## Statistical mechanics: fundamentals and modern applicationsThis book examines the latest developments in statistical mechanics, a branch of physical chemistry and physics that uses statistical techniques to predict the properties and the behavior of chemical and physical systems. It begins with a review of some of the essential concepts and then discusses recent developments in both equilibrium and nonequilibrium statistical mechanics. It covers liquids, phase transitions, renormalization theory, Monte Carlo techniques, and chaos. |

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Page 64

2.3.3 Thermal Wavelength and Degeneracy We have mentioned before that new

quantum effects arise at low

this statement. At a

...

2.3.3 Thermal Wavelength and Degeneracy We have mentioned before that new

quantum effects arise at low

**temperatures**and/or high densities. Let us quantifythis statement. At a

**temperature**T, the thermal energy of a particle is of the order...

Page 69

The left-hand side of this equation is independent of

number density, so the right-hand side should also be independent of

changes with ...

The left-hand side of this equation is independent of

**temperature**at a fixednumber density, so the right-hand side should also be independent of

**temperature**. For high**temperatures**, /x is large and negative, and its valuechanges with ...

Page 75

4tt(2S + l)V 2/3 (2.114) Hence, the Fermi

2mkB 4tt(2S + 1)V 2/3 (2.115) which is the same order of magnitude as the

degeneracy

4tt(2S + l)V 2/3 (2.114) Hence, the Fermi

**temperature**is given by h2 r 3<iV> TF2mkB 4tt(2S + 1)V 2/3 (2.115) which is the same order of magnitude as the

degeneracy

**temperature**[Eq. (2.74)]. The physical significance of this**temperature**is ...### What people are saying - Write a review

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### Contents

Classical Statistical Mechanics | 3 |

Quantum Statistical Mechanics | 45 |

Phase Transitions and Critical Phenomena | 83 |

Copyright | |

14 other sections not shown

### Common terms and phrases

attractor automata average behavior bifurcation Boltzmann Boltzmann equation Brownian motion Brownian particle BZ reaction calculate called canonical ensemble cell cellular automaton chaos Chapter coefficient collisions configuration consider coordinates correlation functions coupling constants critical exponents critical point defined depends derivation dimension discussed distribution function dynamics eigenvalues entropy equilibrium evaluated example ferromagnetic fixed point fluctuations fluid FORTRAN FORTRAN program fractal free energy frequency Gaussian Hamiltonian initial integral interactions Ising model iterations Kramers Langevin equation lattice limit cycle linear magnetization Markovian matrix method microcanonical ensemble microstates molecular nonequilibrium nonlinear number of particles obtained one-dimensional order parameter oscillations partition function Pathria phase space phase transition polymer potential power spectrum probability density problem protein quantities quantum mechanics RANDOM NUMBER random walk scaling Section shown in Figure simulation solution spin glass statistical mechanics steps stochastic temperature theorem thermodynamic limit total number values vector velocity zero