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1. Verfasser:	Cowan, Brian (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	London Imperial College Press 2005
Schriftenreihe:	Imperial College Press advanced physics texts 3
Schlagworte:	Statistische Mechanik
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XVI, 319 S. graph. Darst.
ISBN:	1860945694 1860945643

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adam_text	CONTENTS Preface v 1 The Methodology of Statistical Mechanics 1 1.1 Terminology and Methodology ................ 1 1.1.1 Approaches to the subject ................ 1 1.1.2 Description of states ................... 3 1.1.3 Extensivity and the thermodynamic limit ...... 3 1.2 The Fundamental Principles .................. 4 1.2.1 The laws of thermodynamics .............. 4 1.2.2 Probabilistic interpretation of the First Law ..... 6 1.2.3 Microscopic basis f or entropy ............. 7 1.3 Interactions — The Conditions for Equilibrium ....... 8 1.3.1 Thermal interaction — Temperature .......... 8 1.3.2 Volume change — Pressure ............... 10 1.3.3 Particle interchange — Chemical potential ...... 12 1.3.4 Thermal interaction with the rest of the world — The Boltzmann factor ............ 13 1.3.5 Particle and energy exchange with the rest of the world — The Gibbs factor ............ 15 1.4 Thermodynamic Averages ................... 17 1.4.1 The partition function .................. 17 1.4.2 Generalised expression for entropy .......... 18 1.4.3 Free energy ........................ 20 1.4.4 Thermodynamic variables ............... 21 1.4.5 Fluctuations ....................... 21 ix Topics in Statistical Mechanics 1.4.6 The grand partition function .............. 23 1.4.7 The grand potential ................... 24 1.4.8 Thermodynamic variables ............... 25 1.5 Quantum Distributions ..................... 25 1.5.1 Bosons and fermions .................. 25 1.5.2 Grand potential for identical particles ......... 28 1.5.3 The Fermi distribution ................. 29 1.5.4 The Bose distribution .................. 30 1.5.5 The classical limit — The Maxwell distribution ... 30 1.6 Classical Statistical Mechanics ................. 31 1.6.1 Phase space and classical states ............ 31 1.6.2 Boltzmann and Gibbs phase spaces .......... 33 1.6.3 The Fundamental Postulate in the classical case ... 34 1.6.4 The classical partition function ............. 35 1.6.5 The equipartition theorem ............... 35 1.6.6 Consequences of equipartition ............. 37 1.6.7 Liouville s theorem ................... 38 1.6.8 Boltzmann s H theorem ................. 40 1.7 The Third Law of Thermodynamics .............. 42 1.7.1 History of the Third Law ................ 42 1.7.2 Entropy .......................... 43 1.7.3 Quantum viewpoint ................... 44 1.7.4 Unattainability of absolute zero ............ 46 1.7.5 Heat capacity at low temperatures ........... 46 1.7.6 Other consequences of the Third Law ......... 48 1.7.7 Pessimist s statement of the laws of thermodynamics ..................... 50 Practical Calculations with Ideal Systems 54 2.1 The Density of States ...................... 54 2.1.1 Non-interacting systems ................ 54 2.1.2 Converting sums to integrals .............. 54 2.1.3 Enumeration of states .................. 55 2.1.4 Counting states ...................... 56 2.1.5 General expression for the density of states ..... 58 2.1.6 General relation between pressure and energy . ... 59 2.2 Identical Particles ........................ 61 2.2.1 Indistinguishability ................... 61 2.2.2 Classical approximation ................. 62 Contents xi 2.3 Ideal Classical Gas........................ 62 2.3.1 Quantum approach ................... 