By Kerson Huang
In contrast to such a lot different texts at the topic, this transparent, concise advent to the speculation of microscopic our bodies treats the trendy idea of severe phenomena. presents updated assurance of modern significant advances, together with a self-contained description of thermodynamics and the classical kinetic conception of gases, attention-grabbing functions reminiscent of superfluids and the quantum corridor influence, numerous present learn purposes, The final 3 chapters are dedicated to the Landau-Wilson method of severe phenomena. Many new difficulties and illustrations were extra to this version.
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Extra resources for Statistical Mechanics, 2nd Edition
Sample text
Let/(x):;:. 0 for x E M in some neighborhood of a and { E. g(x) = f(x, 0) has a singularity at some 0 :s; x :s; a. If this singularity is of power or logarithmic type then we say that the integral F (e) has a weak singularity. This Definition is obviously extended for unbounded intervals. Let F(e) = r f(x,e)dx where a> 0 and e > 0 is a small parameter. HerefE CX'([a, 1) x (0, eol) is a smooth function for a :s; x:s; 1,0 < e :s; eo, with some eo. Let the integral converge for e > 0 and diverge for e o. If the function g(x) f (x, 0) is of power or = = Mathematical Basics 42 logarithmic order at x singularity. Definition: Let f M X S ~ lR be a function of two variables and a be a limit point of M and {n} be an asymptotic sequence as x ~ a. Let for any xed YES the function f is expanded in an asymptotic series 00 f(x,y) ~ Lan(Y)n(x), (x~a,xEM). n=O This asymptotic expansion is called uniform with respect to the parameter YES, if the relation 00 RN(x,y) = f(x,y)- L an (y) n (x) = O(N(x», (x ~ a, x E M) n=O is valid uniformly with respect to YES. Theorem: A uniform asymptotic expansion can be integrated with respect to the parameter term by term.