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 ^{3}He and ^{4}He 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 ^{3}He 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)
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.
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)
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