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Aldrovandi R. — Special matrices of mathematical physics (stochastic, circulant and bell matrices)
Aldrovandi R. — Special matrices of mathematical physics (stochastic, circulant and bell matrices)

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Название: Special matrices of mathematical physics (stochastic, circulant and bell matrices)

Автор: Aldrovandi R.

Аннотация:

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.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 323

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint of a matrix      5
Algebra invariants      200
Algebra, defined      5
Algebra, Hopf      120
Algebra, infinite      123
Algebra, Lie      5
Alphabet      5 153
Alphabet of roots      191
Alphabet with one missing letter      208
Alphabet, eigenvalue      196
Alphabet, letters      5
Alphabet, noncommutative      186
Alphabet, reciprocal      193
Alphabet, word      5
Alphabets relations between      191
Alternating function      192
Annihilating polynomial      4
Approximates, Pade      195
Area-preserving, transformation      124
Asymptotic, distribution      29
Asymptotic, equilibrium      29
Attractor of a Markov chain      54
Average on a distribution      29
Basis, matrix      93 106
Bell matrices, eigenvectors      180 226
Bell matrices, group of      167
Bell matrices, introduced      165
Bell matrices, not normal      168
Bell number      159
Bell polynomials and orthogonal polynomials      178
Bell polynomials and partition function      243
Bell polynomials, complete      153 154 177 199
Bell polynomials, definition      151
Bell polynomials, derivatives      181
Bell polynomials, logarithmic      164
Bell polynomials, matrices of      165
Bell polynomials, notation      153 154
Bell polynomials, partial      153
Bell polynomials, power      165
Bell polynomials, properties      155
Bell polynomials, recursion relation      177
Bell polynomials, special cases      160
Bialgebra      120
Boltzmann function      70
Borel transform      155
Bose function      256
Bracket, Moyal      103 114 119 124 133 137 146
Bracket, Poisson      100 103 111 124 132 133
Bracket, Poisson, quantum      129 138
Braid      146
Braid, equation      103
Braid, gas      265
Braid, group      140 236 264
Braid, group, presentation      265
Braid, statistics      264
Braid, statistics and superconductivity      264
Calculus fractional      180
Canonical, ensemble      239
Canonical, partition function      260
Casimir operators      201
Cayley-Hamilton theorem      4 6 84 197
Chapman — Kolmogorov equation      28
Character of a group      123
Character of a group, defined      118
Characteristic, class      203
Characteristic, equation      3
Characteristic, forms      196
Characteristic, matrix      3
Characteristic, polynomial      3 196
Chebyshev polynomials      179 220
Chern, characters      203
Chern, classes      203
Circle theorem      272
Circulant and Fourier transformation      84
Circulant, application of      182
Circulant, basis      88
Circulant, defined      83
Circulant, determinant      84
Circulant, projectors      87
Circulant, semi      169
Circulant, stochastic      53 96
Class, characteristic      203
Classical mechanics      99
Cluster and minor      198
Cluster, cofactor      198
Cluster, expansion      255
Cluster, integral      241
Composition function      151
Condensation      267
Condensation, Lee — Yang theory      270
Condensation, Mayer theory      268
Connected diagram      155
Connected graphs      155 263
Continuous iterate      211
Continuum time in Markov chains      60
Convolution      87 90
Convolution, twisted      102 114 115 123
Coordination number      75
Correlation quantum      251
Correspondence principle      102 112 117
Critical phenomena      267
Cycle decomposition      245 280
Cycle indicator polynomial      234
Cyclic group      85
Darboux theorem      128
Delta Kronecker      85
Derivation      129
Derivative cohomology      131
Detailed balancing      67 68
Detailed balancing and equilibrium      70
Determinant      183
Determinant and characteristic polynomial      197
Determinant and fermions      232
Determinant and traces of powers      185
Determinant, circulant      84
Determinant, Fredholm      276
Determinant, Vandermonde      193
Diagram, connected      155
Differential forms matrix      130
Differintegration      180
Discriminant of a polynomial      195
Displacement operator      89
Dissipation      66
Distribution functions      251
Distribution, equilibrium      29
Distribution, probability      26
Doubly-stochastic matrix      50 96
Duality, Fourier      122
Dynamic quantity, classical      99
Dynamic quantity, classical and quantum      113 117 140
Dynamic quantity, quantum      107
Eigenvalues      4
Eigenvalues of a Fredholm operator      282
Eigenvalues of Bell matrices      219
Eigenvalues of normal matrices      17
Eigenvalues of stochastic matrices      47
Eigenvalues, alphabet      196
Eigenvalues, symmetric functions of      187
Eigenvectors of Bell matrices      226
Eigenvectors of circulants      86
Eigenvectors of stochastic matrices      46 62
Ensemble, Canonical      239
Ensemble, Grand Canonical      253
