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 vii
... Physics with the advent of Quantum Mechanics . Only then have they shown them- selves as unavoidable , essential tools to the understanding of the basic ways of Nature . It is not only ironic that the man responsible for that inaugura ...
... Physics with the advent of Quantum Mechanics . Only then have they shown them- selves as unavoidable , essential tools to the understanding of the basic ways of Nature . It is not only ironic that the man responsible for that inaugura ...
Página viii
... Quantum Mechanics and Noncommutative Geometry . Bell polynomials , after turning up in Differential Geometry and in the theory of gases , promise to be instrumental in the study of chaotic mappings . Stochastic matrices govern , through ...
... Quantum Mechanics and Noncommutative Geometry . Bell polynomials , after turning up in Differential Geometry and in the theory of gases , promise to be instrumental in the study of chaotic mappings . Stochastic matrices govern , through ...
Página xii
... quantum mechanics 10.1 Introduction . 99 99 10.2 Weyl - Heisenberg groups 103 · 10.2.1 Weyl's 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 ...
... quantum mechanics 10.1 Introduction . 99 99 10.2 Weyl - Heisenberg groups 103 · 10.2.1 Weyl's 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 ...
Página xv
... theory 302 303 303 A.8 Statistical mechanics . 304 A.8.1 Microcanonical ensemble 304 A.8.2 Canonical ensemble 304 A.8.3 Grand canonical ensemble . 305 A.8.4 Ideal relativistic quantum gases . 306 Bibliography 309 Index 315 PART 1 BASICS ...
... theory 302 303 303 A.8 Statistical mechanics . 304 A.8.1 Microcanonical ensemble 304 A.8.2 Canonical ensemble 304 A.8.3 Grand canonical ensemble . 305 A.8.4 Ideal relativistic quantum gases . 306 Bibliography 309 Index 315 PART 1 BASICS ...
Página 11
... Quantum Mechanics . Their simplicity comes from the supposed normal character of M. We shall say a little more on normal matrices in section 1.4 . A set of N powers of M is enough to fix the projector basis . Using for F ( M ) in ( 1.11 ) ...
... Quantum Mechanics . Their simplicity comes from the supposed normal character of M. We shall say a little more on normal matrices in section 1.4 . A set of N powers of M is enough to fix the projector basis . Using for F ( M ) in ( 1.11 ) ...
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