A stationary solution of quantum mechanical wave equation is the superposition of eigenfunctions. Each of them corresponds to a vector in the Hilbert space. In a graphene sample one can choose expansion coefficients to get the series convergent solely within the certain circle in the two-dimensional space. Outside this circle the analytic continuation is required in the form of a different series. The exact wave function is referred to as anomalous. It is not a superposition of conventional eigenfunctions and gets ouside the Hilbert space. Anomalous electron and antielectron are possible. The antielectron is not a vacancy in the conventional valence band. The anomalous electron-antielectron pair is created from the anomalous vacuum like the electron-positron pair is created from the electron-positron vacuum. Formation of the anomalous vacuum is not a single electron effect but the collective quantum phenomenon. In the film of graphene the anomalous states are located at the film edge and are expected to be of high conductivity.

The effect of polyvalent cations, like spermine, on the condensation of DNA into very well-defined toroidal shapes has been well studied and understood. A great effort has been made to obtain similar condensed structures from RNA molecules, but so far, it has been elusive. In this work, we show that single-stranded RNA (ssRNA) molecules can easily be condensed into nanoring and globular structures on a mica surface, where each nanoring structure is formed mostly by a single RNA molecule. The condensation occurs in a concentration range of different cations, from monovalent to trivalent, but at a higher concentration, globular structures appear. RNA nanoring structures were observed on mica surfaces by atomic force microscopy (AFM). The samples were observed in tapping mode and were prepared by drop evaporation of a solution of RNA in the presence of one type of the different cations used. As far as we know, this is the first time that nanorings or any other well-defined condensed RNA structures have been reported in the presence of simple salts. The RNA nanoring formation can be understood by an energy competition between the hydrogen bonding forming hairpin stems-weakened by the salts-and the hairpin loops. This result may have an important biological relevance since it has been proposed that RNA is the oldest genome-coding molecule, and the formation of these structures could have given it stability against degradation in primeval times. Even more, the nanoring structures could have the potential to be used as biosensors and functionalized nanodevices.

The effect of polyvalent molecular cations, such as spermine, on the condensation of DNA into very well-defined toroidal shapes have been well studied and understood. However, a great effort has been made trying to obtain similar condensed structures from either ssRNA or dsRNA, which the latter carries similar negative charge density as dsDNA, although it adopts a different helical form. But the analogous condensation of RNA molecules into well-defined structures has so far been elusive. In this work, we show that ssRNA molecules can easily be condensed into nanoring structures on a mice surface, where each nanoring structure is formed mostly by a single RNA molecule. The condensation occurs in a concentration range of different atomic cations, from monovalent to trivalent. The structures of the RNA nanorings on mica surfaces were oberved by atomic force microscopy (AFM). The samples were observed in tapping mode and were prepared by drop evaporation of a solution of RNA in the presence of one type of the different cations used. As far as we know, this is the first time that nanorings or any other well-defined condensed RNA structures have been reported. The RNA nanorings formation can be understood by an energy competition between the hydrogen bonding forming hairpin stems, weakened by the salts, and hairpin loops. This results may have an important biological relevance, since it has been proposed that RNA is the oldest genome coding molecule and the formation of these structures could have given it stability against degradation in primeval times. Even more, the nanoring structures could have the potential to be used as biosensors and functionalized nanodevices.

We propose and investigate numerically a one-dimensional model which exhibits a non-Anderson disorder-driven transition. Such transitions have recently been attracting a great deal of attention in the context of Weyl semimetals, one-dimensional systems with long-range hopping and high-dimensional semiconductors. Our model hosts quasiparticles with the dispersion ±|k|αsignk with α<1∕2 near two points (nodes) in momentum space and includes short-range-correlated random potential which allows for scattering between the nodes and near each node. In contrast with the previously studied models in dimensions d<3, the model considered here exhibits a critical scaling of the Thouless conductance which allows for an accurate determination of the critical properties of the non-Anderson transition, with a precision significantly exceeding the results obtained from the critical scaling of the density of states, usually simulated at such transitions. We find that in the limit of the vanishing parameter ε=2α−1 the correlation-length exponent ν=2∕(3|ε|) at the transition is inconsistent with the prediction νRG=1∕|ε| of the perturbative renormalisation-group analysis. Our results allow for a numerical verification of the convergence of ε-expansions for non-Anderson disorder-driven transitions and, in general, interacting field theories near critical dimensions.

