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

The field dependence of the magnetoconductance in finite-geometry samples is analyzed within the framework of the localization theory. It is found that for high magnetic fields the magnetoconductance acquires the functional field dependence characteristic of a three-dimensional system. This is so even when the inelastic mean free path is much larger than the sample thickness and when the zero-field transport properties of the system are two dimensional in character. The crossover point is obtained once the radius of the Landau level becomes smaller than the sample thickness for both the parallel and the perpendicular field orientations. These theoretical considerations are borne out by experiments on indium oxide films.

Dimensionality crossover induced by a magnetic field in thin metallic films

We treat the question of the existence of Bose-Einstein condensation (BEC) in Bose lattice systems. Simple examples are constructed that do display BEC while having a lattice symmetry. It is suggested, however, that these systems are not crystals in the ordinary sense. When a more conventional definition of a lattice is employed, we generalize the proof of Matsuda and Tsuneto that BEC does not exist in a Bose lattice, for a wider class of wave functions including two-body correlations. A solid with a finite vacancy concentration can display BEC, which is related to the BEC in the vacancy gas. We clarify the relation between BEC of vacancies and particles.

On the possibility of Bose-Einstein condensation in a solid

We show that, in mesoscopic four-terminal thermoelectric devices with two electrodes (the source and the drain) and two heat baths, inelastic-scattering processes can lead to unconventional thermoelectric transport. The source (or the drain) can be cooled by passing a thermal current between the two heat baths, with no net heat exchange between the heat baths and the electrodes. This effect, termed ``cooling by transverse heat current,'' is a mesoscopic heat drag effect. In addition, there is a transverse thermoelectric effect where electrical current and power can be generated by a transverse temperature bias (i.e., the temperature bias between the two heat baths). This transverse thermoelectric effect originates from inelastic-scattering processes and may have advantages for improved figures of merit and power factor due to spatial separation of charge and heat transport. We study the Onsager current-affinity relations, the linear-response transport properties, and the transverse thermoelectric figure of merit of the four-terminal thermoelectric devices for various system parameters. We find that the figures of merit are optimized in different parameter regions for the transverse and the (conventional) longitudinal thermoelectric effects, respectively. Meanwhile, the maximum figure of merit for the transverse thermoelectric effect is higher than the figure of merit for the conventional longitudinal thermoelectric effect. In addition, we investigate the efficiency and power of the cooling by the transverse heat current effect in both linear and nonlinear transport regimes. Finally, we demonstrate that, by exploiting the inelastic transport in the quantum-dot four-terminal systems, a type of Maxwell demon can be realized using nonequilibrium heat baths.

Unconventional four-terminal thermoelectric transport due to inelastic transport: Cooling by transverse heat current, transverse thermoelectric effect, and Maxwell demon

Yoseph Imry

Papers

Dimensionality crossover induced by a magnetic field in thin metallic films

On the possibility of Bose-Einstein condensation in a solid

Unconventional four-terminal thermoelectric transport due to inelastic transport: Cooling by transverse heat current, transverse thermoelectric effect, and Maxwell demon

Self-consistent scaling theory of the metal-insulator transition in disordered systems

Characteristic modes and the transition to chaos of a resonant Josephson circuit