Special Matrices Of Mathematical Physics: Stochastic, Circulant And Bell MatricesWorld Scientific, 2001 M08 17 - 340 páginas 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. |
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Página viii
... evolution courses . The matri- ces finally provide toy models illustrating involved questions like ergodicity , multi - phase systems , dissipation and non - equilibrium . of Circulants , once applied to Quantum Mechanics , lead to ...
... evolution courses . The matri- ces finally provide toy models illustrating involved questions like ergodicity , multi - phase systems , dissipation and non - equilibrium . of Circulants , once applied to Quantum Mechanics , lead to ...
Página ix
... evolution . The the- ory of real gases provides the best physical illustrations of the polynomials and these , in retribution , reveal the presence of a matrix structure in the backstage of the theory . The text is divided into four ...
... evolution . The the- ory of real gases provides the best physical illustrations of the polynomials and these , in retribution , reveal the presence of a matrix structure in the backstage of the theory . The text is divided into four ...
Página 21
... evolution of phys- ical systems whose future history is completely determined by the present state , without any influence of the past . Time evolution of physical systems is prevalently described through one of two standard approaches ...
... evolution of phys- ical systems whose future history is completely determined by the present state , without any influence of the past . Time evolution of physical systems is prevalently described through one of two standard approaches ...
Página 22
... evolution from a given state depends on that state only , and not on its previous history . Stochastic Matrices are deeply related to Markov Chains , which are discrete Markov processes . Markovian systems provide a nice sample of ...
... evolution from a given state depends on that state only , and not on its previous history . Stochastic Matrices are deeply related to Markov Chains , which are discrete Markov processes . Markovian systems provide a nice sample of ...
Página 23
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Contenido
19 | |
CIRCULANT MATRICES | 79 |
BELL MATRICES | 147 |
Appendix A Formulary | 283 |
Bibliography | 309 |
Index | 315 |
Otras ediciones - Ver todas
Special Matrices of Mathematical Physics: Stochastic, Circulant, and Bell ... Ruben Aldrovandi Vista previa limitada - 2001 |
Special Matrices of Mathematical Physics: Stochastic, Circulant, and Bell ... Ruben Aldrovandi Vista previa limitada - 2001 |
Términos y frases comunes
alphabet basis Bell matrices Bell polynomials braid group canonical partition function characteristic polynomial circulant matrices circulant matrix classical cluster integrals column commutative components condition consequently continuum convolution corresponding cyclic defined derivative detailed balancing diagonal differential discrete distribution dynamical eigenvalues eigenvectors entries ep+1 equation equilibrium evolution example factor fermions finite formalism formula Fourier transformations Fredholm geometry given glass grand canonical partition Hamiltonian Hopf algebras identity imprimitive invariant inverse irreducible iterate leads Lie algebra Markov chain noncommutative notation obtained operator particles permutation phase space Phys physical Poisson bracket powers projectors properties QN(B Quantum Mechanics recursion representation Statistical Mechanics stochastic matrix summation symmetric functions symmetric group symplectic Taylor coefficients theorem theory totally regular unitary values variables vector virial Weyl-Wigner Wigner functions Σ Σ