On Lieb's conjecture for the Wehrl entropy of Bloch coherent states

Communications in Mathematical Physics

Volumn 207, Issue 2, 1999, Pages 481-493

  Schupp, Peter ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033517596     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050734     Document Type: Article

References (17)

1. Anderson, A., Halliwell, JJ.: Information-theoretic measure of uncertainty due to quantum and thermal fluctuations. Phys. Rev. D 48, 2753-2765 (1993)
2. Beckner, W.: Inequalities in Fourier analysis. Ann. of Math. 102, 159-182 (1975)
3. Brascamp, H.J., Lieb, E.H.: Best constants in Young's inequality, its converse, and its generalization. Adv. in Math. 20, 151-173(1976)
4. Grabowski, M.: Wehrl-Lieb's inequality for entropy and the uncertainty relation. Rep. Math. Phys. 20, 153-155 (1984)
5. Joint work with B. Jurčo
6. Lieb, E.H.: Proof of an entropy conjecture of Wehrl. Commun. Math. Phys. 62, 35-41 (1978)
7. Lieb, E.H.: Coherent states as a tool for obtaining rigorous bounds. In: Feng, D.H., Klauder, J. (eds.) Coherent states: Past, present, and future. Proceedings, Oak Ridge, Singapore: World Scientific, 1994, pp. 267-278
8. Lieb, E.H.: Some convexity and subadditivity properties of entropy. Bull. Am. Math. Soc. 81, 1-13 (1975)
9. Lieb, E.H.: Gaussian kernels have only Gaussian maximizers. Invent. Math. 102, 179-208 (1990)
10. Lieb, E.H.: Integral bounds for radar ambiguity functions and Wigner distributions. J. Math. Phys. 31, 594-599 (1990)
11. Lieb, E.H., Loss, M.: Analysis. Graduate Studies in Mathematics, 14, Providence, R.I.: American Mathematical Society, 1997
12. Peřina, J., Hradil, Z., Jurčo, B.: Quantum optics and fundamentals of physics. Fundamental Theories of Physics, 63, Dordrecht: Kluwer Academic Publishers Group, 1994
13. Radcliffe, J.M.: Some properties of coherent spin states. J. Phys. A 4, 313-323 (1971)
14. Joint work with W. Spitzer
15. Thomas, L.E., Villegas-Blas, C.: Asymptotic of Rydberg states for the hydrogen atom. Commun. Math. Phys. 187, 623-645 (1997)
16. Wehrl, A.: On the relation between classical and quantum mechanical entropy. Rept. Math. Phys. 16, 353-358 (1979)
17. Zhang, W.-M., Feng, D.H., Gilmore, R.: Coherent states: Theory and some applications. Rev. Mod. Phys. 62, 867-927 (1990)