Basics of Quantum Statistics

Keith S. Stowe

Vyacheslav I. Yukalov

The aim of this tutorial is to present the basic mathematical techniques required for an accurate description of cold trapped atoms, both Bose and Fermi. The term cold implies that considered temperatures are low, such that quantum theory is necessary, even if temperatures are finite. The term atoms means that the considered particles are structureless, being defined by their masses and mutual interactions. Atoms are trapped in the sense that they form a finite quantum system, though their number can be very large, allowing for the use of the methods of statistical mechanics. This tutorial is the first of several, giving general mathematical techniques for both types of particle statistics. The following tutorials will be devoted separately to Bose atoms and Fermi atoms. Carefully explaining basic techniques is important in order to avoid the numerous misconceptions which propagate in the literature.

Inge Svein Helland

The Basic Elements Statistical Theory and Practice Statistical Inference Under Symmetry The Transition from Statistics to Quantum Theory Quantum Mechanics from a Statistical Basis Further Development of Quantum Mechanics Decisions in Statistics Multivariate Data Analysis and Statistics Quantum Mechanics and the Diversity of Concepts.

William Band, Gordon Frank Newell

Richard David Gill

The paper is a tutorial introduction to quantum information theory, developing the basic model and emphasizing the role of statistics and probability.

Don Koks