
BIOGRAPHY OF Herbert Frohlich (1905  1991)
died Jan. 23, 1991, Liverpool, England. 
Herbert Frohlich (1905  1991) was an outstanding Germanborn British theoretical physicist and a Fellow of the Royal Society (1951). In 1927, Frohlich entered the LudwigMaximilians University, Munich, to study physics. He received his doctorate under Arnold Sommerfeld, in 1930. His first position was as Privatdozent at the University of Freiburg. Due to prewar difficulties in Germany and at the invitation of Yakov Frenkel, Frohlich went to the Soviet Union, in 1933, to work at the Ioffe PhysicoTechnical Institute in Leningrad. He went to England in 1935. Except for a short visit to Holland and a brief internment during World War II, he worked in Nevill Francis Mott’s department, at the University of Bristol, until 1948, rising to the position of Reader. At the invitation of James Chadwick, he took the Chair for Theoretical Physics at the University of Liverpool.
From 1973, he was Professor of Solid State Physics at the University of Salford, however, all the while maintaining an office at the University of Liverpool, where he gained emeritus status in 1976 until his death. During 1981, he was a visiting professor at Purdue University. Herbert Frohlich was Honorary Degree Recipient Doctor of Science, Purdue University in 1981.
Herbert Frohlich was an outstanding twentiethcentury physicist who made important contributions to many fields: nuclear forces and meson theory (with the prediction of entirely new particle states), a bilocal extension of the Dirac theory of fundamental particles and quantum mechanics, dielectric loss and breakdown, the theory of metals, 'hot' electron physics, superfluids and the macroscopic quantum state. He is most famous for providing the first successful explanation of superconductivity as the result of an electronphonon interaction.
H. Frohlich is a cofounder of the microscopic theory of the lowtemperature superconductivity.
He published a few seminal papers:
1. Theory of the Superconducting State. I. The Ground State at the Absolute Zero of Temperature
Phys. Rev. 79, 845–856 (1950)
Abstract.
In Bloch's theory of electronic conductivity the scattering of
electrons by lattice vibrations is connected with the absorption
or emission of vibrational quanta. As in field theories this gives
rise to a selfenergy which can be calculated by application of
perturbation theory. The most interesting term as a result of the
Pauli principle has the form of an interaction between electrons
in momentum (k) space. The interaction between two electrons
whose energy difference is small compared with their energy has
a most interesting angular dependence. Roughly speaking, it is
repulsive for equal energies but different directions of k, and
attractive otherwiso. If strong enough it leads in the ground state
to a distribution in momentum space which is different from the
normal (Fermi) distribution. If this is the case then excited states
exist in which some (\Delta Z} electrons in view of their interaction in
momentum space are concentrated in a narrow region in kspace.
These states are stable in the sense that it requires energy to
remove one of the electrons. Their energies are higher than the
ground state by a term proportional to (\Delta Z)^2.
The condition that the abovementioned ground state (identified
with the superconducting state) is realized requires that the interaction
between electrons and lattice vibrations exceeds a certain
value. With the help of the theory of high temperature conductivity,
this condition can be expressed in terms of the resistivity \rho
at O C. It is found that \rho n \nu^5/3 (1/n = atomic volume; \nu = number of
free electrons per atom) must exceed a value depending on universal
constants only. If \nu = 1 is assumed, all monovalent metals
except lithium do not satisfy the required condition, but most
superconductors do. The energy difference between the normal and
the superconducting state at absolute zero is about ms^2 (s = velocity
of sound) per electron. It has thus the correct magnitude corresponding
to a temperature of a fraction of a degree absolute.
No application to higher temperatures or to the influence of
external fields has been made yet.
2. On the Theory of Superconductivity: The OneDimensional Case.
Proc. Roy. Soc. Lond. A, 6 May 1954, vol. 223 no. 1154, p.296305..
Abstract.
The onedimensional case of free electrons interacting with lattice displacements is solved by a selfconsistent method.
