Abstract
We introduce a technique to compare different, but related, quantum systems, thereby generalizing the way that coherent states are used to compare quantum systems to classical systems in semiclassical analysis. We then use this technique to estimate the dependence of the free energy of the quantum Heisenberg model on the spin value, and to estimate the relation between the ferromagnetic and antiferromagnetic free energies.
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References
ArecchiF. T., CourtensE., GilmoreR., and ThomasH., Atomic coherent states in quantum optics, Phys. Rev. A 6, 2211–2237 (1972).
BargmannV., On a Hilbert space of analytic functions and an associated integral transform, part 1, Comm. Pure Appl. Math. 14, 187–214 (1961).
BargmannV., On a Hilbert space of analytic functions and an associated integral transform, part 2, Comm. Pure Appl. Math. 20, 1–101 (1967).
BerezinF. A., Izv. Akad. Nauk SSSR Ser. Mat. 36(5), 1134–1167 (1972). English translation: Covariant and contravariant symbols of operators. Math. USSR-Izv. 6(5), 1117–1151 (1972) and F. A. Berezin. General concept of quantization, Comm. Math. Phys. 40, 153–174 (1975).
FengD. H., GilmoreR., and ZhangW-M., Coherent states: Theory and some applications, Rev. Mod. Phys. 62, 867–927 (1990).
KlauderJ. R., The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbers, Ann. Phys. 11, 123 (1960).
KlauderJ. R., and SkagerstamB-S., Coherent States, World Scientific, Singapore, 1985.
LiebE. H., The classical limit of quantum spin systems, Comm. Math. Phys. 31, 327–340 (1973).
LiebE. H., Proof of an entropy conjecture of Wehrl, Comm. Math. Phys. 62, 35–41 (1978).
PerelomovA., Generalized Coherent States and their Applications, Springer-Verlag, New York, Berlin, Heidelberg, 1986.
SchrödingerE., Der stetige übergang von der Mikro-zur Makromechanik, Naturwiss. 14, 664–666 (1926).
SegalI. E., Mathematical characterizations of the physical vacuum for the linear Bose-Einstein fields, Illinois J. Math. 6, 500–523 (1962).
SimonB., The classical limit of quantum partition functions, Comm. Math. Phys. 71, 247–276 (1980).
ThirringW. E., A lower bound with the best possible constant for Coulomb hamiltonians, Comm. Math. Phys. 79, 1–7 (1981).
WehrlA., On the relation between classical and quantum-mechanical entropy. Rep. Math. Phys. 12, 385 (1977).
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Work supported in part by the U.S. National Science Foundation grant PHY-9019433.
Work supported in part by the U.S. National Science Foundation grant DMS-9002416.