept of Temperature:
Edward Bormashenko
The meaning and evolution of the notion of "temperature" (which is a key concept for the condensed and gaseous matter theories) are addressed from the different points of view. The concept of temperature turns out to be much more fundamental than it is conventionally thought. In particular, the temperature may be introduced for the systems built of "small" number of particles and particles in rest. The Kelvin temperature scale may be introduced into the quantum and relativistic physics due to the fact, that the efficiency of the quantum and relativistic Carnot cycles coincides with that of the classical one. The relation of the temperature to the metrics of the configurational space describing the behavior of the system built from non-interacting particles is demonstrated. The Landauer principle asserts that the temperature of the system is the only physical value defining the energy cost of isothermal erasing of the single bit of information. The role of the temperature the cosmic microwave background in modern cosmology is discussed.

А вот Тимоти Бойер, я его помню еще по статье во "В мире науки" (a.k.a. Sci.Am), он все время пишет, что если аккуратно все смотреть, то многие явления, которые мы ассоциируем с квантовой физикой, проявляются и в классике.

Conflict Between Classical Mechanics and Electromagnetism: The Harmonic Oscillator in Equilibrium with a Bath:
Timothy H. Boyer
It is pointed out that an electric charge oscillating in a one-dimensional purely-harmonic potential is in detailed balance at its harmonics with a radiation bath whose energy Urad per normal mode is linear in frequency ω, Urad=const×ω, and hence is Lorentz invariant, as seems appropriate for relativistic electromagnetism. The oscillating charge is NOT in equilibrium with the Rayleigh-Jeans spectrum which arises from energy-sharing equipartition ideas which are valid only in nonrelativistic mechanics. Here we explore the contrasting behavior of harmonic oscillators connected to baths in classical mechanics and electromagnetism. It is emphasized that modern physics text are in error in suggesting that the Rayleigh-Jeans spectrum corresponds to the equilibrium spectrum of random classical radiation, and in ignoring Lorentz-invariant classical zero-point radiation which is indeed a classical equilibrium spectrum.
Comments: 21 pages
лошадь, диаграмма, Фейнман

ОТО для индийских студентов и пакет MATHEMATICA

A Compendium on General Relativity for Undergraduate Students:
Tushar Kanti Dey, Surajit Sen
We give a pedagogical introduction of the essential features of General Theory of Relativity (GTR) in the format of an undergraduate (UG) project. A set of simple MATHEMATICA code is developed which enables the UG students to calculate the tensorial objects without prior knowledge of any package operation. The orbit equations of light and material particle in Minkowski and Schwarzschild spacetime are solved numerically to illustrate the crucial tests of GTR.
Comments: 17 pages