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Honerkamp J. — Statistical physics: an advanced approach with applications
Honerkamp J. — Statistical physics: an advanced approach with applications



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Название: Statistical physics: an advanced approach with applications

Автор: Honerkamp J.

Аннотация:

The application of statistical methods to physics is essen- tial. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analy- sis of data are discussed as well. The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The second edition has been updated and enlarged with new material on estimators based on a probability dis- tribution for the parameters, identification of stochastic models from observations, and statistical tests and classi- fication methods (Chaps. 10-12). Moreover, a customized set of set of problems with solutions is accessible on the Web.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd

Год издания: 2002

Количество страниц: 529

Добавлена в каталог: 16.12.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Irreversible process      291
Ising model      122 123
Ising model, anisotropic      123
Ising model, one-dimensional      128
Ising model, two-dimensional      139
Isobaric expansion coefficient      79
Isobaric expansivity      79
Isochoric tension coefficient      80
Isothermal compressibility      78
Isothermal compressibility, critical exponent of      110
Isotherms, for a Bose gas      241
Isotherms, in a van der Waals gas      104
Isotropic Heisenberg model      281
Ito type, stochastic integral of      187
Jackknife method      451
Joule — Thomson coefficient      489
Joule — Thomson experiment      489
Kalman filter      421
Kalman filter, backward      422
Kalman filter, extended      423
Kalman filter, forward      421
Kalman gain      421
Kirchhoff's law      252
Kolmogorov system of axioms      6
Lack of information      25
Lame elastic constants      261
Landau free energy      146
Landau level      274
Landau theory of diamagnetism      272
Langevin equation      186
Large deviation property      48
Latent heat      107
Law of mass action      478
Laws of thermodynamics      298
Least-squares estimator      327 332 391 407
Least-squares FIR filter      352
Legendre transform      47
Levy process      204
Lifetime density function      324
Likelihood      322
Limit theorem, central      36
Linear congruence method      471
Liouville equation      163
Log likelihood function      322
Long-range dependence      204
Lorentz distribution      21
Low-pass filter      348
LS estimator      see "Least-squares estimator"
Lyapunov function      305
Macrocanonical system      68
magnetic moment      125
Magnetic susceptibility, in mean field approximation      137
magnetization      125
Magnon      284
MAP      see "Maximum a posteriori estimator"
Marginal density      13
Markov assumption      157
Markov field      118
Markov process      157
Markov process, piecewise deterministic      176
Markov process, temporally homogeneous      157
Markov property      157
Master equation      161
Maximum a posteriori estimator      387 405 407
Maximum entropy method      413
Maximum entropy principle      28 52
Maximum likelihood estimator      322 330 387
Maxwell construction      105
Maxwell relations      81
Maxwell — Boltzmann distribution      35
Mean squared error      311
Median      22
Metropolis algorithm      182
Metropolis sampler      182
Meyer filter      373
Microcanonical system      52
Minimum entropy production, principle of      305
Missing data      400
Mixed state      214
Model selection      405
Molecular dynamics calculation      97
Moment, mth      19
Monte Carlo integration      313
Monte Carlo method, for random fields      181
Morlets      373
Moving Average      348
Moving average filter      349
MSE      see "Mean squared error"
Multilevel logistic model      123
Multiplicative noise      187
Multiresolution      377
n-vector models      144
Neighborhood      117
Neural network      463
Neutron star      234
Normal distribution      10
Normal distribution, covariance matrix      20
Normal distribution, higher moments      19
Nuisance parameter      389
Null hypothesis      445
Number of microstates      53
Nyquist frequency      343
Observation equation      403
Occupation number representation      169 221
Occupation number, average, for quasi-particles      279
Occupation number, average, of ideal Fermi gas      226
One-step process      166
Optical branch      262
Orbitals      220
Ornstein — Uhlenbeck process      188 203
Pade approximation      96
Paramagnetic substance      272
Paramagnetic system, ideal      127
Paramagnetism      277
Parametric model      328
Particle bath      68
Partition function      60 119
Partition function, grand canonical      68
Partition function, macrocanonical      68
Partition function, T-p system      66
Pattern      116
Pauli equation      164
Percus — Yevick equation      100
Periodogram      343
Phase of a filter      348
Phase transition      48
Phase transition, first order      107
Phonon      259
Photon      245
Planck's radiation law      247
Point estimation      310
Poisson distribution      12 22
Poisson process      167 175
