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(Note: This brief obituary is based in part on an article by Erkki Pajanne and Stig Stenholm that will appear in the journal Arkhimedes (in Finnish), and with much additional material by Ray Bishop.)
We are sad to report that our friend and colleague Jouko Sakari Arponen passed away on 1st February of this year at the age of 63, after having endured a long and debilitating illness.
Jouko was born in Jääski, Finland on 12th September 1942, and graduated from the coeducational school in Myllykoski in 1961. He was admitted the same year as an undergraduate into the University of Technology in Otaniemi, Finland, where he stayed on to do his PhD. He passed all of his examinations there with the highest grades and received his doctorate in 1970, nine years after entering. His thesis entitled “On the theory of positron annihilation in an electron gas” was supervised by Academician Pekka Jauho.
In the course of his PhD Jouko worked during the period 1965-68 as an Assistant in physics, and afterwards he completed his doctoral studies by spending two years in Copenhagen at the Institute for Theoretical Physics, NORDITA. The rest of his active scientific life was spent alternating between various teaching and research positions at the University of Technology and the University of Helsinki. He officially retired aged 60 on the grounds of ill health on 30th June 2003.
Jouko was appointed to a permanent Lectureship in quantum mechanics at the University of Technology in 1973 and to a similar position in theoretical physics at the University of Helsinki in 1975. He taught numerous courses in physics, usually at an advanced level, including quantum mechanics, theoretical many-body physics and statistical physics. He wrote an extensive textbook on statistical physics (Limes, 1994) that is still used as a part of the physics curriculum at his former two Universities. Jouko was much appreciated by both his colleagues and by his students as a clear and inspiring lecturer. One could guarantee that the material that he presented in all of his courses would be carefully selected and delivered with the utmost attention to detail. Although his courses were often intellectually very demanding for his audience, the students almost always ended with a deep and thorough understanding of the material.
Over the roughly 30 years of his scientific activity, Jouko Arponen published some 50 extensive and original articles in physics journals. His papers can roughly be divided into two main groups. The first centres largely on “positron physics” and the second on “formal techniques of quantum many-body theory.” Jouko became very well known in both fields, in each of which he had the reputation of producing rigorous and original results that have stood the test of time. He rapidly became a well-respected and leading theorist in both communities.
During the first period (1970-86) Jouko worked mainly at the Research Institute of Theoretical Physics (TFT) at the University of Helsinki, largely in a close and productive collaboration with Erkki Pajanne. Together they studied the so-called boson formalism of interacting fermions, concentrating on the electron gas approximation of metals, which was then the best studied of all quantum many-body problems. The basic idea was to express the fermionic Hamiltonian as a finite Hamiltonian of interacting bosons, where the bosons themselves describe electron-hole pairs. The boson formulation as such was not a new idea, but the earlier works (e.g. in nuclear physics) had produced an expansion in infinite series of boson operators, for which systematic truncation schemes had been difficult to formulate. Jouko’s novel idea, which turned out to be a very powerful one, was to use as a starting-point the random phase approximation (RPA) of Bohm and Pines. As is well known, the RPA is well defined and already includes part of the electron-electron interaction. More specifically, it corresponds to the summation of ring diagrams to all orders in the usual fermionic perturbation theory, and it becomes exact in the non-perturbative high-density regime.
In the bosonic mapping used by Jouko the RPA amounted to a model of non-interacting bosons. The Hamiltonian of the non-interacting boson system is just the much earlier Sawada Hamiltonian, which was itself known to be equivalent to the RPA. The remaining residual interactions between the bosons were dealt with in bosonic perturbation theory. Jouko’s procedure for bosonisation of the fermion problem differed fundamentally from those of previous authors by being firmly anchored on a detailed study of the perturbation theory diagrams of the original fermionic problem. His procedure was formulated so that the individual bosonic perturbation theory diagrams corresponded to the exact summation of certain well-defined sets of fermionic diagrams in the unmapped original problem. One of the great merits of this bosonisation procedure was that one could, in an effective and efficient manner, calculate expectation values of various operators. This was especially useful in the case of a light impurity (such as a positron) in metals, for which many experimental results are also available. The numerical calculations could usually be confined to relatively low-order approximations (such that only a few bosons were needed), and improvement was obtained in a systematic and controlled way.
