
BIOGRAPHY OF LEON VAN HOVE(1924  1990)
died Sep. 2, 1990. 
Leon Charles Prudent Van Hove (Brussels, 1924  2 September 1990), was a Belgian physicist and mathematician. He developed a scientific career from mathematics, over solid state physics, elementary particle and nuclear physics to cosmology. He studied mathematics at the Universite Libre of Brussels. In 1946 he received his Ph.D. on a thesis about a topic in the calculus of variations. It was followed by a series of articles about the calculus of variations, about mathematical problems of differential equations, and about transformation groups.
He started his work in the domain of theoretical physics from the statistical mechanics. He studied the behaviour of the statistical system in the limit
in which the volume of the system becomes infinitely large. This was called the "thermodynamic limit". The
"thermodynamic limit" or infinitevolume limit give results which are independent of which ensemble you employ
and independent of size of the box and the boundary conditions at its edge. And in the grand ensemble it is only in this
limit that phase transitions, in the form of mathematically sharp discontinuities, can appear. Thus the thermodynamic limit
provides a clean mathematical problem from which certain complications have been removed.
LEON VAN HOVE published two papers on this subject (in French):
L. Van Hove, Physica 15 (1949) pp.951961;
L. Van Hove, Physica 16 (1950) pp.137143;
The importance of "thermodynamic limit" or infinitevolume limit was first mentioned by N. N. Bogoliubov in his
seminal monograph "Problems of Dynamical Theory in Statistical Physics" in 1946. Later on, in 1949, N. N. Bogoliubov
published (with B. I. Khatset) a short article on this subject:
"On some mathematical problems of the theory of statistical equilibrium".
Doklady Academy of Sci., USSR, 66 N 3 (1949) pp.321324.
The proof of Van Hove contained some mathematical shortcomings and was improved by M. E. Fisher and D. Ruelle:
M. E. Fisher and D. Ruelle, Journal of Mathematical Physics 7 (1966) 260;
D. Ruelle, Ann.Phys. 25 (1963) 209;
D. Ruelle, Rev.Mod. Phys. 36 (1964) 580;
The complete mathematical treatment of the thermodynamic limit problem was given by N. N. Bogoliubov and collaborators in 1969:
N. N. Bogolyubov, D. Ya. Petrina and B. I. Khatset,
Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism.
Theoretical and Mathematical Physics, 1, N2 (1969) 251274.
See also:
N. S. Gonchar and A. B. Rudyk. Oscillation of the radial distribution function.
Journal of Statistical Physics,
Volume 68, Numbers 56, 10651087, (1992);
DOI: 10.1007/BF01048885.
From 1949 to 1954 LEON VAN HOVE worked at the Princeton Institute for Advanced Study by virtue of his meeting
with Robert Oppenheimer. Later he worked at the Brookhaven National Laboratory.At Princeton LEON VAN HOVE met G. Placzek,
who was working on the theory of neutron scattering. He started to work in this field and published a few important papers
on the subject. Three of them are:
G. Placzek and L. Van Hove, Crystal Dynamics and Inelastic Scattering of Neutrons,
Phys. Rev. 93 (1954) 1207;
L. Van Hove, Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles,
Phys. Rev. 95 (1954) 249;
This paper is cited about 2000 times.
L. Van Hove, TimeDependent Correlations between Spins and Neutron Scattering in Ferromagnetic Crystals,
Phys. Rev. 95 (1954) 1374;
It has ever since served as the foundation of the entire field.
Microscopic descriptions of condensed matter dynamical behavior use the notion of correlations over space and time
(see: B.J. Berne, TimeDependent Properties of Condensed Media).
Correlations over space and time in the density fluctuations of a fluid are responsible for the scattering of light when light passes through the
fluid.
Light scattering from gases in equilibrium was originally studied by Rayleigh and later by Einstein, who derived a formula for the intensity
of the light scattering.
The dynamical properties of a system of interacting particles are all contained in the
response of the system to external perturbations. The basic quantities are then the dynamical susceptibilities, which in the general case describe
the response of the system to external perturbations that vary in both space and time. For simple liquids the two basic susceptibilities describe the
motion of single particles and their relative motions. The fluctuating properties are conveniently described in terms of timedependent correlation
functions formed from the basic dynamical variables, e.g. the particle number density. The fluctuationdissipation theorem, shows that the
susceptibilities can be expressed in terms of the fluctuating properties of the system in equilibrium.
The relation between the crosssections for scattering of slow neutrons by an assembly of nuclei and spacetime correlation functions for the
motion of the scattering system has been given by Van Hove.
The concept of timedependent correlations has been used widely in connection with particle scattering by solids and fluids.
A fundamental formula for the differential scattering cross section of a slow neutron in the Born approximation was deduced by Van Hove.
He derived a compact formula, and related the differential scattering cross section to a spacetime pair correlation function.
As was shown by Van Hove in his seminal paper, the Born approximation scattering cross section can be
expressed in terms of the fourdimensional Fourier transform of a pair distribution function depending on a space vector and
a time variable. The formula obtained by Van Hove provided a convenient method of analyzing the properties of slow neutron scattering by
systems of particles, of light scattering by media, etc.