62 2.3.2 Classical approach.................... 64 2.3.3 Thermodynamic properties ............... 64 2.3.4 The 1/ЛП termín the partition function ........ 66 2.3.5 Entropy of mixing .................... 67 2.4 Ideal Fermi Gas ......................... 69 2.4.0 Methodology for quantum gases ............ 69 2.4.1 Fermi gas at zero temperature ............. 70 2.4.2 Fermi gas at low temperatures — simple model ... 72 2.4.3 Fermi gas at low temperatures — series expansion . 75 Chemical potential ..................... 78 Internal energy ....................... 80 Thermal capacity ...................... 81 2.4.4 More general treatment of low temperature heat capacity ....................... 81 2.4.5 High temperature behaviour — the classical limit . . 84 2.5 Ideal Bose Gas .......................... 87 2.5.1 General procedure for treating the Bose gas ..... 87 2.5.2 Number of particles — chemical potential ...... 88 2.5.3 Low temperature behaviour of Bose gas ....... 89 2.5.4 Thermal capacity of Bose gas — below Tc ....... 91 2.5.5 Comparison with superfluid 4He and other systems ....................... 93 2.5.6 Two-fluid model of superfluid 4He .......... 95 2.5.7 Elementary excitations ................. 96 2.6 Black Body Radiation — The Photon Gas ........... 98 2.6.1 Photons as quantised electromagnetic waves .... 98 2.6.2 Photons in thermal equilibrium — black body radiation ...................... 99 2.6.3 Planck s formula .....................100 2.6.4 Internal energy and heat capacity ...........102 2.6.5 Black body radiation in one dimension ........103 2.7 Ideal Paramagnet ........................105 2.7.1 Partition function and free energy ...........105 2.7.2 Thermodynamic properties ...............106 2.7.3 Negative temperatures .................110 2.7.4 Thermodynamics of negative temperatures .....112 xii Topics in Statistical Mechanics 3 Non-Ideal Gases 120 3.1 Statistical Mechanics .......................120 3.1.1 The partition function ..................120 3.1.2 Cluster expansion ....................121 3.1.3 Low density approximation ..............122 3.1.4 Equation of state .....................123 3.2 The Virial Expansion ......................124 3.2.1 Virial coefficients .....................124 3.2.2 Hard core potential ...................124 3.2.3 Square-well potential ..................126 3.2.4 Lennard-Jones potential ................127 3.2.5 Second virial coefficient for Bose and Fermi gas ... 130 3.3 Thermodynamics ........................130 3.3.1 Throttling ......................... 130 3.3.2 Joule-Thomson coefficient ............... 131 3.3.3 Connection with the second virial coefficient ..... 132 3.3.4 Inversion temperature .................. 134 3.4 Van der Waals Equation of State ................ 134 3.4.1 Approximating the partition function .........134 3.4.2 Van der Waals equation .................135 3.4.3 Microscopic derivation of parameters .......137 3.4.4 Virial expansion .....................138 3.5 Other Phenomenological Equations of State .........139 3.5.1 The Dieterici equation ..................139 3.5.2 Virial expansion .....................139 3.5.3 The Berthelot equation ................. I40 4 Phase Transitions 143 4.1 Phenomenology .........................143 4.1.1 Basicideas ........................143 4.1.2 Phase diagrams .....................145 4.1.3 Symmetry .........................147 4.1.4 Order of phase transitions ...............148 4.1.5 The order parameter ...................149 4.1.6 Conserved and non-conserved order parameters . - 151 4.1.7 Critical exponents ....................152 4.1.8 Scaling theory ......................154 4.1.9 Scaling of the free energy ................158 Contents xiii 4.2 First-Order Transition — An Example .............159 4.2.1 Coexistence ........................ 