Том 192, № 9 (2022)

We review some recent developments in the field of quasi-one-dimensional superconductivity. We demonstrate that low temperature properties of superconducting nanowires are essentially determined by quantum fluctuations. Smooth (Gaussian) fluctuations of the superconducting phase (also associated with plasma modes propagating along a wire) may significantly affect the electron density of states in such nanowires and induce persistent current noise in superconducting nanorings. Further interesting phenomena, such as nonvanishing resistance and shot noise of the voltage in current-biased superconducting nanowires, are caused by non-Gaussian fluctuations of the order parameter—quantum phase slips (QPSs). Such phenomena may be interpreted in terms of the tunneling of fluxons playing the role of effective quantum ‘particles’ dual to Cooper pairs and obeying complicated full counting statistics, which reduces to the Poissonian one in the low frequency limit. We also demonstrate that QPS effects may be particularly pronounced in the thinnest wires and rings, where quantum phase slips remain unbound and determine a nonperturbative length scale $L_c$, beyond which the supercurrent gets suppressed by quantum fluctuations. Accordingly, for $T \to 0$, such nanowires should become insulating at scales exceeding $L_c$, whereas at shorter length scales they may still exhibit superconducting properties. We argue that certain nontrivial features associated with quantum fluctuations of the order parameter may be sensitive to a specific circuit topology and may be observed in structures like a system of capacitively coupled superconducting nanowires.

We consider Fock's fundamental theory of the hydrogen atom in momentum space, which allows a realization of the previously predicted rotation group of a three-dimensional (3D) sphere in four-dimensional (4D) space. We then modify Fock's theory and abandon the momentum-space description. To transform and simplify the theory, we use invariant tensor methods of electrostatics in 3D and 4D spaces. We find a coordinate 4D space where the Schr$\ddot o$dinger equation becomes the 4D Laplace equation. The transition from harmonic 4D polynomials to the original 3D physical space is algebraic and involves derivatives with respect to a coordinate that is interpreted as time. We obtain a differential equation for eigenfunctions in the momentum space and find its solutions. A concise calculation of the quadratic Stark effect is given. The Schwinger resolvent is derived by the method of harmonic polynomials. Ladder operators are also considered.

On June 16, 2021, a scientific session of the Physical Sciences Division of the Russian Academy of Sciences was held online on the topic “Astrophysics of particles in space and geospheres,” dedicated to the 100th anniversary of the birth of A E Chudakov.The agenda of the meeting, announced on the website http://www.gpad.ac.ru of the Physical Sciences Division of the Russian Academy of Sciences, contained the following reports:(1) Lidvansky A S (Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia) “A E Chudakov as scientist/pioneer”;(2) Stenkin Yu V (Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia) “The LHAASO project: first results and prospects”;(3) Domogatsky G V (Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia) “Baikal-GVD neutrino telescope—current status and plans”;(4) Stozhkov Yu I (Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia) “Balloon studies of cosmic rays at the Lebedev Physical Institute, RAS”;(5) Sunyaev R A (Space Research Institute, Russian Academy of Sciences, Moscow, Russia; Max Planck Institute for Astrophysics, Garching, Germany) “Journey over the X-ray sky with the SRG/eROSITA telescope.”Published further in this issue are articles written on the basis of reports 1, 2, and 4.

Recent results of the LHAASO (Large High Altitude Air Shower Observatory) experiment are reviewed. Due to their outstanding characteristics, the facilities incorporated in the project started providing in 2021 the first results in ultra-high energy gamma-astronomy. During a year of operations of only some of the detectors, PeVatrons have been discovered in the Galaxy, many new astrophysical sources of gamma-quanta have been found, and the energy spectra of emitted gamma-quanta have been measured. The most important achievement is that the directions from which the gamma-quanta arrive have been measured with an accuracy as high as 0.05 degrees, implying that their sources can be localized with the same precision. These data enable making certain conclusions regarding the nature of PeVatrons and possible mechanisms of cosmic ray acceleration. Prospects for the further development of the LHAASO experiment are discussed.