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2079 results in Statistical Physics

Page 25 of 104

  • 7 - Quantum Statistical Mechanics

  • Malcolm P. Kennett, Simon Fraser University, British Columbia
  • Book:
    Essential Statistical Physics
    Published online:
    29 August 2020
    Print publication:
    16 July 2020, pp 125-138

  • Summary

    Unlike classical particles, quantum particles are indistinguishable.Fermions and bosons differ in their quantum statistics, and the consequences of this for their statistical mechanics are explored in the grand canonical ensemble.The Fermi--Dirac and Bose--Einstein distribution functions are derived, and utilized to write thermal averages using the density of states.

  • 1 - Introduction

  • Malcolm P. Kennett, Simon Fraser University, British Columbia
  • Book:
    Essential Statistical Physics
    Published online:
    29 August 2020
    Print publication:
    16 July 2020, pp 1-24

  • Summary

    The statistical basis of statistical mechanics is introduced using probability and probability distributions, including the binomial and Gaussian distributions.The example of a random walk is used to illustrate the relationship between these distributions and to introduce the central limit theorem.Microstates of quantum and classical systems are defined, along with the multiplicity function, which counts the number of macroscopically identical microstates in a given macrostate.The enumeration of microstates leads to the idea that ignorance of the exact microstate of a system in a macrostate can be quantified with the entropy.

  • 10 - Phase Transitions and Order

  • Malcolm P. Kennett, Simon Fraser University, British Columbia
  • Book:
    Essential Statistical Physics
    Published online:
    29 August 2020
    Print publication:
    16 July 2020, pp 190-221

  • Summary

    Many different phases of matter can be characterized by the symmetries that they break.The Ising model for interacting spins illustrates this idea.In the absence of a magnetic field, there is a critical temperature, below which there is ferromagnetic ordering, and above which there is not.The magnetization is the order parameter for this transition: it is non-zero only when there is ferromagnetic ordering.The ferromagnetic phase transition in the Ising model is explored using the approximate method of mean field theory.Exact solutions are known for the Ising model in one and two dimensions and are discussed, along with numerical solutions using Monte Carlo simulations.Finally, the ideas of broken symmetry and their relationship to phase transitions are placed in the general framework of Landau theory and compared to results from mean field theory.

A First Course in Network Science
  • Filippo Menczer, Santo Fortunato, Clayton A. Davis
  • Published online:
    05 February 2020
    Print publication:
    23 January 2020
  • Networks are everywhere: networks of friends, transportation networks and the Web. Neurons in our brains and proteins within our bodies form networks that determine our intelligence and survival. This modern, accessible textbook introduces the basics of network science for a wide range of job sectors from management to marketing, from biology to engineering, and from neuroscience to the social sciences. Students will develop important, practical skills and learn to write code for using networks in their areas of interest - even as they are just learning to program with Python. Extensive sets of tutorials and homework problems provide plenty of hands-on practice and longer programming tutorials online further enhance students' programming skills. This intuitive and direct approach makes the book ideal for a first course, aimed at a wide audience without a strong background in mathematics or computing but with a desire to learn the fundamentals and applications of network science.

Page 25 of 104