Related papers: The $k\cdot p$ model: a short overview for beginne…
We give a pedagogical introduction to the theory of resonances, focusing specifically on the spectrum of excited strongly interacting particles. After providing historical context starting from the atomic theory, we summarize the status of…
These lectures provide an introduction to the basic aspects of the Standard Model, $SU(3)_{C} \times SU(2)_{L} \times U(1)_{Y}$.
In order to support students in the development of expertise in quantum mechanics, we asked which concepts and structures can act as organizing principles of the non-relativistic theory. The research question has been addressed in a…
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.
In these notes I review the basic concepts of the effects of interactions on quantum particles. I focuss here mostly on the case of fermions, but several aspects of interacting bosons are mentioned as well. These notes have been voluntarily…
We continue our study of the quantum optics of a single photon interacting with a system of two level atoms. In this work we investigate the case of a periodic arrangement of atoms. We provide a general structure theorem characterizing the…
After reviewing the basics, topics in this talk include an attempted survey of theoretical contributions to this workshop, some extra specific comments on quark models, and a summary.
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
These are the lecture notes for a course that I am teaching at Zhiyuan College of Shanghai Jiao Tong University (available at https://www.youtube.com/derekkorg), though the first draft was created for a previous course I taught at the…
Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are presented. Geometrical interpretations are given.
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical…
Understanding the interactions between atoms and light is at the heart of atomic physics. Being able to `experiment' with various system parameters, produce plots of the results and interpret these is very useful, especially for those new…
A general pedagogical survey of the basics of the Bethe-Salpeter equation and in particular Wick-Cutkosky model is given in great technical details.
This paper provides a brief overview for non-specialists of some of the highlights in the development of the theory of weak interactions during the past century.
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is…
We develop a framework to describe a wide class of flat-band models, with and without a translational symmetry, by using "molecular orbitals" introduced in the prior work (HATSUGAI Y. and MARUYAMA I., \textit{EPL}, \textbf{95}, (2011)…