Ensemble, microcanonical      228
Entire, Chapman — Kolmogorov      28
Entire, characteristic      3
Entire, function      279
Entire, Liouville      127
Entire, master      61
Entire, Maurer — Cartan      129
Entire, Schroeder      222
Entire, secular      3 197
Entire, Yang — Baxter      103 120 143
Equation braid      103
Equation of state, Boyle Mariotte      268
Equation of state, Mayer      268
Equation of state, virial      256
Equilibrium      46 54
Equilibrium and detailed balancing      70
Equilibrium, asymptotic      29
Equilibrium, distribution      29 53
Equilibrium, unstable      66
Ergodic, theorem      67 74
Eternel retour      66
Evanescent root      53
Faa di Bruno formula      153 161 181
Fermi function      256
Feynman diagrams number of      242
Fibonacci numbers      164
Formula, Faa di Bruno      153 161 181
Formula, Lagrange      173
Formula, Leibniz      172
Formula, Matsubara      263
Formula, Mayer      256
Formula, Newton      191
Formula, Prakash- Sudarshan      237
Formula, Viete      194
Formula, Wronski      169
Fourier transformation and circulants      84
Fourier transformation and cyclic groups      85
Fourier transformation and quantum groups      122
Fourier transformation, double      95
Fourier transformation, operator      113
Fourier, duality      122
Fractional calculus      180
Fredholm, alternative      275
Fredholm, determinant      276
Fredholm, first      278
Fredholm, minor      185
Fredholm, theory      185 245 274
Free energy, Helmholtz      247
Frobenius, spectral theorem      47 49
Fugacity      254
Function of a Bell matrix      207
Function of a circulant      91
Function of a matrix      8
Function, Bose      256
Function, composition      151
Function, entire      279
Function, Fermi      256
Function, Heaviside      195
Function, inverse      157
Fundamental group      265
Fundamental theorem of symmetric functions      187
Gas, braid      265
Gas, ideal      245
Gas, quantum      248 256 260
Gas, real      243 256 267
Gas, relativistic      248 260
Gas, ultrarelativistic      262
Gegenbauer, polynomials      178
Generating function for Bell numbers      160
Generating function for Bell polynomials      153 177
Generating function for conditional partition numbers      211
Generating function for Hermite polynomials      178
Generating function for Legendre polynomials      178
Generating function for number of partitions      153
Generating function for Stirling numbers      158
Generating function for symmetric functions, elementary      187 208
Generating function for symmetric functions, homogeneous      187
Generating function for symmetric functions, power-sum      188
Generating function, Chebyshev polynomials      179
Generating function, cycle indicator as      234
Generating function, Gegenbauer polynomials      178
Generating function, manipulations      162
Generators of the braid group      141 265
Generators of the symmetric group      235
Gibbs potential      253
Gibbs — Di Marzio law      34 39 78
Glass, binary      72 77
Golden ratio      164
grand canonical ensemble      253
Grand canonical ensemble, graphs connected      155 245 263
Grand canonical ensemble, partition function      188 253 260
Group      26
Group of permutations      26 234
Group, braid      140 264 265
Group, compact      201
Group, complex linear      203
Group, cyclic      85
Group, Heisenberg      104 108 111 116 123
Group, Lorentz      202
Group, orthogonal      202
Group, Poincare      202
Group, rotation      201
Group, semisimple      201
Group, symmetric      26 234
Group, unitary      203
Hamiltonian, approach to Markov chains      61
Harmonic analysis      122
harmonic oscillator      221
Heaviside function      195
Heisenberg, group      104 108 111 116 123
Helmholtz free energy      247
Hermite polynomials      178
Hermitian conjugate of a matrix      5
Hermitian matrix      5
Homotopy, integration by      256
Hopf algebra      120
Hypermatrix      49 136
Hypersensibility to initial conditions      66
Ideal gas      245
Idempotent number      163
Imprimitivity      48
INDEX      71
Insensibility to      56
Interpolating polynomial Lagrange      11 12
Invariants of a Lie algebra      200
Invariants of a matrix      199
Invariants, Casimir      201
Invariants, Killing      201
Inverse of a function      157
Inverse of a matrix      9 198
Inverse of a series      173
Involution      193
Ising model and circulants      87
Ising model and detailed balancing      70
Ising model, stochastic approach      58
Iterate, continuous      211 215
Jacobi identity      5
Kerner model      23
Killing — Cartan metric      201
Kronecker delta      85
Lagrange, interpolation      11 12
Lagrange, series inversion      171
Lah number      163
Law, Gibbs — Di Marzio      34 39 78
Lee-Yang, circle theorem      272
Lee-Yang, matrix      274
Lee-Yang, phase transition theory      270
Legendre polynomials      178
Leibniz, formula      172
Lie algebra      5
Lie algebra invariants      200
Lie derivative      128
Liouville, canonical form      128 138
Liouville, equation      127
Lissajous curve      221
Logarithmic Bell polynomials      164
Logistic map      166 219
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