159 4.2.2 Van der Waals fluid................... 162 4.2.3 The Maxwell construction ............... 163 4.2.4 The critical point ..................... 165 4.2.5 Corresponding states .................. 166 4.2.6 Dieterici s equation ................... 168 4.2.7 Quantum mechanical effects .............. 169 4.3 Second-Order Transition — An Example ........... 170 4.3.1 The ferromagnet ..................... 170 4.3.2 The Weiss model ..................... 172 4.3.3 Spontaneous magnetisation .............. 173 4.3.4 Critical behaviour .................... 176 4.3.5 Magnetic susceptibility ................. 177 4.3.6 Goldstone modes .................... 178 4.4 The lsing and Other Models .................. 180 4.4.1 Ubiquity of the lsing model .............. 180 4.4.2 Magnetic case of the lsing model ........... 182 4.4.3 lsing model in one dimension ............. 184 4.4.4 lsing model in two dimensions ............. 185 4.4.5 Mean field critical exponents .............. 188 4.4.6 The XY model ...................... 190 4.4.7 The spherical model ................... 191 4.5 Landau Treatment of Phase Transitions ............ 191 4.5.1 Landau free energy ...................191 4.5.2 Landau free energy for the ferromagnet .......193 4.5.3 Landau theory — second-order transitions ......196 4.5.4 Thermal capacity in the Landau model ........198 4.5.5 Ferromagnet in a magnetic field ............199 4.6 Ferroelectricity ..........................201 4.6.1 Description of the phenomenon ............ 201 4.6.2 Landau free energy ................... 202 4.6.3 Second-order case .................... 203 4.6.4 First-order case ...................... 204 4.6.5 Entropy and latent heat at the transition ....... 208 4.6.6 Soft modes ........................ 209 4.7 Binary Mixtures ......................... 210 4.7.1 Basic ideas ........................210 4.7.2 Model calculation ....................211 xiv Topics in Statistical Mechanics 4.7.3 System energy ......................212 4.7.4 Entropy .......................... 213 4.7.5 Free energy ........................214 4.7.6 Phase separation — the lever rule ...........215 4.7.7 Phase separation curve — thebinodal ........217 4.7.8 The spinodal curve ...................219 4.7.9 Entropy in the ordered phase ..............220 4.7.10 Thermal capacity in the ordered phase ........222 4.7.11 Order of the transition and the critical point .....223 4.7.12 The critical exponent β .................225 4.8 Quantum Phase Transitions ..................226 4.8.1 Introduction .......................226 4.8.2 The transverse Ising model ...............228 4.8.3 Revision of mean field Ising model ..........228 4.8.4 Application of a transverse field ............230 4.8.5 Transition temperature .................232 4.8.6 Quantum critical behaviour ..............233 4.8.7 Dimensionality and critical exponents ........234 4.9 Retrospective ...........................236 4.9.1 The existence of order ..................236 4.9.2 Validity of mean field theory ..............237 4.9.3 Features of different phase transition models .... 238 5 Fluctuations and Dynamics 243 5.1 Fluctuations ...........................244 5.1.1 Probability distribution functions ...........244 5.1.2 Mean behaviour of fluctuations ............246 5.1.3 The autocorrelation function ..............250 5.1.4 The correlation time ...................253 5.2 Brownian Motion ........................254 5.2.1 Kinematics of a Brownian particle ...........255 5.2.2 Short time limit ......................257 5.2.3 Long time limit ......................258 5.3 Langevin s Equation .......................260 5.3.1 Introduction .......................260 5.3.2 Separation of f orces................... 