In the course of his extensive investigations of the electron gas Jouko first became acquainted around 1980 or so with the well-known coupled cluster method (CCM) of microscopic quantum many-body theory. Thus, for example, in his earliest use of the CCM, the exact ground-state wave function of the electron gas was expressed as |Ψ> = eS |ΦRPA>, where the model or starting (“uncorrelated”) wave function |ΦRPA> corresponds to the exact RPA ground state of non-interacting Sawada bosons, and the CCM correlation operator, S ≡ ∑m Sm, is composed of partitions Sm formed from the products of m creation operators for interacting Sawada (or RPA) bosons.
CCM calculations are typically performed at the so-called SUBn level of approximation where all m-body partitions Sm of the many-body correlation operator S with m ≤ n are retained, but all interactions with larger subsystems described by amplitudes Sm with m > n are neglected. CCM calculations of the electron gas using the SUB2 approximation and beyond had been performed previously by earlier authors in the original fermionic scheme. Jouko’s novel contribution was to use the CCM on his equivalent bosonic Hamiltonian discussed above. Thus, the fermion system was first bosonised according to the Dyson transformation, and then the Sawada (RPA) canonical transformation among the bosons was performed before using the normal CCM SUB2 scheme. This had the very clever effect that, since the RPA transformation had already been performed at the zeroth-order level of the starting approximation |ΦRPA> for the model or “uncorrelated” wave function, the bosonic SUB2 scheme summed not only all of the fermionic SUB2 graphs of Goldstone many-body perturbation theory, but also a huge number of graphs coming from higher-order fermionic clusters Sn with n > 2.
After this early foray into the CCM, almost all of Jouko’s remaining publications were concerned with the second of the two main themes of his scientific work, viz., that connected with formal techniques of quantum many-body theory. He became particularly interested in the formal properties of the CCM, and in the course of his analysis made some profound developments of the method. He showed how the CCM could be placed on a proper variational (or, more precisely, bi-variational) footing, using the Rayleigh-Ritz principle for the ground-state energy. He first made contact with the conventional CCM, or what henceforth became known as the normal CCM (NCCM), and showed how it could be formulated in such a way that the ground-state expectation values of arbitrary operators could be calculated systematically in a way that was fully consistent with the very important Hellmann-Feynman theorem at all levels of approximation. This was itself a real breakthrough since prior attempts, based largely on diagram analysis, had been problematical. Even more importantly, it showed how to generalise the method to treat time-dependent phenomena by extending the variational principle to one for the action. This opened up the method to a much larger arena, allowing one to calculate, for example, the linear (or, indeed, nonlinear) static or dynamic response of a system to external perturbations.
He also showed how the method could be extended at a very deep level to what has since become known as the extended CCM (ECCM). In both the NCCM and the ECCM the Hilbert (or Fock) space of the interacting many-body system is parameterised in terms of two formally independent sets of cluster amplitudes, one each for the ket states and bra states. The ket-state operator encapsulating these amplitudes in both variants is the linked-cluster operator S above. Jouko showed how the corresponding bra-state operator in the NCCM did not satisfy the cluster property, and thus contained unlinked Goldstone diagrams in its expansion. Although this led to no extensivity problems for many-body expectation values, Jouko realised that there could be both formal and practical advantages for a scheme in which all of the fundamental amplitudes obeyed the cluster property. This led him to formulate the ECCM as a method which shared all of the advantages and pleasant properties of the NCCM, but which repaired what he saw as its primary formal shortcoming.
From this point on, in the second period of his research career, Jouko began an extensive collaboration with Ray Bishop in Manchester that lasted some ten years (1984-1994). During this period they investigated the properties of both the NCCM and ECCM and applied them to various physical systems. They showed, for example, that although the ECCM at the SUBn level of approximation can be specified exactly in terms of (vast sets of) Goldstone perturbation theory diagrams, the degree of renormalisation was, perhaps uniquely for any such method, high enough to be able to describe strong qualitative changes in the ground state, such as phase transitions. They also showed how the new formalism could be interpreted, very intriguingly and very deeply, as an exact bosonisation of the original quantum many-body system in which the concept of bosonisation is carried to its logical extreme, viz., where the resulting generalised coherent boson states are identifiable with classical fields. The increased degree of locality of the basic ECCM (bra-state) amplitudes over their NCCM counterparts thus opens up applications to such important themes in quantum field theory and quantum many-body theory as topological excitations and to situations where a particular symmetry is spontaneously broken.
