Condensed Matter Field Theory by Altland A., Simons B.D.

By Altland A., Simons B.D.

Sleek experimental advancements in condensed subject and ultracold atom physics current bold demanding situations to theorists. This publication offers a pedagogical creation to quantum box thought in many-particle physics, emphasizing the applicability of the formalism to concrete difficulties. This moment variation includes new chapters constructing course quintessential techniques to classical and quantum nonequilibrium phenomena. different chapters conceal a variety of themes, from the advent of many-body suggestions and useful integration, to renormalization staff equipment, the speculation of reaction services, and topology. Conceptual elements and formal technique are emphasised, however the dialogue makes a speciality of functional experimental functions drawn mostly from condensed subject physics and neighboring fields. prolonged and tough issues of totally labored options offer a bridge among formal manipulations and research-oriented considering. geared toward raising graduate scholars to a degree the place they could interact in self reliant learn, this publication enhances graduate point classes on many-particle conception

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Condensed Matter Field Theory

Sleek experimental advancements in condensed subject and ultracold atom physics current ambitious demanding situations to theorists. This e-book offers a pedagogical advent to quantum box conception in many-particle physics, emphasizing the applicability of the formalism to concrete difficulties. This moment variation includes new chapters constructing course essential methods to classical and quantum nonequilibrium phenomena.

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Assume that the atomic exchange constants remain the same in all directions). Show that the dispersion generalizes to ωk = v|k|, where k = (n1 , . . , nd )2π/L and ni ∈ Z. Show that the specific heat shows the temperature dependence cv ∼ T d . Answer: As discussed in the text, the quantum eigenstates of the system are given by |n1 , n2 , . . , where nm is the number of phonons of wavenumber km = 2πm/L, E|n1 ,n2 ,... = nm m ωkm (nm + 1/2) ≡ m m the eigenenergy, and ωm = v|km |. In the energy representation, the quantum partition function then takes the form Z = tr e−β H = e−βEstate = ˆ states ∞ m=1,2,...

Compute the energy density u = −(1/L)∂β ln Z of one-dimensional longitudinal phonons ˆ with dispersion ωk = v|k|, where Z = tr e−β H denotes the quantum partition function. 8 Problems 37 −1 where nB ( ) = eβ − 1 is the Bose–Einstein distribution function. Approximate the sum over k by an integral and show that cv ∼ T . At what temperature Tcl does the specific heat cross over to the classical result cv = const? e. assume that the atomic exchange constants remain the same in all directions). Show that the dispersion generalizes to ωk = v|k|, where k = (n1 , .

The next chapter is devoted to a more comprehensive discussion of both the formal aspects and applications of this formulation. 8 Problems Electrodynamics from a variational principle Choosing the Lorentz-gauged components of the vector potential as generalized coordinates, the aim of this problem is to show how the wave equations of electrodynamics can be obtained as a variational principle. Electrodynamics can be described by Maxwell’s equations or, equivalently, by wave-like equations for the vector potential.

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