Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T14:06:04.568Z Has data issue: false hasContentIssue false
  • English
  • Français

On a quantum mechanical model for a maser I†

Published online by Cambridge University Press:  24 October 2008

Martin Hasler
Martin Hasler
Affiliation:
Bedford College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

The model is closely connected with a model by Lamb and Scully (10). Atoms described as two-level systems, initially in an incoherent superposition of the two levels, interact successively during a time T with an electromagnetic field of which only one mode is taken into consideration. In the limit as infinitely many atoms have interacted, it is shown that the field either approaches a thermal distribution or is excited to arbitrarily high Photon numbers according to whether or not the lower level of the atoms is initially more probable than the upper level. It is also shown that in any case the correlations between pure Photon number states converge to 0. If the atoms are initially in the upper level it is proved that the Photon number grows roughly as the square root of the number of atoms that have interacted. Throughout the discussion number-theoretical properties of T play a disturbing role. The last mentioned result in fact depends on a sharp (but arbitrary) value for T and is therefore disqualified for physical interpretation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 2 , March 1976 , pp. 351 - 371
Copyright
Copyright © Cambridge Philosophical Society 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Cassels, J. W. S.An introduction to diophantine approximation (Cambridge Tracts in Mathematics and Mathematical Physics, University Press, Cambridge, 1957).Google Scholar
(2)Cassels, J. W. S.Some metrical theorems of diophantine approximation II. J. London Math. Soc. 25 (1950).Google Scholar
(3)Chung, K. L.Markov chains with stationary transition probabilities (Springer; Berlin-Heidelberg-New York, 1960).CrossRefGoogle Scholar
(4)Doob, J. L.Stochastic processes (Wiley; London-New York, 1950).Google Scholar
(5)Feller, W.An introduction to probability theory and its applications I. (Wiley; London-New York, 1950.)Google Scholar
(6)Gnedenko, B. V. and Kolmogorov, A. N.Limit distributions for sums of independent random variables (Addison-Wesley; London, 1954).Google Scholar
(7)Hasler, M. Ueber ein quantenmechanisches Masermodell. Thesis, ETH Zürich, 1973, unpublished.Google Scholar
(8)Kato, T.Perturbation theory for linear operators (Springer; Berlin-Heidelberg-New York, 1966).Google Scholar
(9)Kemeny, J. G., Snell, J. L. and Knapp, A. W.Denumerable Markov chains (Van Nostrand; Princeton, 1966).Google Scholar
(10)Lamb, W. E. and Scully, M. O.Quantum theory of an optical maser I. Phys. Rev. 159 (1967).Google Scholar
(11)Leveque, W. J.On the frequency of small fractional parts in certain real sequences III. J. Reine Angew. Math. 202 (1959).Google Scholar