Sonoluminescence as a Physical Vacuum Excitation

We are discussing Schwinger'idea that physical mechanism of sonoluminescence is a physical vacuum excitation. This theory was based on the assumption that the sudden change of the rate of bubble collapse leads to the jump of dielectric constant of the gas trapped inside the bubble. We show that the dependence of the dielectric constant on the gas density really leads to the jump of the dielectric constant at shock-wave propagation in a collapsing gas bubble.Comment: 3 pages, Latex 2.0

Magnetic susceptibility of topological semimetals

We give a review of theoretical and experimental results concerning the magnetic susceptibility of the Weyl, Dirac, and nodal-line semimetals. In particular, dependences of the susceptibility on the chemical potential, temperature, and magnitude of the magnetic field are discussed. The presented results show that the specific features of the magnetic susceptibility can serve as a hallmark of the topological semimetals, and hence magnetic measurements can be useful in investigating these materials.Comment: Invited review article submitted to the special issue of J. Low Temp. Phys.; 26 pages, 10 figures; in 2nd revision new references were adde

Dirac points of electron energy spectrum, band-contact lines, and electron topological transitions of 3 1/2 kind in three-dimensional metals

In many of three-dimensional metals with the inversion symmetry and a weak spin-orbit interaction, Dirac points of the electron energy spectrum form band-contact lines in the Brillouin zones of these crystals, and electron topological transitions of 3 1/2 kind are due to certain points of these lines. We theoretically study these transitions in detail, and point out that they can be detected with the magnetic susceptibility which exhibits a giant diamagnetic anomaly at the 3 1/2 -order transitions.Comment: 5 pages, 3 figure

Flag Spaces in KP Theory and Virasoro Action on \det D_j and Segal-Wilson \tau-Function

It is well-known that the algebra of vector fields on the circle acts on the space of Riemann surfaces with a marked point and a local parameter at this point. We show that this action has a natural realization in the soliton theory, indeed it coincides with the action of some non-isospectral Kadomtsev-Petviashvili symmetries on the finite-gap solutions. A technique based on the so-called Cauchy-Baker-Akhiezer kernel is developed. The deformations of the \tau-function corresponding to the Baker-Akhiezer forms of tensor weight j generate representations of the Virasoro algebra with a central charge 6j^2-6j+1. A system including the Kadomtsev-Petviashvili hierarchy and the Toda lattice simultaneously is considered. The Virasoro representations corresponding to such a system explicitly depend on an extra discrete time t_0. The tau-function for this system is defined in terms of infinite dimensional flag spaces, generalizing the grassmanians.Comment: LaTeX, 24 page

Spontaneous symmetry breaking of magnetostriction in metals with multi-valley band structure

We show that a first-order phase transition can take place in a metal in a strong magnetic field if an electron Landau level approaches the Fermi energy of the metal. This transition is due to the electron-phonon interaction and is characterized by a jump in magnetostriction of the metal. If there are several equivalent groups of charge carriers in the metal, a spontaneous symmetry breaking of the magnetostriction can occur when the Landau level crosses the Fermi energy, and this breaking manifests itself as a series of the structural phase transitions that change a crystal symmetry of the metal. With these results, we discuss unusual findings recently discovered in bismuth.[ In the new version more explanations and examples added.]Comment: 10 pages, 3 fi

Instanton propagator in scalar model: exact expression and contribution to instanton induced processes

The propagator in the instanton background in the -lambda phi^4 scalar model in four dimensions is studied. Leading and sub-leading terms of its asymptotics for large momenta and its on-shell double residue are calculated. These results are applied to the analysis of the initial state and initial-final state corrections and the calculation of the next-to-leading (propagator) correction to the exponent of the cross section of multiparticle scattering processes.Comment: 17 pages, Latex, 1 ps figure. Based on the talk given by Yu.K. at the XIVth Workshop on Quantum Field Theory and High Energy Physics (May 27 - June 2, 1999, Mosco

Prime Lie algebras satisfying the standard Lie identity of degree 5

For every commutative differential algebra one can define the Lie algebra of special derivations. It is known for years that not every Lie algebra can be embedded to the Lie algebra of special derivations of some differential algebra. More precisely, the Lie algebra of special derivations of a commutative algebra always satisfy the standard Lie identity of degree $5$. The problem of existence of such embedding is a long-standing problem (see \cite{YuPSt5,PoinsotAAM,Poinsot}), which is closely related to the Lie algebra of vector fields on the affine line (see \cite{YuPSt5}). It was solved by Razmyslov in \cite{YuPSt5} for simple Lie algebras satisfying this identity (see also \cite[Th. 16]{Poinsot}). We extend this result to prime (and semiprime) Lie algebras over a field of zero characteristic satisfying the standard Lie identity of degree~$5$. As an application, we prove that for any semiprime Lie algebra the standard identity $St_5$ implies all other identities of the Lie algebra of polynomial vector fields on the affine line. We also generalize some previous results about primeness of the Lie algebra of special derivations of a prime differential algebra to the case of non-unitary differential algebra

Magnetization of topological line-node semimetals

Using an approximate expression for the Landau levels of the electrons located near a nodal line of a topological line-node semimetal, we obtain formulas for the magnetization of this semimetal at an arbitrary shape of its line. It is also shown that the dependence of the chemical potential on the magnetic field can be strong in these materials, and this dependence can essentially influence the de Haas - van Alphen oscillations. The obtained results are applied to the rhombohedral graphite which is one of the line-node semimetals. For this material, we find temperature and magnetic field dependences of its magnetic susceptibility.Comment: 20 pages, 5 figures. Added figures, and citation

Electromagnetic field with induced massive term: Case with spinor field

We consider an interacting system of spinor and electromagnetic field, explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced non-trivial rest-mass. This system of interacting spinor and scalar fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the electromagnetic field vanishes at $t \to \infty$ and the isotropization process of the expansion takes place.Comment: 8 page

Search for intrinsic charm in vector boson production accompanied by heavy flavor jets

Up to now, the existence of intrinsic (or valence-like) heavy quark component of the proton distribution functions has not yet been confirmed or rejected. The LHC with pp-collisions at $\sqrt{s}$ = 7-13 TeV can supply us with extra unique information concerning this hypothesis. On the basis of our theoretical studies, it is demonstrated that investigations of the intrinsic heavy quark contributions look very promising in processes like $pp \rightarrow Z/W + c(b) + X$. A ratio of $Z+$ heavy jets over $W+$ heavy jets differential cross section as a function of the leading jet transverse momentum is proposed to maximize the sensitivity to the intrinsic charm component of the proton.Comment: 14 pages, 11 figure