The Thirring-Wess model is a theoretical framework used in quantum field theory that describes the dynamics of fermionic fields. It is primarily a two-dimensional model that provides insights into the behavior of quantum fields with interactions. The model is notable because it exhibits non-trivial interactions between fermions and can lead to rich phenomena such as spontaneous symmetry breaking and the emergence of various phases. The model is characterized by its Lagrangian density, which typically includes terms for free fermions and interaction terms.

Topological quantum numbers are integer values that arise in the context of topological phases of matter and quantum field theories, particularly in condensed matter physics. They characterize different phases of a system based on their global properties rather than local properties, which can be crucial for understanding phenomena that are stable against local perturbations. A few key points about topological quantum numbers are: 1. **Robustness**: Topological quantum numbers are robust against small perturbations or changes in the system.

The Mathematical Optimization Society (MOS) is an international organization dedicated to promoting the study and application of mathematical optimization. Founded in 1978, the society serves as a platform for researchers, educators, and practitioners in the field of optimization to share knowledge, collaborate, and advance the theory and methods related to optimization. MOS provides a variety of resources and activities, including: 1. **Publications**: The society publishes journals and newsletters that feature original research, survey articles, and news related to optimization.

The Swedish Operations Research Association (Svenska Operativa Föreningen, SOF) is a professional organization in Sweden that focuses on the field of operations research (OR). The association aims to promote the development, practice, and education of operations research methodologies and applications within various industries. It serves as a platform for researchers, practitioners, and students interested in operations research to connect, collaborate, and share knowledge.

Anita Schöbel is a respected figure in the field of mathematics and statistics, particularly known for her contributions to operations research and optimization. She has been involved in various academic and research pursuits, particularly in areas related to mathematical programming and decision-making processes.

M. Grazia Speranza is known for her work in the field of operations research, particularly in areas such as optimization, logistics, and decision-making processes. She has contributed significantly to the academic community through research, publications, and participation in conferences related to operations research and applied mathematics. Her work often focuses on practical applications of optimization techniques in various domains, including transportation and supply chain management.

Michael Trick is a well-known figure in the field of operations research and management sciences. He is a professor at Carnegie Mellon University, where he has contributed significantly to optimization, especially in the areas of integer programming and combinatorial optimization. His work often involves developing algorithms and computational methods to solve complex decision-making problems. In addition to his academic contributions, Trick is also recognized for his involvement in the operations research community, including organizing conferences and workshops.

As indicated by its name, the journal contains mostly short letters sent to the editor, often 2 or 3 pages long, which allows for a faster publication cycle and dissemination of new results. This is notably useful for experimental physics.

Chemistry is fun. Too hard for precise physics (pre quantum computing, see also quantum chemistry), but not too hard for some maths like social sciences.

And it underpins biology.

Theory that atoms exist, i.e. matter is not continuous.

Much before atoms were thought to be "experimentally real", chemists from the 19th century already used "conceptual atoms" as units for the proportions observed in macroscopic chemical reactions, e.g. $2H_2+O_2\leftrightarrow H_{2}O$. The thing is, there was still the possibility that those proportions were made up of something continuous that for some reason could only combine in the given proportions, so the atoms could only be strictly consider calculatory devices pending further evidence.

Subtle is the Lord by Abraham Pais (1982) chapter 5 "The reality of molecules" has some good mentions. Notably, physicists generally came to believe in atoms earlier than chemists, because the phenomena they were most interested in, e.g. pressure in the ideal gas law, and then Maxwell-Boltzmann statistics just scream atoms more loudly than chemical reactions, as they saw that these phenomena could be explained to some degree by traditional mechanics of little balls.

Confusion around the probabilistic nature of the second law of thermodynamics was also used as a physical counterargument by some. Pais mentions that Wilhelm Ostwald notably argued that the time reversibility of classical mechanics + the second law being a fundamental law of physics (and not just probabilistic, which is the correct hypothesis as we now understand) must imply that atoms are not classic billiard balls, otherwise the second law could be broken.

Pais also mentions that a big "chemical" breakthrough was isomers suggest that atoms exist.

Very direct evidence evidence:

Less direct evidence:

Subtle is the Lord by Abraham Pais (1982) page 40 mentions several methods that Einstein used to "prove" that atoms were real. Perhaps the greatest argument of all is that several unrelated methods give the same estimates of atom size/mass:

Subtle is the Lord by Abraham Pais (1982) mentions that this has a good summary of the atomic theory evidence that was present at the time, and which had become basically indisputable at or soon after that date.

On Wikimedia Commons since it is now public domain in most countries: commons.wikimedia.org/w/index.php?title=File:Perrin,_Jean_-_Les_Atomes,_F%C3%A9lix_Alcan,_1913.djvu

An English translation from 1916 by English chemist Dalziel Llewellyn Hammick on the Internet Archive, also on the public domain: archive.org/details/atoms00hammgoog

Was the first model to explain the Balmer series, notably linking atomic spectra to the Planck constant and therefore to other initial quantum mechanical observations.

This was one of the first major models that just said:

It still treats electrons as little points spinning around the nucleus, but it makes the non-classical postulate that only certain angular momentums (and therefore energies) are allowed.

Bibliography:

Bagic jump between orbitals in the Bohr model. Analogous to the later wave function collapse in the Schrödinger equation.

Causality and quantum jumps are incompatible.

How atomic clock works? answer by Ciro Santilli on Physics Stack Exchange.

Refinement of the Bohr model that starts to take quantum angular momentum into account in order to explain missing lines that would have been otherwise observed TODO specific example of such line.

They are not observe because they would violate the conservation of angular momentum.

Introduces the azimuthal quantum number and magnetic quantum number.

TODO confirm year and paper, Wikipedia points to: zenodo.org/record/1424309#.yotqe3xmjhe

This technique is crazy! It allows to both:You actually see discrete peaks at different minute counts on the other end.

It is based on how much the gas interacts with the column.

Detection is usually done burning the sample to ionize it when it comes out, and then you measure the current produced.

The procedure remind you a bit of gel electrophoresis, except that it is in gaseous phase.