261 5.3.3 The Langevin equation .................263 5.3.4 Mean square velocity and equipartition ........264 Contents xv 5.3.5 Velocity autocorrelation function ...........265 5.3.6 Electrical analogue of the Langevin equation .....267 5.4 Linear Response — Phenomenology .............268 5.4.1 Definitions ........................268 5.4.2 Response to a sinusoidal excitation ..........270 5.4.3 Fourier representation ..................271 5.4.4 Response to a step excitation ..............272 5.4.5 Response to a delta function excitation ........273 5.4.6 Consequence of the reality of X(r) ...........274 5.4.7 Consequence of causality ................275 5.4.8 Energy considerations ..................277 5.4.9 Static susceptibility ...................278 5.4.10 Relaxation time approximation ............280 5.5 Linear Response — Microscopies ...............281 5.5.1 Onsager s hypothesis .................. 281 5.5.2 Nyquist s theorem .................... 283 5.5.3 Calculation of the step response function ....... 285 5.5.4 Calculation of the autocorrelation function ...... 286 Appendixes 291 Appendix 1 The Gibbs-Duhem Relation ................291 АЛЛ Homogeneity of the fundamental relation ......291 A.1.2 The Euler relation ....................291 АЛ.З A caveat ..........................292 A.I. 4 The Gibbs-Duhem relation ...............292 Appendix 2 Thermodynamic Potentials ................293 А.2Л Equilibrium states ....................293 A.2.2 Constant temperature (and volume): the Helmholtz potential ...................295 A.2.3 Constant pressure and energy: the Enthalpy function ....................296 A.2.4 Constant pressure and temperature: the Gibbs free energy ........................296 A.2.5 Differential expressions for the potentials ......297 A.2.6 Natural variables and the Maxwell relations .....298 Appendix 3 Mathematica Notebooks ..................299 A.3.1 Chemical potential of Fermi gas at low temperatures ....................299 xvi Topics in Statistical Mechanics A.3.2 Internal energy of the Fermi gas at low temperatures ....................301 A.3.3 Fugacity of the ideal gas at high temperatures — Fermi, Maxwell and Bose cases . . . 303 A.3.4 Internal energy of the ideal gas at high temperatures — Fermi, Maxwell and Bose cases . . . 307 Appendix 4 Evaluation of the Correlation Function Integral .....310 A.4.1 Initial domain of integration ..............310 A.4.2 Transformation of variables ..............310 A.4.3 Jacobian of the transformation .............311 Index 313
adam_txt	CONTENTS Preface v 1 The Methodology of Statistical Mechanics 1 1.1 Terminology and Methodology . 1 1.1.1 Approaches to the subject . 1 1.1.2 Description of states . 3 1.1.3 Extensivity and the thermodynamic limit . 3 1.2 The Fundamental Principles . 4 1.2.1 The laws of thermodynamics . 4 1.2.2 Probabilistic interpretation of the First Law . 6 1.2.3 Microscopic basis f or entropy . 7 1.3 Interactions — The Conditions for Equilibrium . 8 1.3.1 Thermal interaction — Temperature . 8 1.3.2 Volume change — Pressure . 10 1.3.3 Particle interchange — Chemical potential . 12 1.3.4 Thermal interaction with the rest of the world — The Boltzmann factor . 13 1.3.5 Particle and energy exchange with the rest of the world — The Gibbs factor . 15 1.4 Thermodynamic Averages . 17 1.4.1 The partition function . 17 1.4.2 Generalised expression for entropy . 18 1.4.3 Free energy . 20 1.4.4 Thermodynamic variables . 21 1.4.5 Fluctuations . 21 ix Topics in Statistical Mechanics 1.4.6 The grand partition function . 