We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Theory of Dynamic Critical Phenomena

The superconducting transition temperature is calculated as a function of the electron-phonon and electron-electron coupling constants within the framework of the strong-coupling theory. Using this theoretical result, we find empirical values of the coupling constants and the "band-structure" density of states for a number of metals and alloys. It is noted that the electron-phonon coupling constant depends primarily on the phonon frequencies rather than on the electronic properties of the metal. Finally, using these results, one can predict a maximum superconducting transition temperature.

Transition temperature of strong-coupled superconductors.

The Renormalization group and the epsilon expansion

Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

Statistical physics of social dynamics

Irreversible Statistical Mechanics and the Principle of Maximum Entropy.

Cuprate superconducting thin films are being used to make compact low power microwave devices. In recent years, with improved materials and designs, there has been a steady improvement in device performance, notably an increase in resonator Q and a decrease in the nonlinear intermodulation. It is important to understand how much improvement can be expected. Here we discuss the intrinsic limiting behavior that one might achieve with a perfect film, review the present status, and discuss what the limiting behavior implies for high temperature superconducting filters. Our analysis indicates that increases in unloaded Q to ∼106 and decreases in intermodulation by a factor of ∼104, compared with today’s values, might be achieved.

Intrinsic limits on the Q and intermodulation of low power high temperature superconducting microstrip resonators

We present the predictions of an RPA-like theory for the transverse nuclear relaxation time, τ, of the Cu(2) nuclei in YBa2Cu3O7 below Tc. We find that s and dwave type gap symmetries yield distinctively different results for the τ−1: for an swave gap τ−1 decays rapidly below Tc, while for a dwave gap it remains nearly constant. Results for the temperature dependence of τ−1 in the normal state are also given.

RPA calculation of the transverse nuclear relaxation rate for YBa2Cu3O7 in the superconducting state

Author(s): Feiguin, AE; White, SR; Scalapino, DJ; Affleck, I | Abstract: We perform the numerical equivalent of a phase sensitive experiment on doped $t-J$ ladders We apply proximity effect fields with different complex phases at both ends of an open system and we study the transport of Cooper pairs Measuring the response of the system and the induced Josephson current, Density Matrix Renormalization Group calculations show how, depending on the doping fraction, the rung-leg parity of the pair field changes from minus to plus as the density of holes is increased We also study the pair charge stiffness, and we observe a supression of the superconductivity in the region where static stripes appear We compare our results with predictions from bosonization and renormalization group analysis

https://arxiv.org/pdf/cond-mat/0612636.pdf

Douglas J. Scalapino

Papers

Irreversible Statistical Mechanics and the Principle of Maximum Entropy.

Intrinsic limits on the Q and intermodulation of low power high temperature superconducting microstrip resonators

RPA calculation of the transverse nuclear relaxation rate for YBa2Cu3O7 in the superconducting state

Probing the pairing symmetry and pair charge stiffness of doped $t-J$ ladders

Test of the screening approximation (n-1 expansion) for the one-dimensional Ginzburg-Landau field