Related papers: The $k\cdot p$ model: a short overview for beginne…
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We give a general method to calculate photonic band structure in the form of wave number $k$ as a function of frequency $\omega$, which is required whenever we want to calculate signal intensity related with photonic band structure. This…
These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…
Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show…
For Encyclopedia of Complexist and System Science No abstract given I. Definition and Introduction II. Ising Model III. Fractals IV. Diffusion on Fractals V. Ising Model on Fractals VI. Other Subjects ? VII. Networks VIII. Future Directions
The production of p K+ {\Lambda} in elementary p + p collision was investigated using the Bonn Gatchina Partial Wave Analysis framework. This approach allows the determination of possible participating production wave depending on the…
This is the written version of a set of introductory lectures on string theory.
A new lattice model of interacting electrons is presented. It can be viewed as a classical Hubbard model in which the energy associated to electron itinerance is proportional to the total number of possible electron jumps. Symmetry…
Quantum information theory gives rise to a straightforward definition of the interaction of electrons $I_{p,q}$ in two orbitals $p$, $q$ for a given many-body wave function. A convenient way to calculate the von Neumann entropies needed is…
Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically…
Lecture Goals: (i) Introduction to the basic concepts, meaning that the emphasis is, in the first instance, on the single-particle aspects. (ii) Service for Experimental Solid State Physics. (iii) Emphasis on the explanation of concepts and…
Previous studies have suggested complementary models of the elementary particles as (a) quantum knots and (b) preonic nuclei that are field and particle descriptions, respectively, of the same particles. This earlier work, carried out in…
A number of old and new methods for computing $K\to\pi\pi$ amplitudes on the lattice are reevaluated. They all involve a non-perturbative determination of matching coefficients. I will show how problems related to operator mixing can be…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…
We highlight recent progress in the study of artificial flat band systems with a threefold focus. First, we discuss single-particle flat band physics, which has advanced through the design of various flat band generators. These generators…
Examples are given of the usefulness of electrons in interaction with nuclei for probing fundamental interactions and structure
We review the major trends over the past decades in the theoretical and experimental approaches to the underlying physics of Many Polaron systems, concentrating on the cross-over between large an small polaronic charge carriers.