On the representation of linear operators in L2 spaces by means of ''generalized matrices''
This paper concerns the representation of linear operators of L2 spaces by means of ''generalized matrices'' as it is usual, following Dirac, in quantum mechanics and in electronics. The known possibi...
This paper concerns the representation of linear operators of L2 spaces by means of ''generalized matrices'' as it is usual, following Dirac, in quantum mechanics and in electronics. The known possibi...
Quantization of the Liouville mechanics for systems with singular Lagrangians
Quantum mechanics, in phase space formulation, is directly deduced from the Liouville mechanics by a correspondence principle. The latter is applied to systems with singular Lagrangians.
Quantum mechanics, in phase space formulation, is directly deduced from the Liouville mechanics by a correspondence principle. The latter is applied to systems with singular Lagrangians.
Entropy of an n-system from its correlation with a k-reservoir
J. Math. Phys. 19, 1028 (1978); doi:10.1063/1.523763
Issue Date: May 1978
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Let a random pure state vector be chosen in nk-dimensional Hilbert space, and consider an n-dimensional subsystem's density matrix P. P will usually be close to the totally unpolarized mixed state if k is large. Specifically, the rms deviation of a probability from the mean value 1/n is [(1−1/n2)/(kn +1)]1/2. ''Random'' refers to unitarily invariant Haar measure.
Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
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REFERENCES (4)
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- Lucretius, On the Nature of the Universe, translated by R. E. Latham (Penguin, Toronto, 1951), p. 66.
- L. D. Landau,
Z. Physik 45, 430 (1927) ; - or J. Von Neuman, Mathematical Foundations of Quantum Mechanics, translated by R. Beyer (Princeton U.P., Princeton, N.J., 1955), Sec. VI. 2.
- Adapted from I.S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 369, or induction through integration by parts.
- This extreme, pure-case answer
= n−1(n−1)1/2 coincides with the specialization to k = 1 of Eq. (1), because k = 1 1 forces purity by eliminating the reservoir. This is another check of (l).
