Table of contents

A consistent method of calculating the linear response to an external magnetic field that allows obtaining the result in a manifestly gauge-invariant form is proposed. Within the diagram technique for nonequilibrium processes, the self-consistency equations for the order parameter in an arbitrary-gauge field allow deriving an equation that determines the phase of the order parameter as a function of the external field. Such a method automatically accounts for the existence of collective excitations in superconductors, which must be taken into consideration in accordance with the continuity equation. The possible types of collective excitations in pure superconductors at different temperatures are considered. The authors present a microscopic theory that explains the possibility of observing collective modes in superconducting tunnel junctions.

Papers are discussed in which the quantum dynamics of individual molecules and semiconductor nanocrystals is studied from their fluctuating fluorescence. Presented are the fundamental tenets of the theory of photon emission by a single nanoparticle irradiated by continuous laser light. Fluorescence fluctuations which occur only for single nanoparticles are shown to open up entirely new opportunities for investigating nanoparticle quantum dynamics. It is shown how the theory can be harnessed to analyze the fluorescence fluctuations of an individual polymer molecule and a semiconductor nanocrystal and how the corresponding microscopic models can be constructed proceeding from this analysis.

Binary radio pulsars, first discovered by Hulse and Taylor in 1974 [1], are a unique tool for experimentally testing general relativity (GR), whose validity has been confirmed with a precision unavailable in laboratory experiments. In particular, indirect evidence of the existence of gravitational waves has been obtained. Radio pulsars in binary systems (which have come to be known as recycled) have completed the accretion stage, during which neutron star spins reach millisecond periods and their magnetic fields decay 2 to 4 orders of magnitude more weakly than ordinary radio pulsars. Among about a hundred known recycled pulsars, many have turned out to be single neutron stars. The high concentration of single recycled pulsars in globular clusters suggests that close stellar encounters are highly instrumental in the loss of the companion. A system of one recycled pulsar and one 'normal' one discovered in 2004 is the most compact among binaries containing recycled pulsars [2]. Together with the presence of two pulsars in one system, this suggests new prospects for further essential improvements in testing GR. This paper considers theoretical predictions of binary pulsars, their evolutionary formation, and mechanisms by which their companions may be lost. The use of recycled pulsars in testing GR is discussed and their possible relation to the most intriguing objects in the universe — cosmic gamma-ray bursts — is examined.

The mechanisms responsible for anomalously strong acoustic nonlinearities in multiphase, defected, and structurally inhomogeneous media are summarized, and nonlinear diagnostics — a fast-growing applied area of recent years — is reviewed in terms of its methods and applications. This paper is an expanded version of the introductory talk at the September 18, 2005 session of the RAS Physical Sciences Division. An abridge version of other talks presented in the session is also given in this issue of Physics–Uspekhi.

A joint scientific session of the Physical Sciences Division of the Russian Academy of Sciences (RAS) and the Joint Physical Society of the Russian Federation was held on September 28, 2005 in the Conference Hall of the Lebedev Physics Institute, RAS under the name "Nonlinear acoustic diagnostics". The following reports were presented at the session:

(1) Rudenko O V (Lomonosov Moscow State University) "Giant nonlinearities in structurally inhomogeneous media and the fundamentals of nonlinear acoustic diagnostics methods"; (2) Zaitsev V Yu, Nazarov V E, Talanov V I (Institute of Applied Physics, RAS, Nizhny Novgorod) "'Nonclassical' manifestations of microstructure-induced nonlinearities: new prospects for acoustic diagnostics"; (3) Esipov I B, Rybak S A, Serebryanyi A N (Andreev Acoustics Institute, RAS) "Nonlinear acoustic diagnostics of the ocean and rock"; (4) Preobrazhenskii V L (Research Center for Wave Studies, Prokhorov Institute of General Physics, RAS, European Laboratory in Nonlinear Magneto-acoustics (LEMAC)) "Parametrically phase-conjugate waves: applications in nonlinear acoustic imaging and diagnostics".

An expanded version of the report by Rudenko is published in the 'Physics of our days' section of this issue. An abridged version of reports 2 — 4 is given below. • 'Nonclassical' manifestations of microstructure-induced nonlinearities: new prospects for acoustic diagnostics, V Yu Zaitsev, V E Nazarov, V I Talanov Physics-Uspekhi, 2006, Volume 49, Number 1, • Nonlinear acoustic diagnostics of the ocean and rock, I B Esipov, S A Rybak, A N Serebryanyĭ Physics-Uspekhi, 2006, Volume 49, Number 1, • Parametrically phase-conjugate waves: applications in nonlinear acoustic imaging and diagnostics, V L Preobrazhenskii Physics-Uspekhi, 2006, Volume 49, Number 1,

An elementary derivation of the fundamental relation T/S = 4γ between the tensor and scalar modes of cosmological perturbations in the early universe is given. Statements by L P Grishchuk on this problem are commented on.