A Guide to Monte Carlo Simulations in Statistical Physics, by David P. Landau, Kurt Binder PDF

By David P. Landau, Kurt Binder

ISBN-10: 0521842387

ISBN-13: 9780521842389

I agree that it covers loads of themes, a lot of them are vital. they really comprise even more themes within the moment version than the 1st one. although, the authors seldomly speak about one subject greater than a web page. it is like examining abstracts of papers. So if you happen to already be aware of the stuff, you don't want this booklet. simply opt for a few papers (papers are a minimum of as much as date). in case you have no idea whatever approximately Monte Carlo sampling, this e-book won't assist you an excessive amount of. So do not waste your cash in this ebook. Newman's e-book or Frenkel's ebook is far better.

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Extra resources for A Guide to Monte Carlo Simulations in Statistical Physics, Second Edition

Example text

Such gaseous systems constitute a propitious place to begin our study of statistical thermodynamics because by invoking the assumption of independent particles, our upcoming statistical analyses can be based rather straightforwardly on probability theory describing independent events, as summarized in Chapter 2. While considering assemblies of independent particles, we will pursue new insight with respect to three basic concepts important to classical thermodynamics. First, we will seek a whole new statistical understanding of entropy.

For statistical purposes, we will eventually need to know the distribution of molecules among these energy states, as discussed further in Chapter 3. We now move toward this goal by considering the number of ways that N objects (molecules) can be placed in M containers (energy states) on a single shelf (energy level). Before we can make such combinatorial calculations, however, we must introduce two other important features of quantum mechanics, the details of which we again defer to later discussion (Chapter 5).

30) corresponds to Fermi–Dirac statistics, and Eq. 31) corresponds to Bose–Einstein statistics. 5 Determine the number of ways of placing two balls in three numbered containers for (a) Boltzmann statistics, (b) Fermi–Dirac statistics, and (c) Bose–Einstein statistics. Construct a table that identifies each of the ways for all three cases. Solution (a) For Boltzmann statistics, the balls are distinguishable with no limit on the number per container. Hence, from Eq. 29), W3 = MN = 32 = 9. Employing closed and open circles to identify the two distinguishable balls, these nine distributions can be identified as follows: Way 1 2 3 4 5 6 7 8 9 Container 1 •◦ Container 2 •◦ • ◦ • ◦ ◦ • • ◦ Container 3 •◦ ◦ • ◦ • (b) For Fermi–Dirac statistics, the balls are indistinguishable, but with a limit of one ball per container.

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A Guide to Monte Carlo Simulations in Statistical Physics, Second Edition by David P. Landau, Kurt Binder


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