Statistical Mechanics: Fundamentals and Modern ApplicationsA valuable learning tool for students and an indispensable resource for professional scientists and engineers Several outstanding features make this book a superior introduction to modern statistical mechanics: It is the only intermediate-level text offering comprehensive coverage of both basic statistical mechanics and modern topics such as molecular dynamic methods, renormalization theory, chaos, polymer chain folding, oscillating chemical reactions, and cellular automata. It is also the only text written at this level to address both equilibrium and nonequilibrium statistical mechanics. Finally, students and professionals alike will appreciate such aids to comprehension as detailed derivations for most equations, more than 100 chapter-end exercises, and 15 computer programs written in FORTRAN that illustrate many of the concepts covered in the text. Statistical Mechanics begins with a refresher course in the essentials of modern statistical mechanics which, on its own, can serve as a handy pocket guide to basic definitions and formulas. Part II is devoted to equilibrium statistical mechanics. Readers will find in-depth coverage of phase transitions, critical phenomena, liquids, molecular dynamics, Monte Carlo techniques, polymers, and more. Part III focuses on nonequilibrium statistical mechanics and progresses in a logical manner from near-equilibrium systems, for which linear responses can be used, to far-from-equilibrium systems requiring nonlinear differential equations. |
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Page 48
... eigenvalues and g ; ) are the eigenkets . The eigenvalue equation ( 2.4 ) implies that any measurement of the physical observable G can result only in the real numbers g ;. Any other value , for example , ( g2 + 11g3 ) / 7 , where g2 ...
... eigenvalues and g ; ) are the eigenkets . The eigenvalue equation ( 2.4 ) implies that any measurement of the physical observable G can result only in the real numbers g ;. Any other value , for example , ( g2 + 11g3 ) / 7 , where g2 ...
Page 169
... eigenvalues are functions of b such that λ ; ( b ) λ ; ( b ' ) λ ( bb ' ) , which puts restrictions on the form of the function λ ; ( b ) , keeping in mind that λ¡ ( b ) must be a scalar . The only function that will do this is one of ...
... eigenvalues are functions of b such that λ ; ( b ) λ ; ( b ' ) λ ( bb ' ) , which puts restrictions on the form of the function λ ; ( b ) , keeping in mind that λ¡ ( b ) must be a scalar . The only function that will do this is one of ...
Page 294
... eigenvalues depend on the relative signs of tr J , | J | and the discriminant ; several possibilities arise . - - - 1. tr J > 0 , J > 0 , and D > 0 give the results that both the eigenvalues are positive ( ^ 1 > 0 and λ2 > 0 ) . These ...
... eigenvalues depend on the relative signs of tr J , | J | and the discriminant ; several possibilities arise . - - - 1. tr J > 0 , J > 0 , and D > 0 give the results that both the eigenvalues are positive ( ^ 1 > 0 and λ2 > 0 ) . These ...
Contents
Classical Statistical Mechanics | 3 |
Quantum Statistical Mechanics | 45 |
Ideal BoseEinstein and FermiDirac gases | 67 |
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Common terms and phrases
A₁ attractor automata average behavior bifurcation Boltzmann Boltzmann equation Brownian motion Brownian particle BZ reaction calculate called cell cellular automaton chaos Chapter Chem chemical reactions coefficient coordinates correlation functions critical point defined derivation discussed distribution function dynamics eigenvalues equation equilibrium evaluated exponents ferromagnetic fixed point fluctuations fluid FORMAT 1X FORTRAN FORTRAN program fractal dimension free energy Gaussian Hamiltonian initial configuration integral interactions Ising model ITERATE Kramers Langevin equation lattice limit cycle linear logistic magnetization Markovian matrix mean-field method microstates molecular molecules Monte Carlo NEIGHBORHOOD nonequilibrium nonlinear number of particles obtained one-dimensional oscillating p₁ partition function Pathria phase space phase transition Phys physical polymer potential probability density protein quantum mechanics RANDOM NUMBER random walk scaling Section shown in Figure simulation solution spin glass statistical mechanics steps stochastic temperature theory thermodynamic limit total number trajectory values vector velocity Wolfram zero Zwanzig