23 1.4.7 The grand potential . 24 1.4.8 Thermodynamic variables . 25 1.5 Quantum Distributions . 25 1.5.1 Bosons and fermions . 25 1.5.2 Grand potential for identical particles . 28 1.5.3 The Fermi distribution . 29 1.5.4 The Bose distribution . 30 1.5.5 The classical limit — The Maxwell distribution . 30 1.6 Classical Statistical Mechanics . 31 1.6.1 Phase space and classical states . 31 1.6.2 Boltzmann and Gibbs phase spaces . 33 1.6.3 The Fundamental Postulate in the classical case . 34 1.6.4 The classical partition function . 35 1.6.5 The equipartition theorem . 35 1.6.6 Consequences of equipartition . 37 1.6.7 Liouville's theorem . 38 1.6.8 Boltzmann's H theorem . 40 1.7 The Third Law of Thermodynamics . 42 1.7.1 History of the Third Law . 42 1.7.2 Entropy . 43 1.7.3 Quantum viewpoint . 44 1.7.4 Unattainability of absolute zero . 46 1.7.5 Heat capacity at low temperatures . 46 1.7.6 Other consequences of the Third Law . 48 1.7.7 Pessimist's statement of the laws of thermodynamics . 50 Practical Calculations with Ideal Systems 54 2.1 The Density of States . 54 2.1.1 Non-interacting systems . 54 2.1.2 Converting sums to integrals . 54 2.1.3 Enumeration of states . 55 2.1.4 Counting states . 56 2.1.5 General expression for the density of states . 58 2.1.6 General relation between pressure and energy . . 59 2.2 Identical Particles . 61 2.2.1 Indistinguishability . 61 2.2.2 Classical approximation . 62 Contents xi 2.3 Ideal Classical Gas. 62 2.3.1 Quantum approach . 62 2.3.2 Classical approach. 64 2.3.3 Thermodynamic properties . 64 2.3.4 The 1/ЛП termín the partition function . 66 2.3.5 Entropy of mixing . 67 2.4 Ideal Fermi Gas . 69 2.4.0 Methodology for quantum gases . 69 2.4.1 Fermi gas at zero temperature . 70 2.4.2 Fermi gas at low temperatures — simple model . 72 2.4.3 Fermi gas at low temperatures — series expansion . 75 Chemical potential . 78 Internal energy . 80 Thermal capacity . 81 2.4.4 More general treatment of low temperature heat capacity . 81 2.4.5 High temperature behaviour — the classical limit . . 84 2.5 Ideal Bose Gas . 87 2.5.1 General procedure for treating the Bose gas . 87 2.5.2 Number of particles — chemical potential . 88 2.5.3 Low temperature behaviour of Bose gas . 89 2.5.4 Thermal capacity of Bose gas — below Tc . 91 2.5.5 Comparison with superfluid 4He and other systems . 93 2.5.6 Two-fluid model of superfluid 4He . 95 2.5.7 Elementary excitations . 96 2.6 Black Body Radiation — The Photon Gas . 98 2.6.1 Photons as quantised electromagnetic waves . 98 2.6.2 Photons in thermal equilibrium — black body radiation . 99 2.6.3 Planck's formula .100 2.6.4 Internal energy and heat capacity .102 2.6.5 Black body radiation in one dimension .103 2.7 Ideal Paramagnet .105 2.7.1 Partition function and free energy .105 2.7.2 Thermodynamic properties .106 2.7.3 Negative temperatures .110 2.7.4 Thermodynamics of negative temperatures .112 xii Topics in Statistical Mechanics 3 Non-Ideal Gases 120 3.1 Statistical Mechanics .120 3.1.1 The partition function .120 3.1.2 Cluster expansion .121 3.1.3 Low density approximation .122 3.1.4 Equation of state .123 3.2 The Virial Expansion .124 3.2.1 Virial coefficients .124 3.2.2 Hard core potential .124 3.2.3 Square-well potential .126 3.2.4 Lennard-Jones potential .127 3.2.5 Second virial coefficient for Bose and Fermi gas . 130 3.3 Thermodynamics .130 3.3.1 Throttling . 130 3.3.2 Joule-Thomson coefficient . 131 3.3.3 Connection with the second virial coefficient . 132 3.3.4 Inversion temperature . 134 3.4 Van der Waals Equation of State . 