Matveevich Eliashberg, has turned 90. G M Eliashberg was born on July 26, 1930 in Leningrad. In 1947, he entered the Physical Faculty of Leningrad University and graduated with honors in 1952. Five years later, he worked at the Leningrad plant Krasny Khimik (Red Chemist), where he had been assigned on graduating from university. In 1959, GM Eliashberg entered the postgraduate course of the Physical-Technical Institute in Leningrad. That same year, he published a paper formulating the theory of the superconducting state occurring owing to electron±electron interaction through the crystal lattice oscillations. In this study, he wonderfully combined the J Bardeen, L Cooper, J Schrieffer theory of superconductivity that had appeared two years before, the field theoretical formulation of this theory developed at that time by Lev Gor'kov, and A B Migdal's theory of electron±phonon interaction in normal metals. Being the basis of the microscopic description of superconductivity, the Eliashberg theory became with time a well-developed part of modern condensed state physics. Different modifications of this theory are being actively examined in application to new classes of superconductors and other mechanisms of electron±electron attraction. The remarkable recent discovery of lithium hydride superconductivity at a temperature of 250 K and a pressure of several megabars is only one of the examples of such examinations. In 1961, GMEliashberg became a junior research worker at the Physical-Technical Institute. There, he carried out a number of studies of transport phenomena in Fermi liquid. He developed the technique of analytical continuation that allowed finding frequency dependences of kinetic quantities calculated using the temperature diagram technique. This approach is conventional and is invariably used in theoretical studies, sometimes even without mentioning the name of its author. After defending his candidate thesis in 1963, GM Eliashberg left Leningrad for Chernogolovka, where he began working at the theoretical department of a branch of the Institute of Chemical Physics and then from 1965 at the newly founded Institute of Theoretical Physics (now Landau Institute for Theoretical Physics), where he has been working till the present day. In 1972, G M Eliashberg became Doctor of Physical and Mathematical Sciences, and in 1990 he was elected a corresponding member and in 2000 a full member of the Russian Academy of Sciences. In Chernogolovka, GMEliashberg taught at theMoscow Institute of Physics and Technology, first at the chair of theoretical physics in Dolgoprudnyi and then at the chair of problems of theoretical physics at the Landau Institute. The educational process is always closely related to the teacher's personality. The scientific style of Eliashberg is known for a skillful mastery of complicated analytical methods remarkably combined with a precision of the physical statement of the problem. Intercourse with G M Eliashberg gave students not only facts and knowledge, but also scientific culture, while inculcating good manners and teaching lucidity of mind. B Ivlev, L Levitov, Yu Nazarov, and others are among his disciples. When at Chernogolovka, G M Eliashberg carried out a number of studies that remained significant for many years after. In 1965, he and L P Gor'kov formulated the theory of small metallic particles. Describing an ensemble of such particles with the Wigner±Dyson distribution, the authors arrived at a number of conclusions accessible for experimental verification and anticipating the results of mesoscopyÐ the contemporary theory of quantum properties of disordered metals. In the late 1960s ± early 1970s, G M Eliashberg together with L P Gor'kov developed a consistent theory of superconducting state kinetics and derived a nonstationary generalization of the Ginzburg±Landau equations. One of the most remarkable phenomena established by him here was the amplification of superconductivity by a high-frequency field. This work by G M Eliashberg made an impact on extensive Uspekhi Fizicheskikh Nauk 190 (9) 1007 ± 1008 (2020) Translated by M V Tsaplina PERSONALIA PACS number: 01.60.+q

Different electron states in atom are proposed. The states are bound to the electrostatic field of atomic nucleus cut off on its size. These relativistic states are singular and thus non-physical. Under a macroscopic acceleration of the atom the singularity is cut off and during the acceleration the states become physical with the binding energy in 10 MeV range. Electron transition to this anomalous state result in gamma radiation. It arises from a non-radioactive matter influenced by a macroscopic perturbation providing the atomic acceleration. This is not nuclear energy. Those high energy electron transitions can also activate nuclear degrees of freedom resulting in neutron emission. The electron-photon interaction displaces the singularity at various positions also leading to its cut off and thus to a physical state. The heavy cloud of virtual photons assists this anomalous state and its spontaneous creation is impossible. Nature allows the anomalous neutron (anomalous electron bound to proton), which exhibits itself as stable and neutral Bose particle, of approximately neutron mass and size, and carrying non-zero baryon and lepton numbers.

