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

Phase diagram of spin-1 quantum Ising models: Applications to systems of weakly coupled classical Ising chains

We consider the currents flowing in a solid-state interferometer under the effect of both an Aharonov-Bohm phase and a bias potential. Expressions are obtained for these currents, allowing for electronic or electron-boson interactions, which may take place solely on a quantum dot placed on one of the interferometer arms. The boson system can be out of equilibrium. The results are used to obtain the transport current through the interferometer, and the current circulating around it under the effect of the Aharonov-Bohm flux. The modifications of both currents, brought about by coupling the quantum dot to an incoherent sonic or electromagnetic source, are then analyzed. By choosing the appropriate range of the boson source intensity and its frequency, the magnitude of the interference-related terms of both currents can be controlled.

https://arxiv.org/pdf/cond-mat/0311609.pdf

Effects of external radiation on biased Aharonov-Bohm rings

Quantum oscillations in small rings at low temperatures

The intermittent-type chaos occurring in rf- and dc-current-driven Josephson junctions is investigated numerically and analytically. A simple physical model is proposed and is used for an analytic calculation of the temporal correlation function and the power spectrum. The latter has a broadband part whose behavior near threshold is discussed. Comparison with numerical results shows good quantitative agreement. Further generalizations of this approach needed for a quantitative agreement with the numerical results are outlined. The ''effective noise temperature'' for the chaotic state is discussed.

Studies of the intermittent-type chaos in ac- and dc-driven Josephson junctions

We study nonlinear transport effects on the maximum efficiency and power for both inelastic and elastic thermoelectric generators The former refers to phonon-assisted hopping in double quantum-dots, while the latter is represented by elastic tunneling through a single quantum-dot We find that nonlinear thermoelectric transport can lead to enhanced efficiency and power for both types of devices A comprehensive survey of various quantum-dot energy, temperature, and parasitic heat conduction reveals that the nonlinear transport induced improvements of the maximum efficiency and power are overall much more significant for inelastic devices than the elastic devices, even for temperature biases as small as $T_h=12T_c$ ($T_h$ and $T_c$ are the temperatures of the hot and cold reservoirs, respectively) The underlying mechanism is revealed as due to the fact that, unlike the Fermi distribution, the Bose distribution is not bounded when the temperature bias increases A large flux density of absorbed phonons leads to great enhancement of the electrical current, the output power, and the energy efficiency, dominating over the concurrent increase of the parasitic heat current Our study reveals that nonlinear transport effects can be a useful tool for improving thermoelectric performance

Yoseph Imry

Papers

Phase diagram of spin-1 quantum Ising models: Applications to systems of weakly coupled classical Ising chains

Effects of external radiation on biased Aharonov-Bohm rings

Quantum oscillations in small rings at low temperatures

Studies of the intermittent-type chaos in ac- and dc-driven Josephson junctions

Enhancing Thermoelectric Performance Using Nonlinear Transport Effects