134 3.4.1 Approximating the partition function .134 3.4.2 Van der Waals equation .135 3.4.3 Microscopic "derivation" of parameters .137 3.4.4 Virial expansion .138 3.5 Other Phenomenological Equations of State .139 3.5.1 The Dieterici equation .139 3.5.2 Virial expansion .139 3.5.3 The Berthelot equation . I40 4 Phase Transitions 143 4.1 Phenomenology .143 4.1.1 Basicideas .143 4.1.2 Phase diagrams .145 4.1.3 Symmetry .147 4.1.4 Order of phase transitions .148 4.1.5 The order parameter .149 4.1.6 Conserved and non-conserved order parameters . - 151 4.1.7 Critical exponents .152 4.1.8 Scaling theory .154 4.1.9 Scaling of the free energy .158 Contents xiii 4.2 First-Order Transition — An Example .159 4.2.1 Coexistence . 159 4.2.2 Van der Waals fluid. 162 4.2.3 The Maxwell construction . 163 4.2.4 The critical point . 165 4.2.5 Corresponding states . 166 4.2.6 Dieterici's equation . 168 4.2.7 Quantum mechanical effects . 169 4.3 Second-Order Transition — An Example . 170 4.3.1 The ferromagnet . 170 4.3.2 The Weiss model . 172 4.3.3 Spontaneous magnetisation . 173 4.3.4 Critical behaviour . 176 4.3.5 Magnetic susceptibility . 177 4.3.6 Goldstone modes . 178 4.4 The lsing and Other Models . 180 4.4.1 Ubiquity of the lsing model . 180 4.4.2 Magnetic case of the lsing model . 182 4.4.3 lsing model in one dimension . 184 4.4.4 lsing model in two dimensions . 185 4.4.5 Mean field critical exponents . 188 4.4.6 The XY model . 190 4.4.7 The spherical model . 191 4.5 Landau Treatment of Phase Transitions . 191 4.5.1 Landau free energy .191 4.5.2 Landau free energy for the ferromagnet .193 4.5.3 Landau theory — second-order transitions .196 4.5.4 Thermal capacity in the Landau model .198 4.5.5 Ferromagnet in a magnetic field .199 4.6 Ferroelectricity .201 4.6.1 Description of the phenomenon . 201 4.6.2 Landau free energy . 202 4.6.3 Second-order case . 203 4.6.4 First-order case . 204 4.6.5 Entropy and latent heat at the transition . 208 4.6.6 Soft modes . 209 4.7 Binary Mixtures . 210 4.7.1 Basic ideas .210 4.7.2 Model calculation .211 xiv Topics in Statistical Mechanics 4.7.3 System energy .212 4.7.4 Entropy . 213 4.7.5 Free energy .214 4.7.6 Phase separation — the lever rule .215 4.7.7 Phase separation curve — thebinodal .217 4.7.8 The spinodal curve .219 4.7.9 Entropy in the ordered phase .220 4.7.10 Thermal capacity in the ordered phase .222 4.7.11 Order of the transition and the critical point .223 4.7.12 The critical exponent β .225 4.8 Quantum Phase Transitions .226 4.8.1 Introduction .226 4.8.2 The transverse Ising model .228 4.8.3 Revision of mean field Ising model .228 4.8.4 Application of a transverse field .230 4.8.5 Transition temperature .232 4.8.6 Quantum critical behaviour .233 4.8.7 Dimensionality and critical exponents .234 4.9 Retrospective .236 4.9.1 The existence of order .236 4.9.2 Validity of mean field theory .237 4.9.3 Features of different phase transition models . 238 5 Fluctuations and Dynamics 243 5.1 Fluctuations .244 5.1.1 Probability distribution functions .244 5.1.2 Mean behaviour of fluctuations .246 5.1.3 The autocorrelation function .250 5.1.4 The correlation time .253 5.2 Brownian Motion .254 5.2.1 Kinematics of a Brownian particle .255 5.2.2 Short time limit .257 5.2.3 Long time limit .258 5.3 Langevin's Equation .260 5.3.1 Introduction .260 5.3.2 Separation of f orces. 261 5.3.3 The Langevin equation .263 5.3.4 Mean square velocity and equipartition .264 Contents xv 5.3.5 Velocity autocorrelation function .265 5.3.6 Electrical analogue of the Langevin equation .267 5.4 Linear Response — Phenomenology .268 5.4.1 Definitions .268 5.4.2 Response to a sinusoidal excitation .270 5.4.3 Fourier representation .271 5.4.4 Response to a step excitation .272 5.4.5 Response to a delta function excitation .273 5.4.6 Consequence of the reality of X(r) .274 5.4.7 Consequence of causality .275 5.4.8 Energy considerations .277 5.4.9 Static susceptibility .278 5.4.10 Relaxation time approximation .280 5.5 Linear Response — Microscopies .281 5.5.1 Onsager's hypothesis . 