научная статья по теме REMEMBERING YAKOV ABRAMOVICH SMORODINSKY Физика

Текст научной статьи на тему «REMEMBERING YAKOV ABRAMOVICH SMORODINSKY»

HUEPHAH 0H3HKA, 2009, moM 72, № 5, c. 927-928

= IN MEMORY OF YAKOV ABRAMOVICH SMORODINSKY =

REMEMBERING YAKOV ABRAMOVICH SMORODINSKY

© 2009 F. Calogero*

Dipartimento di Fisica, University di Roma "La Sapienza", Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy

Received October 14, 2008

PACS: 01.60.+q

This is a very brief contribution reflecting my intervention at the Conference on Symmetries in Physics held from 27-29 March 2008 and dedicated to Yakov Abramovich Smorodinsky on the 90th anniversary of his birth.

I met Yakov Abramovich, probably more than thirty years ago, in Dubna, where I came more than once in the context of my collaboration with Yuri Simonov and his wife Alla Badalyan, on the approach to nuclear physics based on the expansion of the many-nucleon wave function in hyperspherical harmonics. At the time contacts among scientists living in the Soviet Union and those of us living in the "capitalist world" were still quite complicated: my visits to the Soviet Union were certainly carefully monitored by the KGB, and had to respect many rules, most of which I was supposed to ignore as they were meant to constrain the behavior of my Russian colleagues. As a consequence, social contacts with my fellow physicists were, as a rule, difficult, although this did not prevent me — and my family, when we spent the academic year 1969—1970 in Moscow — to develop a strong and lasting bond of friendship with a few colleagues who were prepared to take some risks and ignore the rules which were indeed primarily meant just to prevent such friendships to flourish. Having become at least partly aware and accustomed to this situation, I was rather surprised and greatly heartened by the friendly and open disposition of Yakov Abramovich, when I met him for the first time in Dubna: he immediately invited me for dinner to his home, where I met his family and enjoyed a warm and most cordial hospitality. His conversation was moreover quite fascinating, due to the very broad range of his interests, in science and, even more so, in just about every field of intellectual endeavour; and the freedom from any ideological conformity which he displayed in these interactions was remarkable and unusual. I seem to remember that he was particularly

E-mail: francesco.calogero@roma1.infn.it, frances-

co.calogero@uniroma1.it

interested in literature, especially the contemporary literature in the rest of the world which was difficult to access in the Soviet Union, where foreign writers were translated, and even published in their original language, but only if they passed some test of ideological acceptability to the Soviet regime. Indeed I remember that Yakov Abramovich did not hesitate to offer me a kind of bargain: I was to provide him with literary works (mainly new novels in English), and he would in exchange give me art books, of which there was a good, and relatively inexpensive, production in Russia, albeit to have access to it generally required having good relations with the official artistic and publishing establishments; connections which Yakov Abramovich evidently did master. As it happens, circumstances — including probably my laziness — did not allow our bargain to flourish, and I became particularly sorry for this when I got the sorry news of his untimely death.

I am happy to take part in this meeting, paying thereby my tribute to the memory of an individual remarkable both for his scientific achievements and for his congenial personality.

As for the scientific substance of my contribution to this conference, I reported recent findings obtained in collaboration with Francois Leyvraz. Since these results are already published — see [1] as well as Section 5.5 of the monograph [2] — I limit my report of them here to an extremely terse description of their essence.

Taking as starting point the Hamiltonian describing the most general many-body problem respecting overall translation invariance, we have shown how it is possible to manufacture a modified (albeit not too different) Hamiltonian depending on a positive parameter T (which can be chosen arbitrarily, and is, dimensionally, a time). This modified Hamiltonian features — in the classical context — the following two properties:

(i) Starting from generic initial data, the dynamics yielded by the modified Hamiltonian is — up to a

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rescaling of the independent variable ("time") by a constant real factor (which might, however, have either sign) — essentially identical to that yielded by the original (unmodified, "realistic") Hamiltonian, over times which are short with respect to T, t < < T (but let us re-emphasize that T can be assigned arbitrarily).

(ii) The time evolution yielded by the modified Hamiltonian is isochronous with period T, namely, from any initial data it yields closed trajectories in phase space, periodic in all degrees of freedom with period T.

The simultaneous validity of these two properties has obviously remarkable implications, especially re-

garding the statistical mechanics and thermodynamics associated with these Hamiltonians.

We have also shown that, in the quantal context, the modified Hamiltonian features an (infinitely degenerate) equispaced spectrum, consistently with its property of isochrony.

REFERENCES

1. F. Calogero and F. Leyvraz, New J. Phys. 10, 023042 (2008).

2. F. Calogero, Isochronous Systems (Oxford University Press, Oxford, 2008).

aflEPHAa OH3HKA tom 72 № 5 2009

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