Stochastic Models for Many Body Systems I Infinite Systems in Thermal Equilibr
Stochastic Models for Many Body Systems I Infinite Systems in Thermal Equilibr
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In our eReader you can find the full English version of the book. Read Stochastic Models for Many Body Systems I Infinite Systems in Thermal Equilibr Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Stochastic Models for Many Body Systems I Infinite Systems in Thermal Equilibr
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9) et seq. It is clear that the only change in the expansion for S, ( ^ ) is that the factor '^^^Y^ ^ in rule b) K a pqx o P"-^ 22 above must be replaced by the factor ^ V . We readily find that ■^ '^ n. M;p-s p-s ^9 precisely the same diagrams survive in the present case as for the pre- vious ladder model. We shall illustrate the equivalence by two examples.
Consider first the diagram of Fig. 12c and equip it vith momentum labels as in Fig. 6a. Its contribution contains the factors j-i[(k-s)+(...s-s')+(s'-k)]. D^^^l (6. 11) according to our rules and to (2. 9). The phase of this expression is identically zero, and consequently the contribution survives when it is summed over the particle labels n and m in accord with rule c) . Next, however, consider the ring diagram Fig. 12d, with momentum labels as in Fig. 7a- • Its contribution contains the factors VVV exp -iq-(d +d +d )L (6. 12) qqq \_ ^ n, i t, m m, nj where q = k-s and we have used the momentum conservation relations. The phase of this expression fluctuates at random as we sum over all values of n, t, and m, so that the contribution does not survive in the limit jj ^ M^ il -^ 00 .
What to read after Stochastic Models for Many Body Systems I Infinite Systems in Thermal Equilibr?
You can find similar books in the "Read Also" column, or choose other free books by R H Kraichnan to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
9) et seq. It is clear that the only change in the expansion for S, ( ^ ) is that the factor '^^^Y^ ^ in rule b) K a pqx o P"-^ 22 above must be replaced by the factor ^ V . We readily find that ■^ '^ n. M;p-s p-s ^9 precisely the same diagrams survive in the present case as for the pre- vious ladder model. We shall illustrate the equivalence by two examples.
Consider first the diagram of Fig. 12c and equip it vith momentum labels as in Fig. 6a. Its contribution contains the factors j-i[(k-s)+(...s-s')+(s'-k)]. D^^^l (6. 11) according to our rules and to (2. 9). The phase of this expression is identically zero, and consequently the contribution survives when it is summed over the particle labels n and m in accord with rule c) . Next, however, consider the ring diagram Fig. 12d, with momentum labels as in Fig. 7a- • Its contribution contains the factors VVV exp -iq-(d +d +d )L (6. 12) qqq \_ ^ n, i t, m m, nj where q = k-s and we have used the momentum conservation relations. The phase of this expression fluctuates at random as we sum over all values of n, t, and m, so that the contribution does not survive in the limit jj ^ M^ il -^ 00 .
What to read after Stochastic Models for Many Body Systems I Infinite Systems in Thermal Equilibr?
You can find similar books in the "Read Also" column, or choose other free books by R H Kraichnan to read onlineMoreLess
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