281 5.5.2 Nyquist's theorem . 283 5.5.3 Calculation of the step response function . 285 5.5.4 Calculation of the autocorrelation function . 286 Appendixes 291 Appendix 1 The Gibbs-Duhem Relation .291 АЛЛ Homogeneity of the fundamental relation .291 A.1.2 The Euler relation .291 АЛ.З A caveat .292 A.I. 4 The Gibbs-Duhem relation .292 Appendix 2 Thermodynamic Potentials .293 А.2Л Equilibrium states .293 A.2.2 Constant temperature (and volume): the Helmholtz potential .295 A.2.3 Constant pressure and energy: the Enthalpy function .296 A.2.4 Constant pressure and temperature: the Gibbs free energy .296 A.2.5 Differential expressions for the potentials .297 A.2.6 Natural variables and the Maxwell relations .298 Appendix 3 Mathematica Notebooks .299 A.3.1 Chemical potential of Fermi gas at low temperatures .299 xvi Topics in Statistical Mechanics A.3.2 Internal energy of the Fermi gas at low temperatures .301 A.3.3 Fugacity of the ideal gas at high temperatures — Fermi, Maxwell and Bose cases . . . 303 A.3.4 Internal energy of the ideal gas at high temperatures — Fermi, Maxwell and Bose cases . . . 307 Appendix 4 Evaluation of the Correlation Function Integral .310 A.4.1 Initial domain of integration .310 A.4.2 Transformation of variables .310 A.4.3 Jacobian of the transformation .311 Index 313
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id	DE-604.BV021517103
illustrated	Illustrated
index_date	2024-07-02T14:21:14Z
indexdate	2024-07-09T20:37:37Z
institution	BVB
isbn	1860945694 1860945643
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-014733646
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open_access_boolean
owner	DE-91G DE-BY-TUM DE-703 DE-355 DE-BY-UBR
owner_facet	DE-91G DE-BY-TUM DE-703 DE-355 DE-BY-UBR
physical	XVI, 319 S. graph. Darst.
publishDate	2005
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publisher	Imperial College Press
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series	Imperial College Press advanced physics texts
series2	Imperial College Press advanced physics texts
spelling	Cowan, Brian Verfasser aut Topics in statistical mechanics Brian Cowan London Imperial College Press 2005 XVI, 319 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Imperial College Press advanced physics texts 3 Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s DE-604 Imperial College Press advanced physics texts 3 (DE-604)BV021517089 3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014733646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Cowan, Brian Topics in statistical mechanics Imperial College Press advanced physics texts Statistische Mechanik (DE-588)4056999-8 gnd
subject_GND	(DE-588)4056999-8
title	Topics in statistical mechanics
title_auth	Topics in statistical mechanics
title_exact_search	Topics in statistical mechanics
title_exact_search_txtP	Topics in statistical mechanics
title_full	Topics in statistical mechanics Brian Cowan
title_fullStr	Topics in statistical mechanics Brian Cowan
title_full_unstemmed	Topics in statistical mechanics Brian Cowan
title_short	Topics in statistical mechanics
title_sort	topics in statistical mechanics
topic	Statistische Mechanik (DE-588)4056999-8 gnd
topic_facet	Statistische Mechanik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014733646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV021517089
work_keys_str_mv	AT cowanbrian topicsinstatisticalmechanics

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