Special Matrices of Mathematical Physics: Stochastic, Circulant, and Bell Matrices (Google eBook)

Front Cover
World Scientific, Jan 1, 2001 - Mathematics - 340 pages
0 Reviews
This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas concerning Lie algebra invariants, differential geometry and real gases, and their matrices are instrumental in the study of chaotic mappings. Contents: Basics: Some Fundamental Notions; Stochastic Matrices: Evolving Systems; Markov Chains; Glass Transition; The Kerner Model; Formal Developments; Equilibrium, Dissipation and Ergodicity; Circulant Matrices: Prelude; Definition and Main Properties; Discrete Quantum Mechanics; Quantum Symplectic Structure; Bell Matrices: An Organizing Tool; Bell Polynomials; Determinants and Traces; Projectors and Iterates; Gases: Real and Ideal. Readership: Mathematical physicists, statistical physicists and researchers in the field of combinatorics and graph theory.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Some fundamental notions
3
Evolving systems
21
Glass transition
31
Formal developments
45
Equilibrium dissipation and ergodicity
63
Prelude
81
Discrete quantum mechanics
99
Quantum symplectic structure
127
Determinants and traces
183
Projectors and iterates
207
real and ideal
227
Appendix A Formulary
283
Circulant matrices
289
Bell matrices
302
Index
315
Copyright

An organizing tool
149

Common terms and phrases

Popular passages

Page ix - Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) for the support to this work.

Bibliographic information