It is found that for a certain range of the interaction parameter a single sinusoidal lattice displacement is strongly excited in the
lowest level of the system. Its wavelength is such as to create an energy gap in the singleelectron energy spectrum with all states below
it filled, and all above it empty. This periodic lattice displacement plays the role of an 'inner field' and leads to periodic fluctuation
in the electronic density in such a way that the two stabilize each other. In an infinite medium described by a periodic boundary condition
they are not fixed absolutely in space, but only relative to each other. Excitation of electrons across the gap leads to a decrease in both
the electronic density fluctuations and the width of the gap. The whole system, electrons plus lattice displacements, can move through the
lattice without being disturbed provided the velocity v is sufficiently small. The inertia of this system is equal to that of all electrons
augmented by a term due to the lattice displacements. Elastic scattering of individual electrons which normally leads to the residual
resistance is impossible if v is sufficiently small. The linear specific heat of normal electrons is eliminated and replaced by an exponential
term.
3. Isotope effect in superconductivity.
Proc. Phys. Soc. A 63, p.778 (1950).
(A short note which was related to two experimental papers:
C.A. Reynolds et al.
Superconductivity of isotopes of mercury.
Phys. Rev. 79, p.487 (1950).
E. Maxwell. Isotope effect in the superconductivity of mercury.
Phys. Rev. 79 p.477 (1950).)
He elaborated and developed further the concept of POLARON (bound electronphonon state  Frohlich polaron)
in ionic crystals.
A conduction electron in an ionic crystal or a polar semiconductor is the prototype of a polaron.
A polaron is a quasiparticle composed of a charge and its accompanying polarization field.
A slow moving electron in a dielectric crystal, interacting with lattice ions through longrange forces will permanently
be surrounded by a region of lattice polarization and deformation caused by the moving electron. Moving through the crystal,
the electron carries the lattice distortion with it, thus one speaks of a cloud of phonons accompanying the electron.
The induced polarization will follow the charge carrier when it is moving through the medium. The carrier together with the
induced polarization is considered as one entity, which is called a polaron.
Herbert Frohlich proposed a model Hamiltonian
for this polaron through which its dynamics are treated quantum mechanically (Frohlich electronphonon Hamiltonian).
For longwave longitudinal (optical) phonons this electronphonon interaction is characterized
by the dimensionless coupling constant \alpha.
For many ionic crystals the relation \alpha >> 1 holds. In this case the charge
carriers are dressed in a phonon cloud. These carriers are called polarons.
They may have a large radius (Rp >> a) (where a is the lattice constant), in which case they are large polarons
or a small one (Rp << a). Research on
large polarons began long before research on small polarons, on the conjecture
by Landau. The theory of large polarons was developed actively
by Pekar, N.N. Bogoliubov, S.V. Tyablikov, H. Frohlich, and later
R. Feynman.
see: H. Frohlich, "Electrons in lattice fields". Adv. Phys. 3, 325 (1954).
G.C. Kuper , G.D. Whitfield (eds.) "Polarons and Excitons". Oliver and Boyd, Edinburgh (1963).
Polarons in Ionic Crystals and Polar Semiconductors. J.T. Devreese (ed.),
Amsterdam, NorthHolland, (1972).
T.K. Mitra, Ashok Chatterjee and S. Mukhopadhyay, Polarons, Phys.Rep. Vol.153. P.91 (1987).
B. Gerlach and H. Lowen, Rev.Mod.Phys. Vol.63. P.63 (1991).
Polarons and Applications. V.D. Lakhno (ed.), New York: John Wiley and Sons, (1994).
H. Frohlich was a pioneer in introducing quantum field theory methods into solidstate physics. Indeed,
the concept of Frohlich polaron
basically consists of a single fermion interacting with a scalar Bose field of ion displacements.
H. Frohlich, H. Pelzer, and S. Zienau, Phil. Mag. 41, 221 (1950).
These innovative ideas were developed independently in a brilliant way by N.N. Bogoliubov and collaborators:
