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
... operators to character- istic classes and characters . Furthermore , a Bell polynomial is related to a mapping . A matrix formed with the Bell polynomials of a mapping is a linear representation of that mapping . Function composition is ...
... operators to character- istic classes and characters . Furthermore , a Bell polynomial is related to a mapping . A matrix formed with the Bell polynomials of a mapping is a linear representation of that mapping . Function composition is ...
Página xii
... operators 104 10.2.2 The Schwinger basis 105 10.2.3 Continuum limit and interpretation 110 10.3 Weyl - Wigner transformations 112 10.3.1 Products and commutators 114 10.3.2 On convolutions , straight and twisted 10.3.3 The c xii Contents.
... operators 104 10.2.2 The Schwinger basis 105 10.2.3 Continuum limit and interpretation 110 10.3 Weyl - Wigner transformations 112 10.3.1 Products and commutators 114 10.3.2 On convolutions , straight and twisted 10.3.3 The c xii Contents.
Página 14
... operators . In Quantum Mechanics , for example , they proceed to increase the number of operators up to the point at which all degeneracy is removed . In that case , they stop only at a complete set of intercommuting operators , whose ...
... operators . In Quantum Mechanics , for example , they proceed to increase the number of operators up to the point at which all degeneracy is removed . In that case , they stop only at a complete set of intercommuting operators , whose ...
Página 18
... operators in quantum physics is not strange to this fact . The decomposition into components , however , holds also when M is not normal ( as a Bell matrix ) , though in that case , as said , the components may lose some of their most ...
... operators in quantum physics is not strange to this fact . The decomposition into components , however , holds also when M is not normal ( as a Bell matrix ) , though in that case , as said , the components may lose some of their most ...
Página 27
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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