Gamma emission of nuclear energy scale (∼ 3MeV), caused by electron transitions in anomalous wells, is predicted to occur in acoustic experiments with solids. The anomalous well for electrons is formed by a local reduction of electromagnetic zero point energy in a vicinity of a nucleus which can be a lattice site of a solid [1]. The well width is ∼ 10^-11cm and the well depth is ∼ 3MeV. An energy spectrum in anomalous wells is continuous and non-decaying. Unusual experimental results, on unexpected emission from lead of ∼ 1keV x-rays under acoustic pulses, are likely explained by formation of anomalous wells [2]. The experimentally observed keV quanta are naturally supplemented by MeV emission to be revealed. This conclusion is drawn on the basis of an exact solution within a model generic with quantum electrodynamics. An energy of emitted quanta (x-rays and gamma) comes from a reduction of electromagnetic zero point energy (energy from "nothing").

The action of focused underwater weak shock waves on a lead sample is revealed to be not restricted by a mechanical influence only. A strong unexpected x-ray emission was registered from the lead foil exposed to shock waves (sound into x-rays) which were extremely adiabatic compared to processes of x-ray generation. The lead foil, exposed to shock waves, lost a part of its area having the shape of a polygonal hole of the size of ∼ 2mm. The missing polygon of lead foil looks as a delicately removed part with no damage at the hole surroundings as it should be after a mechanical breaking. This points to a non-mechanical mechanism of hole formation. That missing polygonal lead matter seems to be "disappeared" because the total lead volume was reduced by that amount after exposure to acoustic waves (matter collapse). Both paradoxical phenomena cannot be explained by a combination of known effects and a fundamentally new mechanism is required to underlie them. The concept of electron anomalous states, which encouraged the experiments and specified main features of them, is likely that mechanism.

In the recent experiments [1] the unusual oscillatory magnetoresistance in superconductors was discovered with a periodicity essentially independent on magnetic field direction and even material parameters. The nearly universal period points to a subatomic mechanism of the phenomenon. This mechanism is related to formation inside samples of subatomically thin (10−11 cm) threads in the form of rings of approximately Bohr radius. Electron states of rings go over into conduction electrons which carry the same spin imbalance in energy as rings. The imbalance occurs due to spin interaction with the orbital momentum of the ring. The conductivity near Tc is determined by fluctuating Cooper pairs consisting of electrons with shifted energies. Due to different angular momenta of rings these energies periodically depend on magnetic field resulting in the observed oscillatory magnetoresistance. Calculated universal positions of peaks (n + 1/2)∆H (∆H \simeq 0.18T and n = 0, 1, 2...) on the R(H) curve are in a good agreement with measurements.

In experiments on irradiation of metal surfaces by ions of keV energy, the emission of X-ray laser beams from the metal was observed not only during irradiation but also 20 h after it was switched off (from the “dead” sample). In contrast to a usual laser, the emitted collimated X-ray beams were of continuous frequency. In this paper the mechanism of that phenomenon is proposed. Subatomic electron states are formed inside the metal. These states are associated with anomalous wells within the subatomically small (10−11 cm) region. An anomalous well is formed by the local reduction (of MeV scale) in that region of zero point electromagnetic energy. States in anomalous wells are long-lived, which results in population inversion and the subsequent laser generation observed. The energies of emitted X-ray beams are due to the conversion of zero point electromagnetic energy (X-ray laser beams from vacuum).

By the certain macroscopic perturbations in condensed matter anomalous electron wells can be formed due to a local reduction of electromagnetic zero point energy. These wells are narrow, of the width ∼ 10^-11cm, and with the depth ∼ 1MeV. Such anomalous states, from the formal standpoint of quantum mechanics, correspond to a singular solution of a wave equation produced by the non-physical δ(R⃗) source. The resolution, on the level of the Standard Model, of the tiny region around the formal singularity shows that the state is physical. The creation of those states in an atomic system is of the formal probability exp(-1000). The probability becomes not small under a perturbation which rapidly varies in space, on the scale 10^-11cm. In condensed matter such perturbation may relate to acoustic shock waves. In this process the short scale is the length of the standing de Broglie wave of a reflected lattice atom. Under electron transitions in the anomalous well (anomalous atom) keV X-rays are expected to be emitted. A macroscopic amount of anomalous atoms, of the size 10^-11cm each, can be formed in a solid resulting in collapsed matter with 10^9 times enhanced density.

Unusual chemical bonds are proposed. Each bond is characterized by the thread of a small radius, 10−11 cm, extended between two nuclei in a molecule. An analogue of a potential well, of the depth of MeV scale, is formed within the thread. This occurs due to the local reduction of zero point electromagnetic energy. This is similar to formation of the Casimir well. The electron–photon interaction only is not sufficient for formation of thread state. The mechanism of electron mass generation is involved in the close vicinity, 10−16 cm, of the thread. Thread bonds are stable and cannot be created or destructed in chemical or optical processes.

