There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2-3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT-1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.

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Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain

Anyons in an exactly solved model and beyond

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Using the Kubo formula and a simplified Holstein model to calculate the Hall effect in the Anderson insulator, it is found that at low frequencies σ xy ∞ω 2 (with nonanalytical corrections). The coefficient is evaluated for strong localization and found to lead to the same order of magnitude as the usual classical result for the Hall coefficient

Zero-temperature-frequency-dependent Hall conductivity of the Anderson insulator.

We start by reviewing some interesting results in mesoscopic physics illustrating nontrivial insights on Quantum Mechanics. We then review the general principles of dephasing (sometimes called "decoherence") of Quantum-Mechanical interference by coupling to the environment degrees of freedom. A particular recent example of dephasing by a current-carrying (nonequilibrium) system is then discussed in some detail. This system is itself a manifestly Quantum Mechanical one and this is another illustration of detection without the need for "classical observers" etc. We conclude by describing briefly a recent problem having to do with the orbital magnetic response of conduction electrons (another manifestly Quantum Mechanical property): The magnetic response of a normal layer (N) coating a superconducting cylinder (S). Some recent very intriguing experimental results on a giant paramagnetic component of this response are explained using special states in the normal layer. It is hoped that these discussions illustrate not only the vitality and interest of mesoscopic physics but also its extreme relevance to fundamental issues in Quantum Mechanics.

https://iopscience.iop.org/article/10.1238/Physica.Topical.076a00171/pdf

Mesoscopic Physics and the Fundamentals of Quantum Mechanics

We consider the combined effect of shot and thermal noise on (i) the stationary distribution of fluctuations about the nonzero voltage state of an underdamped hysteretic Josephson junction, and (ii) the noise induced transition rate from the nonzero voltage to the zero voltage state. We find that the distribution is nonsymmetric in that the positive voltage fluctuations are more probable than the negative ones. We also find that the transition rates are larger than those due to thermal noise alone.

Shot noise effect on the nonzero voltage state of the hysteretic Josephson junction

We suggest a straightforward approach to the calculation of the dephasing rate in a fermionic system, which correctly keeps track of the crucial physics of Pauli blocking. Starting from Fermi's golden rule, the dephasing rate can be written as an integral over the frequency transferred between system and environment, weighted by their respective spectral densities. We show that treating the full many-fermion system instead of a single particle automatically enforces the Pauli principle. Furthermore, we explain the relation to diagrammatics. Finally, we show how to treat the more involved strong-coupling case when interactions appreciably modify the spectra. This is relevant for the situation in disordered metals, where screening is important.

/pdf/dephasing-rate-formula-in-the-many-body-context-1r6mw8qbct.pdf

Dephasing rate formula in the many-body context

The effect of fluctuations on a Landau-Ginzburg model of a first-order phase transition in one dimension is studied. Extremely sharp pseudotransitions can be obtained. The critical region or width of the transition is found to vanish exponentially with the effective number of interacting units across a cross section of the system. The results are physically interpreted in the context of the Landau-Lifschitz proof that phase equilibrium is impossible in one dimension.

Yoseph Imry

Papers

Zero-temperature-frequency-dependent Hall conductivity of the Anderson insulator.

Mesoscopic Physics and the Fundamentals of Quantum Mechanics

Shot noise effect on the nonzero voltage state of the hysteretic Josephson junction

Dephasing rate formula in the many-body context

Pseudo - first - order phase transitions in one dimension