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SPECIAL MATRICES OF MATHEMATICAL PHYSICS
Stochastic, Circulant and Bell Matrices
by R Aldrovandi (State University of São Paulo, Brazil)
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.
"Its user-friendly character is achieved via a hierarchy of abstracts, step-by-step explanations and pre-processing summaries. All this makes the book easily accessible precisely to its target group of readers."
"This book confirms that the study of different types of matrices, which have deep physics connections, is a fruitful exercise ... it is strongly recommended to scientists interested in modern developments in applications of matrices in physics."
| 340pp |
Pub. date: Aug 2001 |
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