PROFESSOR ISAAK M. KHALATNIKOV



    Academician of Russian Academy of Sciences
    Foreign Member of Royal Society
    Honorary Director of L.D. Landau Institute
    for Theoretical Physics of RAS

   The name of professor Isaak Khalatnikov is widely known. The scientific activities cover fields of modern theoretical physics - from superfluidity theory to quantum field theory and general relativity.

   A particular place in these activities is allotted to fundamental studies of the theory of quantum liquids. Initiated by L.D. Landau, the studies of superfluidity (Landau-Khalatnikov equations of hydrodynamics of the superfluid liquid) were taken up by I.M. Khalatnikov, who for many years has been the leading expert in this field of the theoretical physics. He has constructed the theory of viscosity and relaxational processes in liquid. He has investigated different hydrodynamics effects in it (including shock waves); has constructed the hydrodynamics and kinetics of the solution of 3He and 4He isotopes; has developed the hydrodynamic theory of the rotating superfluid liquid (the Khalatnikov-Bekarevich equations); has given the theory of the temperature gap on the interface of liquid He and solids (Kapitza gap); has formulated the general phenomenological theory of the Fermi-Bose liquid mixtures. I.M. Khalatnikov has formulated the canonical (Lagrangian and Hamiltonian) methods in hydrodynamics of quantum liquids (1952), these methods have been further developed in the works on hydrodynamics of the anisotropic superfluid 3He liquid. The Hamiltonian approach has also made it possible to solve nonlinear problems of hydrodynamics of quantum liquids and, in particular, the problem of the parametric excitation of various kinds of acoustic oscillations.

   The work of I.M. Khalatnikov (together with L.D. Landau), devoted to the absorption of sound in the vicinity of second order phase transition points, has become the basis for future advance of the dynamical phase transition theory. All these works, no doubt, have produced a strongest stimulating effect upon the studies of superfluidity all over the world.

   The works of I.M. Khalatnikov are always on the forefront of science, such have been his fundamental studies in the field of quantum electrodynamics (realized jointly with L.D. Landau and A.A. Abrikosov). In these works the problem of the asymptotical behavior of the main functions of the field theory (Green's functions of photon and electron) at large momenta has first been formulated and solved. Here also the original method of summing up infinite sequences of Feynman diagrams has been found (1954), this method has later on become widely applied in statistical physics (diagrams technique and renormalisation group). The problem of gradient transformations of Green's functions has been solved. He has been the first to formulate the methods of functional integration for Fermi fields widely adopted in the quantum field and solid state theories.

  The investigations carried out by I.M. Khalatnikov in the field of cosmology and relativistic astrophysics are particularly noteworthy. The work on many years on the problem of singularity in the general relativity theory has brought about the discovery of a new type of oscillatory behaviour of relativistic cosmological models in the vicinity of the time singularity. This type of singularity has proved to be of a most general character and has promonted construction of the general cosmological solution of the Einstein equations with the time singularity. These results have been confirmed by the works of S. Hawkin and R. Penrose. This series of works also involves development of original qualitative methods of investigating the evolution of the Universe with dissipative processed taken into account and also the exact solution of the problem of stochastic properties of the evolution of homogeneous models of the Universe (chaos in cosmology).

   I.M. Khalatnikov has carried out studies of the inflationary stages in cosmology and found the conditions of their realization for models with a scalar massive field. The degree of a generality of inflationary solutions in cosmological models with a scalar massive field was estimated. Using qualitative theory of dynamical systems it is shown that the majority of solutions undergoes the inflationary stage in flat and open models. In closed model the ratio of the number of solutions without adequate inflation to the number of the total solution is finite.

   Among the recent results. Particulary deserve note also the development of the theory of hydrodynamic fluctuations and of the diagram technique permitting to calculate the contribution of fluctuation to dynamic effects of different systems (two-dimensional systems, liquid crystals).

