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Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…

Elementary particle physics is the quadrant of nature whose laws can be written in a few lines with absolute precision and the greatest empirical adequacy. If this is the case, as I believe it is, it must be possible and is probably useful…

Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…

This write--up gives a rather elementary introduction into particle physics aspects of the cosmological Dark Matter puzzle. A fairly comprehensive list of possible candidates is given; in each case the production mechanism and possible ways…

Physical properties of materials are seldom studied in the context of packing problems. In this work we study the behavior of semifluids: materials with particular characteristics, that share properties both with solids and with fluids. We…

This article will summarize selected aspects of the semiclassical theory of gravity, which involves a classical gravitational field coupled to quantum matter fields. Among the issues which will be discussed are the role of quantum effects…

This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…

Dark matter (comprising a quarter of the Universe) is usually assumed to be due to one and only one weakly interacting particle which is neutral and absolutely stable. We consider the possibility that there are several coexisting…

Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schr{\"o}dinger-type equation in R d. We describe quantitatively the localisation of the energy in a long-time…

A modest aim of this pedagogical presentation is to analyze, critically, certain fundamental physical concepts to illustrate the physical principles behind the special theory of relativity and, hence, to also illustrate the limitations of…

Propagation of ultrashort optical pulses in a dense resonant medium is considered in the semiclassical limit. In our analysis, we place emphasis on several main points. First, we study transformations of spectra in the process of pulse…

We start by surveying the history of the idea of a fundamental conservation law and briefly examine the role conservation laws play in different classical contexts. In such contexts we find conservation laws to be useful, but often not…

Many of the classic problems of particle physics appear in a very different light when viewed from the perspective of the multiverse. Most importantly the two great ``fine tuning'' problems that motivate the field are far less serious when…

One of the most important issues in quantum gravity is to identify its semi-classical regime. First the issue is to define for we mean by a semi-classical theory of quantum gravity, then we would like to use it to extract physical…

In these lectures I describe some of the open questions in the standard model relating to the nature and origin of mass, forces and matter and discuss some of the speculative theoretical ideas put forth in this regard. Some of the topics…

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…

Electron conductivity is an important material property that can provide a wealth of information about the underlying system. Especially, the response of the conductivity with respect to electromagnetic fields corresponds to various…

These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.

These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black…