Among many other results from this collaboration, they showed how the ECCM could be applied both to excited states to give a consistent hierarchy of generalisations of the RPA, and to give a fully microscopic derivation of the hydrodynamics of strongly-interacting condensed Bose fluids at zero temperature. In a further series of papers they showed how the configuration-interaction method (or many-body shell model), the NCCM and the ECCM form a rather natural hierarchy of formulations of increasing sophistication for describing interacting systems of quantum-mechanical particles or fields. They denoted these methods generically as independent-cluster parameterisations in view of the way in which they incorporate the many-body correlations via sets of amplitudes that describe the various correlated clusters within the fully interacting system as mutually independent entities. They showed how the members of the triad differ primarily by the way in which they incorporate the exact locality and separability properties. They investigated in great detail both the algebraic structure of the underlying classical mappings represented by each member of the triad and the geometrical structure of each of the associated phase spaces.
One of Jouko’s greatest strengths became increasingly apparent during this period, namely his incredibly deep and intuitive understanding of many-body perturbation theory that, in our view, has possibly never been surpassed by any other theorist anywhere. Although the NCCM is able to sum large subsets of the Goldstone diagrams of quantum many-body perturbation theory, Jouko realised early on that it does not take full advantage of the so-called generalised time-ordering technique. Central to his description of the ECCM was a careful analysis of the structure of Goldstone diagrams, where he showed that all diagrams could be grouped into classes represented by partially ordered trees. Although his methodology was firmly based on the variational principle, the various CCM operators had no obvious a priori description in terms of perturbation theory. Nevertheless, although it was formally quite unnecessary to do so, Jouko also realised the value in establishing the possible connections of his formulation of the CCM with more conventional methods such as diagrammatic expansions. This eased the acceptance of the methodology into the wider many-body community, where it both invoked considerable interest and led to Jouko being invited to many meetings to present his results.
Although his health had prevented him from travelling in recent years, he was usually present in spirit at many of the quantum many-body theory and related meetings, at which his work was often discussed. Although Jouko’s last journal publication was in 1997, it is particularly fitting that his very last paper to appear in print was as part of a proceedings volume entitled 150 Years of Quantum Many-Body Theory: A Festschrift in Honour of the 65th Birthdays of John W. Clark, Alpo J. Kallio, Manfred L. Ristig, and Sergio Rosati, that formed the proceedings of a meeting held in Manchester, UK in July, 2000. Despite the fact that his health was already so poor that he could not attend this meeting to help celebrate the scientific careers of four of his friends and colleagues, he submitted an especially apposite and insightful article to the volume entitled “Diagrams are a Theoretical Physicist’s Best Friends.”
On the professional front there is no doubt that the depth and breadth of Jouko’s knowledge of theoretical and mathematical physics was impressive. This made him a formidable theorist and an excellent choice of collaborator. It was typical of him that no detail in an article under preparation, whether theoretical, numerical or grammatical, escaped his keen eye. His collaborators well recall that the choice of every word and every comma of every publication was debated at length for maximal clarity and accuracy. We think that this characteristic of Jouko’s to strive constantly for perfection may partly explain his relatively modest scientific output when considered purely in terms of the total number of his publications. On the other hand, it is also responsible for the fact that all of his works are models of clarity, many of which repay re-reading many times over due to their depth and profundity. None of his works are derivative or slight. We feel sure that they will outlive Jouko by many years to come, and that they offer a fit and proper testament to him.
On the more personal front, we recall that one of Jouko’s lifelong hobbies was music. He sang actively during his years of study in a student choir and his favourite composer was Gustav Mahler, whose songs and technically brilliant symphonies were particularly to Jouko’s taste. Some of the foremost characteristics of Jouko Arponen that all who came into contact with him soon learned were his absolute integrity and honesty as a scientist and his helpfulness as a friend. We remember with fondness and affection too his dry wit, warm humour, and all of those other personal characteristics that made him such an excellent companion.
It is deeply regrettable that the early weakening of his health limited so strongly his overall activity, for it is certain that he had much more to offer the worldwide physics community had he been able to work longer. It is fortunate, however, that he obtained from both his scientific work and his family the strength, pleasure and support to go on for as long as he did.
We, his friends and colleagues, miss Jouko Arponen very much. His loss will be felt too by the wider physics community, especially by those working in the field of quantum many-body theory, who knew and greatly respected him both as a man and as a talented theoretical physicist. He is survived by his wife Outi and by his three children Antti, Heikki and Anni, to whom we offer our heartfelt condolences.
10th April 2006 Ray Bishop, Erkki Pajanne, Stig Stenholm |