   Noteworthy are also the works of I.M. Khalatnikov on relativistic hydrodynamics (these results have been applied to the theory of multiple particle creation) as well as the virtuose, in terms of the mathematical methods, work on the threedimensional semi-classical scattering in quantum mechanics.

   For several years (1946-1954) I.M. Khalatnikov, together with L.D. Landau, was participating in the analysis of physical processes in extreme conditions at very high temperatures and pressures. They (with N. Meiman) developed the theory of stability of numerical methods of integration of differential equations with partial derivatives (independent from J. von Neumann). I.M.K. first introduced implicit difference schemes.

   I.M. Khalatnikov initiated the establishment of the Institute for Theoretical Physics (1964), named after L.D. Landau, within the USSR Academy of Sciences He headed this institute from the beginning as its Director. He succeeded in gathering a strong group of theoreticians and in creating a scientific center which has played a prominent role in the development of theoretical physics.

(written by E.M. Lifshiz, 1985)

Same Recent work

   A new direction in physical hydrodynamics was opened in the work on Hamiltonian description of nonlinear processes in compressible liquids with a free boundary. For a compressible liquid the standard canonical method is not applicable. The new approach permits one to calculate the interaction of bulk and surface waves in the presence of a free surface (bulk acoustic modes and surface capillary and gravitational waves).

   A new direction in quantum cosmology was initiated during the past years based on a model of gravity induced by complex scalar field. In this model it is possible to analyze the evolution of the universe from quantum to classical inflationary stages. A compact Euclidean (classically forbidden) region is observed in minisuperspace and propagation of an instanton in this region defines most probable initial conditions for a quantum birth of the universe.

   The classical dynamics of the closed isotropic cosmological models with a scalar field was investigated. The classification of non-singular (bounced) trajectories was elaborated and the possible fractal nature of asset of infinitely bounced trajectories was discussed. The chaotic dynamics wass studied in different Friedmann-Robertson-Walker cosmological models with scalar (inflaton) field and hydronamical matter. The powerful method of calculation of the topological entropy for dynamical systems was developed. The topological entropy was calculated for some particular cases.

   The perturbation theory for calculation of the effective conductivity of the plane consisting of pieces of different conductivities is constructed and the convenient diagram technique for this perturbation theory is elaborated (conductitivy of the multi-component two-dimensional composites). It is shown that for the chessboard perturbative calculations give results which are in agreement with the well-known Keller formula.


CURRICULUM VITAE

    I.M. Khalatnikov born in Dniepropetrovsk 17 Oktober 1919

    1941 - graduated from Dniepropetrovsk State University (Physical Department)

    1948 - Candidate of Physics and Mathematics

    1952 - Doctor of the Physics and Mathematics

    1972 - Correspondent Member of the USSR Academy of Sciences

    1984 - Full Member of the USSR Academy of Sciences (academician)

    1945-1965 - researcher, head of departament. P.L. Kapitsa Institute of Physical Problems of the USSR Academy of Sciences

    1965-1992 - Director of the L.D. Landau Institute for Theoretical Physics of the USSR Academy of Sciences (now Russian Academy of Sciences)

    Since 1993 -Honorary Director of L.D. Landau Institute for Theoretical Physics Professor, Tel Aviv University, School of Physics and Astronomy

    Since 1994 - President, Landau Network - Centro Volta, Como, Italy

    Since 1954 - Professor, Moscow Institute for Physics and Technology (Phystech)

Honors and Awards

    1953 - State Prize of the USSR

    1968 - Lorentz Professor, Leiden University

    1974 - Landau Prize of the USSR Academy of Sciences

    1989 - Alexander-von-Humboldt Award

    1994 - Foreign Member of Royal Society

    1999 - Kiwanis Prize "For Science and Disarmament"

    2010 - I.E. Tamm Gold Medal of the Russian Academy of Sciences for the series of works on asymptotic behavior of the Green's functions in quantum electrodynamics

    2012 - Marcel Grossman award for the discovery of a general solution of the Einstein equations with a cosmological singularity of an oscillatory chaotic character