The Bi2Te3/FeTe heterostructure intersects several phenomena and key classes of materials in condensed matter physics: topological insulators, superconductivity, magnetism, and the physics of interfaces. While neither the topological insulator (Bi2Te3) nor the iron chalcogenide (FeTe) are themselves superconductors, superconductivity forms in a thin 7nm interfacial layer between the two. The restricted dimensionality and the extraordinarily conductive normal state, possibly sourced by the topologically protected surface states, have led to the observation of novel phenomena such as the Likharev vortex explosion and transitions in behavior resulting from the interplay between current induced depairing and the Berezinski-Kosterlitz-Thouless regime. Bi2Te3/FeTe also displays the anomalous oscillatory magnetoresistance phenomenon, which we had previously observed in cuprates.

Experimentally observed X-ray and neutron emissions by acoustic perturbations of liquids and solids look paradoxical. All acoustically driven effects are extremely adiabatic with respect to typical times ħ/1keV∼ 10^-18s for X-ray and ħ/1MeV∼ 10^-21s for neutron processes. A direct application of this mechanism would result in negligible (exponentially small) emission probabilities. As argued in this paper, high energy process of X-ray and neutron emissions are caused by electron transitions in deep (∼ 1MeV) and narrow (∼ 10^-11cm) anomalous well created by the local reduction of electromagnetic zero point energy. The formation of anomalous states cannot be described solely by quantum electrodynamics since the mechanism of electron mass generation is involved.

The motion of a particle in a potential well is studied when the particle is attached to an infinite elastic string. This is generic with the problem of dissipative quantum mechanics investigated by Caldeira and Leggett (Ann. Phys. 149, 374 (1983). doi: 10.1016/0003-4916(83)90202-6 ). Besides the dissipative motion there is another scenario of interaction of the string with the particle attached. Stationary particle–string states exist with string deformations accompanying the particle. This is like polaronic states in solids. Our polaronic states in the well are non-decaying and have a continuous energy spectrum. These states may have a link to quantum electrodynamics.

We have discovered an oscillatory magnetoresistance phenomenon in a wide range of superconducting systems, with a periodicity that is essentially independent of temperature, transport current, magnetic field, and even material parameters. The nearly universal period points to a possible fundamental mechanism deeper than superconductivity itself, and may result from intrinsic pair-breaking mechanisms at sub-atomic length scales.

An unusual phenomenon, observed in experiments, is studied. X-ray laser bursts of keV energy are emitted from a metal where long-living states, resulting in population inversion, are totally unexpected. Anomalous electron-photon states are revealed to be formed inside the metal. These states are associated with narrow, 10(-11) cm, potential well created by the local reduction of zero point electromagnetic energy. In contrast to analogous van der Waals potential well, leading to attraction of two hydrogen atoms, the depth of the anomalous well is on the order of 1 MeV. The states in that well are long-living which results in population inversion and subsequent laser generation observed. The X-ray emission, occurring in transitions to lower levels, is due to the conversion of zero point electromagnetic energy.

In experiments on irradiation of metal surfaces by ions of keV energy, the emission of X-ray laser beams from the metal was observed not only during the irradiation but also 20 hours after it was switched off (from the "dead" sample). In contrast to an usual laser, the emitted collimated X-ray beams were of continuous frequency. In this paper the mechanism of that phenomenon is proposed. Subatomic electron states are formed inside the metal. These states are associated with anomalous well within the subatomically narrow ($10^{-11}cm$) region. Anomalous well is formed by the local reduction (of $MeV$ scale) in that region of the vacuum energy of the mass-generating field. States in anomalous well are long-living which results in population inversion and the subsequent laser generation observed. The energy of emitted X-ray beams are due to the conversion of the vacuum energy of the mass-generating field (X-ray laser beams from vacuum).

The solution of the wave equation for electron in a solid can be formally singular on some line. The singularity is smeared out within the distance ~ 10-11cm due to electron "vibrations" caused by its interaction with photons. Because of this localization, the large momentum uncertainty results in the local increase of the electron kinetic energy ~ 1 MeV. This energy enhancement is compensated by the local reduction of zero point energy of photons which can be considered as a potential well producing anomalous electron binding. The electron in this well gets to its bottom emitting photons of the total energy ~ 1 MeV (anomalous emission). These effects can occur in a solid when its surface is bombarded by ions with the energy ~ 1 keV. Photons, produced inside the solid, escape from it and can be detected in addition to the usual Bremsstrahlung of incident ions