Special Matrices of Mathematical Physics: Stochastic, Circulant, and Bell MatricesWorld Scientific, 2001 - 340 páginas Ch. 1. Some fundamental notions. 1.1. Definitions. 1.2. Components of a matrix. 1.3. Matrix functions. 1.4. Normal matrices -- ch. 2. Evolving systems -- ch. 3. Markov chains. 3.1. Non-negative matrices. 3.2. General properties -- ch. 4. Glass transition -- ch. 5. The Kerner model. 5.1. A simple example: Se-As glass -- ch. 6. Formal developments. 6.1. Spectral aspects. 6.2. Reducibility and regularity. 6.3. Projectors and asymptotics. 6.4. Continuum time -- ch. 7. Equilibrium, dissipation and ergodicity. 7.1. Recurrence, transience and periodicity. 7.2. Detailed balancing and reversibility. 7.3. Ergodicity -- ch. 8. Prelude -- ch. 9. Definition and main properties. 9.1. Bases. 9.2. Double Fourier transform. 9.3. Random walks -- ch. 10. Discrete quantum mechanics. 10.1. Introduction. 10.2. Weyl-Heisenberg groups. 10.3. Weyl-Wigner transformations. 10.4. Braiding and quantum groups -- ch. 11. Quantum symplectic structure. 11.1. Matrix differential geometry. 11.2. The symplectic form. 11.3. The quantum fabric -- ch. 12. An organizing tool -- ch. 13. Bell polynomials. 13.1. Definition and elementary properties. 13.2. The matrix representation. 13.3. The Lagrange inversion formula. 13.4. Developments -- ch. 14. Determinants and traces. 14.1. Introduction. 14.2. Symmetric functions. 14.3. Polynomials. 14.4. Characteristic polynomials. 14.5. Lie algebras invariants -- ch. 15. Projectors and iterates. 15.1. Projectors, revisited. 15.2. Continuous iterates -- ch. 16. Gases: real and ideal. 16.1. Microcanonical ensemble. 16.2. The canonical ensemble. 16.3. The grand canonical ensemble. 16.4. Braid statistics. 16.5. Condensation theories. 16.6. The Fredholm formalism. |
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... recursion 176 13.4.2 Relations to orthogonal polynomials 178 . 13.4.3 Differintegration . . . 13.4.4 Homogeneity degree Chapter 14 Determinants and traces 14.1 Introduction . . 14.2 Symmetric functions . 14.3 Polynomials . . 14.4 ...
... recursion 176 13.4.2 Relations to orthogonal polynomials 178 . 13.4.3 Differintegration . . . 13.4.4 Homogeneity degree Chapter 14 Determinants and traces 14.1 Introduction . . 14.2 Symmetric functions . 14.3 Polynomials . . 14.4 ...
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Contenido
Some fundamental notions 336 | 3 |
Evolving systems | 21 |
Glass transition | 31 |
The SeleniumGermanium glass | 41 |
CIRCULANT MATRICES | 78 |
Discrete quantum mechanics | 99 |
Quantum symplectic structure | 127 |
An organizing tool | 149 |
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 bosons braid group canonical partition function characteristic polynomial classical closed expression cluster integrals column commutative components consequently continuum corresponding cyclic decomposition defined diagonal diagram differential discrete distribution dynamical eigenvalues eigenvectors entries ep+1 equation equilibrium example factor fermions finite formalism formula Fourier transformations Fredholm gases given grand canonical partition Hamiltonian identity interaction invariant inverse irreducible iterate leads Lie algebra Markov chain Math multinomial theorem noncommutative noncommutative geometry notation obtained operator P₁ particles permutation phase space Phys physical Poisson bracket powers projectors properties QN(B Quantum Mechanics relativistic representation result Statistical Mechanics stochastic matrix summation symmetric functions symmetric group symplectic theorem theory unitary v₁ values variables vector virial Wigner