Statistical Theory of the Energy Levels of Complex Systems. V
1.F. J. Dyson, J. Math. Phys. 3, 140, 157166, 1191and 1199 (1962), quoted in what follows as I, II, III, BMM and TW respectively;
1.F. J. Dyson and M. L. Mehta, J. Math. Phys. 4, 701 (1963) is quoted as IV.
2.K. Wilson, J. Math. Phys. 3, 1040 (1962).
3.The determinant (3) is called a “confluent alternant,” since it is obtained as a limiting form of the simple alternant Det when the become equal in pairs. For a proof that the confluent alternant is equal to Eq. (1) with see H. W. Segar, Messenger of Mathematics 22, 57 (1893).
4.J. Gunson, J. Math. Phys. 3, 752 (1962).
5.M. Gaudin, Nucl. Phys. 25, 447 (1960).
6.Peter B. Kahn, “Energy‐Level Spacing Distributions,” Brookhaven preprint, No. 6392.
7.M. L. Mehta, Nuclear Phys. 18, 395 (1960);
7.M. L. Mehta and M. Gaudin, Nuclear Phys. 18, 420 (1960)., Nucl. Phys.
8.M. L. Mehta, Nucl. Phys. 18, 395 (1960), and other references given there.
8.See also N. G. de Bruijn, J. Ind. Math. Soc. 19, 133 (1955); we are very sorry that we came to know of this important reference only recently.
9.M. Gaudin (private communication).
10.T. J. Stieltjes, Sur Quelques Théorèmes d’Algèbre, Oeuvres Complètes 1, 440–441 (P. Noordhoff Ltd., Groningen, The Netherlands, 1914).
11.This result is contained in an unpublished manuscript of Professor E. P. Wigner. We are grateful to Professor Wignei for permission to quote from his unpublished work.
12.J. E. Mayer and M. G. Mayer, Statistical Mechanics, (John Wiley & Sons, Inc., New York, 1940).
13.E. P. Wigner, Ann. Math. 62, 548 (1955).
14.H. Weyl, The Classical Groups, Their Invariants and Representations (Princeton University Press, Princeton, New Jersey, 1939).
15.B. A. Rozenfel’d, Doklady Akad. Nauk S.S.S.R. 106, 600 (1956).
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