The advantage of using the Van Hove formula for analysis of scattering data is its compact form and intuitively
clear physical meaning (see: W. Marshall and S. W. Lovesey, Theory of Thermal Neutron Scattering. (Oxford University Press, Oxford, 1971).
Although there have have been many light and neutron scattering investigations of complex statistical systems during last
decades, it is true to say that until recently the properties and implications of the particle scattering by the nonequilibrium statistical medium were not yet understood
fully. There was not a fully satisfactory theoretical formalism of the interpretation of the light or thermal neutron scattering experiments for a
system in the nonequilibrium state.
The solution to this problem was formulated by A.L. Kuzemsky in 19701971 (unpublished) and published at the paper:
A.L. Kuzemsky
Generalized Van Hove Formula for Scattering of Neutrons by the Nonequilibrium Statistical Medium.
International Journal af Modern Physics (2012) V.B 26, No. 13, p.1250092 (34 pages).
The theory of scattering of particles (e.g., neutrons) by statistical medium was recast for the nonequilibrium statistical
medium. The correlation scattering function of the relevant variables give rise to a very compact and entirely general
expression for the scattering crosssection of interest. The formula obtained by Van Hove provides a convenient method of
analyzing the properties of slow neutron and light scattering by systems of particles such as gas, liquid or solid in the
equilibrium state. In this paper the theory of scattering of particles by manybody system was reformulated and generalized
for the case of nonequilibrium statistical medium. A new method of quantumstatistical derivation for the space and time
Fourier transforms of the Van Hove correlation function was formulated. Thus in place of the usual Van Hove scattering
function, a generalized one was deduced and the result was shown to be of greater potential utility than those previously
given in the literature. This expression gives a natural extension of the familiar Van Hove formula for scattering of slow
neutrons for the case in which the system under consideration is in a nonequilibrium state. The feasibility
of light and neutronscattering experiments to investigate the appropriate problems in real physical systems was
discussed briefly.
Since 1954 LEON VAN HOVE was a professor and Director of the Theoretical Physics Institute at the University of Utrecht in the Netherlands. In 1958, he was awarded the Francqui Prize on Exact Sciences. He studied the irreversible processes in manyparticle systems and investigated the derivation of the master equation by special perturbation technique.
He also known for his work on Van Hove Singularity.
A Van Hove singularity is a kink in the density of states (DOS) of a solid. The wavevectors at which Van Hove
singularities occur are often referred to as critical points of the Brillouin zone. (The critical point found in phase
diagrams is a completely separate phenomenon.) The most common application of the Van Hove singularity concept comes in
the analysis of optical absorption spectra. The occurrence of such singularities was first analyzed by
Van Hove in 1953 for the case of phonon densities of states.
L. Van Hove, "The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal,"
Phys. Rev. 89, 1189–1193 (1953).
In 1961, he received an invitation to become Leader of the Theory Division
at the CERN in Geneva, where he would spend three decades.
After coming to CERN
in 1961, he brought his experience in
statistical physics to bear on multiparticle
production. He emphasised the importance
of nonresonant particle production, and the
role of longitudinal phase space. He also
took an active interest in quarkgluon
plasma dynamics, particularly in the nonperturbative
transition from the plasma to
conventional hadrons, and maintained this
interest until his death. In all his work in
particle physics, he stressed the importance
of phenomenology in the quest for new
understanding.
Van Hove was leader of the CERN
theoretical physics division from 1961 to
1970, playing a key role in its formation and
orientation. He was subsequently chairman
of the Max Planck Institute for Physics and
Astrophysics in Munich from 1971 to 1974.
In 1976 he became research director general
of CERN and provided, together with Sir
John Adams, the visionary leadership that
brought the laboratory to the forefront of
high energy physics. He saw clearly the
physics opportunities provided by the SPS
protonantiproton collider project and took
a strong personal interest in its approval,
execution and subsequent success.
He also
laid essential groundwork for the approval
of LEP and its experimental programme.
His vital contribution to the development of
this laboratory still bears fruit today.
He continued to offer scientific leadership
in the decade after stepping down from the
director generalship of CERN, chairing the
scientific policy committee of ESA while a
dynamic new phase of its activity was being
planned, and helping to establish the joint
ESO/CERN symposia on astronomy, cosmology
and fundamental physics. Indeed,
the interface between particle physics and
cosmology was one of his active research
interests during his last few years, and
provided the subject of his last scientific
paper.
Van Hove was a man of great culture,
with a wide field of interest in art and
literature as well as the sciences. He was a
true European, speaking French, Flemish,
German and English fluently, and with a
university career spanning several countries.
He was a man of great honesty, who
expressed his opinions clearly and abhorred
trivialities. He never favoured his own
personal interest, and was always devoted to
the cause of science. His detachment and
objectivity, even close to the end, were
almost Olympian, but he had a keen awareness
of the needs of others. His humanity
found expression in the defence of those
weaker than himself, and even his readiness
to act the dinosaur in a CERN theory
division Christmas party play.
There are a few places where the biography of LEON VAN HOVE can be found.
Wikipedia electronic Encyclopedia(http://en.wikipedia.org/) , an article LEON VAN HOVE.
N. G. van Kampen, Leon Charles Prudent Van Hove, in: Royal Dutch Academy of Arts and Sciences. Obituaries, 1992.
The PDF file of this page: VanHove_Leon