Related papers: Lectures on Statistical Mechanics
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical…
Lecture notes for a one-semester master-level course on analytical mechanics and classical field theory, covering: 0 Mathematical Introduction, 1 Lagrangian Mechanics, 2 Application: Motion in Central Fields, 3 Hamiltonian Mechanics, 4…
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum…
Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.
This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School "Integrability in Atomic and Condensed Matter Physics" in the summer of 2018. The school had its focus on the application of…
These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory;…
This book includes my lectures, together with their problem sets and solutions, on 1) classical mechanics (one semester), 2) thermodynamics and statistical mechanics (one semester), and 3) quantum mechanics (one semester), which I have been…
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different…
This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and…
These lectures notes are aimed at introducing the reader to some recent mathematical tools and results for the mean-field limit in statistical dynamics. As a warm-up, lecture 1 reviews the approach to the mean-field limit in classical…
These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere…
This chapter seeks to outline a few basic problems in quantum statistical physics where recent experimental advances from the atomic physics community offer the hope of dramatic progress. The focus is on nonequilibrium situations where the…
A four part series of lectures on the connection of statistical mechanics and quantum field theory. The general principles relating statistical mechanics and the path integral formulation of quantum field theory are presented in the first…
The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
A lecture notes style review of the non-equilibrium statistical mechanics of recurrent neural networks with discrete and continuous neurons (e.g. Ising, graded-response, coupled-oscillators). To be published in the Handbook of Biological…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…