Potts model      124
Power of a test      451
Pressure      63
probability      7
probability distribution      8
Probability, conditional      14
Probability, joint      14
Process without memory      157
Product of random variables      34
Pseudo-inverse      330
Pure state      214
Quantile      22
Quantile of standard normal distribution      23
Quasi-particles      233 278
Quasi-static process      292
Radial distribution function      85 170
Radiation pressure      254
Radioactive decay      166 174
Random number      9
Random number generator      37 471
Random sample      310 327
Random variable      9
Random variable, $F_{k,q}$-distributed      35
Random variable, $\Chi^{2}$-distributed      34 335
Random variable, Bernoulli distributed      10
Random variable, binomally distributed      10
Random variable, gamma distributed      49
Random variable, Gaussian distributed      10
Random variable, Poisson distributed      12 22
Random variable, t-distributed      35
Random variable, uniformly distributed      10
Random walk      166 173
Randomvector      12
Rayleigh — Jeans formula      248
Realization      6
Recursive filter      350
Red noise      159
Regularization method      414
Regularization parameter      414
Rejection method      482 497
Relative frequency interpretation      309
Relaxation-time spectrum      414
Relaxator      210
Response function      76 190
Reversible process      291 292
Riemann zeta function      237
Roton      286
Sample      310
Sample, independent      322
Sampling frequency      339
Sampling time      339
Scale, of a base function      379
Scaling function, in multiresolution      378
Scaling relations      111
Self-consistent method      409
Self-similar processes      203
Set of events, complete and disjoint      7 15 24
Short-time expansion      160
Significance level      445
Simulation, of a piecewise deterministic Markov process      177
Singular value      331
Singular value decomposition      330 335
Six-vertex model      144
Sixteen-vertex model      144
Smoothed pseudo-Wigner distribution      365
Smoothing filter      348
Solar constant      254
Space of events      6
Specific heat      76
Specific heat, critical exponent of      110
Specific heat, for ideal Bose gas      241
Spectrogram      363
Spectrum of a process      340
Spin wave      284
Spontaneous expansion      293
Spontaneous magnetization      284
Stable density      39
Standard deviation      19
Standard method      316
Standard method for Monte Carlo integration      314
Standard normal distribution      10
State space model      404
Static structure function      89
Stationary distribution      158
Stationary quantities, simulation      180
Statistical dependence      15
Statistical independence      20
Statistical system with dissipation      191
Stefan — Boltzmann constant      248
Stefan — Boltzmann law      253
Stochastic differential equation      185
Stochastic differential equation, numerical integration      189
Stochastic integral      186
Stochastic process      156
Stochastic process, Gaussian      188
Stochastic time step, algorithm with      178
Stop-band      348
Stratonovich type, stochastic integral of      187
Strictly stable density      39
Structure function, dynamical      90
Structure function, static      89
Student t-distribution      35
Sum rule for random variablevS      33
Superconductivity      287
Superfluid $^{4}He$      243
Superfluidity      286
susceptibility      76 126 190
Sweep      183
Symlets      373
Taper      357
Temperature      56
Temporally homogeneous Markov process      157
Tensor product      331
Test quantity      445
Test statistic      445
Test, $\Chi^{2}$-Test      455
Test, F-Test      454
Test, F-Test for least-squares estimators      458
Test, Kolmogorov — Smirnov Test      457
Test, Likelihood-Ratio Test      459
Test, t-Test      452
Test, z-Test      452
Texture      117
Thermodynamic limit      48
Thermodynamic potential      222
Thermodynamic potential for molecules with inner degrees of freedom      266
Thermodynamic potential, ideal Bose gas      234
Thermodynamic potential, ideal Fermi gas      225
Thermodynamic potential, photon gas      248
Throw of a die      7
Time-frequency distribution      363
Transfer function      347
Transfer matrix      129
Transfer matrix for the two-dimensional Ising model      141
Transition probability      157
Tschebyshev filter      354
Two-time covariance      158
Unbiased estimator      311
Uncertainty relation      53
Uniform prior      391
valence electrons      231
Van Leeuwen, theorem of      272
Vapor pressure curve      107
Variance      19
Variance of normal distribution      19
Virial coefficients      92
Virial expansion      92
Virial theorem      87
Viterbi algorithm      417
Volume bath      65
Waiting time distribution      179
Wavelet      379
Weighted average      325
Weiss domain      285
White dwarfs      233
White noise      121 158 159
White random field      127
Widom relation      151
Wien's displacement law      248
Wien's radiation law      248
Wiener — Khinchin theorem      344
Wigner — Ville distribution      365
Wigner — Ville spectrum      364
Window function      351
Work      290
Zero point pressure      231
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