Upper Bounds on Bogolubov’s Inner Product: Quantum Systems of Anharmonic Oscillators
Conference paper
Abstract
An upper bound on the so-called Bogolubov Inner Product for creation and annihilation bose operators is obtained in the case of certain quantum systems of anharmonic oscillators as a straightforward application of domination of semigroups.
Keywords
Selfadjoint Operator Anharmonic Oscillator Trace Inequality Inner Product Grand Canonical Partition Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- [C-S]M. Corgini, and D.P. Sankovich, Rigorous estimates for cor-relation functions and existence of phase transitions in some models of interacting Bosons, Intl. J. of Mod. Phys. B 11 (28) (1997), 3329–3341.ADSCrossRefGoogle Scholar
- [C-S-T]M. Corgini, D.P. Sankovich, N.I. Tanaka, On a nonideal Bose gas model. Gaussian domination and Bose condensation, Theoret. and Math. Phys. 120 (1) (1999), 130–143.MathSciNetGoogle Scholar
- [H-S-U]H. Hess, R. Schrader, D. Uhlenbruck, Domination of semi-groups and generalization of Kato’s inequality, Duke Math. J. 24 (4) (1977), 893–904.CrossRefGoogle Scholar
- [R-S]M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vols. II, IV, Academic Press, New York, 1975, 1978.Google Scholar
- [C-F-K-S]H. Cycon, R. Froese, W. Kirsch, B. Simon, Schrödinger Op-erators with Applications to Quantum Mechanics and Global Geometry, Springer-Verlag, New York, 1987.Google Scholar
- [BOG]N. N. Bogolubov, The theory of superconductivity, Phys. Abh. S. U. 1(1962), p. 113.Google Scholar
- [K]T. Kato: Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966.MATHGoogle Scholar
Copyright information
© Springer Science+Business Media New York 2000