N. N. Bogolyubov, Ukrainian Math. Zhurnal 2, 3 (1950).
N. N. Bogolyubov, Fortschr. Physik 4, 1 (1961).
S. V. Tyablikov, Zh. Eksp. Teor. Fiz. 18, 1023 (1948).
S. V. Tyablikov, Dokl. Akad. Nauk USSR 6, 3 (1950).
S. V. Tyablikov, Dokl. Akad. Nauk SSSR 81, 31 (1951).
S. V. Tyablikov, Zh. Eksp. Teor. Fiz. 21, 17 (1951).
S. V. Tyablikov, Zh. Eksp. Teor. Fiz. 21, 377 (1951).
S. V. Tyablikov, Zh. Eksp. Teor. Fiz. 23, 381 (1952).
S. V. Tyablikov, Fiz. Tverd. Tela 3, 3445 (1961).
S. V. Tyablikov, Fortschr. Physik 4, 231 (1961).
V. A. Moskalenko, P. Entel and D.F. Digor. Phys.Rev. B. Vol.59. P.619 ( 1999).
For a review see the book:
N. N. Bogolyubov and N. N. Bogolyubov, Jr., Aspects
of Polaron Theory (Fizmatlit., Moscow, 2004) [in Russian].
Frohlich proposed a new fundamental idea which is known as a theory of Frohlich coherence.
Reference:
H. Frohlich, Long Range Coherence and Energy Storage in Biological Systems, Int. J. Quantum Chem., v.II, 641649 (1968)
Coherence is a matter of phase relationships, which are readily destroyed by almost any perturbation.
There are several distinct but very closely interrelated uses of the term "coherence" in physics:
'pure states' are coherent and manyparticle states may exhibit macrosopic quantum coherence.
Two of these share in common that a quantum wavefunction informs the evolution of a physical system as a whole.
The Frohlich effect is a paradigm of how quantum coherence can exist and play a physical role at biological scales.
Herbert Frohlich, one of the great pioneers in superstate physics, described a model of a system of coupled molecular
oscillators in a heat bath, supplied with energy at a constant rate. When this rate exceeds a certain threshold then a
condensation of the whole system of oscillators takes place into one giant dipole mode, similar to BoseEinstein
condensation. Thus, a coherent, nonlocal order emerges.
Because this effect takes place far from equilibrium, Frohlich coherence is in that sense related to the principles
underlying the laser (another pumped, coherent system).
But what can this coherence accomplish? Frohlich emphasized the lossless transmission of energy from one "mode" to another.
Frohlich published a few books and numerous reserch papers and review articles.
Books:
[1] Herbert Frohlich. Elektronentheorie der Metalle. (Struktur und Eigenschaften der Materie in Eigendarstellung, Bd.18). (Springer, 1936, 1969)
[2] Herbert Frohlich. Elektronentheorie der Metalle (Ann Arbor: Edwards Brothers, First US edition, in German, 1943) ISBN 1114566489
[3] Herbert Frohlich. Theory of Dielectrics: Dielectric Constant and Dielectric Loss (Clarendon Press, 1949, 1958)
[4] Herbert Frohlich and F. Kremer. Coherent Excitations in Biological Systems (SpringerVerlag, 1983)
[5] Herbert Frohlich, (ed.) Biological Coherence and Response to External Stimuli (Springer, 1988) ISBN 9780387187396
Bibliography:
[1] T. W. Barrett and H. A. Pohl, Energy Transfer Dynamics: Studies and Essays in Honor of Herbert
Frohlich on His Eightieth Birthday (SpringerVerlag, (1987)) ISBN 9783540175025
[2] G.J. Hyland and P. Rowlands (eds), Herbert Frohlich FRS: A Physicist Ahead of his Time.
(University of Liverpool (2006), 2nd edition (2008).) ISBN 9780906370575
This book describes Herbert Frohlich's
holistic outlook which led him to the brilliantly daring introduction of the
concepts of modern theoretical physics, in particular that of coherence, into the open, dissipative
systems encountered in biology. The potentially massive significance of this development is only now being fully
considered.
The Symposium brought together physicists and biologists, particularly those who either knew Frohlich personally or
collaborated with him at some stage during his long and illustrious life, not only to reflect on past glories,
but also to evaluate the impact of his legacy on present developments in physics and biology. To this end, ten invited
speakers covered the different fields in which Frohlich contributed to significantly to our understanding, thereby
influencing future developments.
There are a few places where the biography of Herbert Frohlich can be found. Wikipedia electronic Encyclopedia(http://en.wikipedia.org/) , an article Herbert_Frohlich.