Centre de diffusion de revues académiques mathématiques


Séminaire Équations aux dérivées partielles (Polytechnique)

Table des matières de ce volume | Article précédent | Article suivant
Jan Dereziński
Fermi Golden Rule, Feshbach Method and embedded point spectrum
Séminaire Équations aux dérivées partielles (Polytechnique) (1998-1999), Exp. No. 23, 11 p.
Article PDF | Analyses MR 1721341 | Zbl 1055.81530

Résumé - Abstract

A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jak${\check{\rm s}}$ić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.


[AC] Aguilar, J., Combes J.M.: A class of analytic perturbations for one-body Schrödinger Hamiltonians, Commun. Math. Phys. 22, 269 (1971). Article |  MR 345551 |  Zbl 0219.47011
[AH] Arai, A, Hirokawa, M.: On the existence and uniqueness of ground states of the spin-boson Hamiltonian, J. Func. Anal. 151, 455 (1997).  MR 1491549 |  Zbl 0898.47048
[BFS1] Bach, V., Fröhlich, J., Sigal, I.: Quantum electrodynamics of confined non-relativistic particles, Adv. Math. 137 (1998), 299-395  MR 1639713 |  Zbl 0923.47040
[BFSS] Bach, V., Fröhlich, J., Sigal, I., Soffer, A.: Positive commutators and spectrum of non-relativistic QED, preprint.
[BC] Balslev, E., Combes, J.-M.: Spectral properties of many-body Schrödinger operators with dilation analytic interactions, Comm. Math. Phys. 22, 280 (1971). Article |  MR 345552 |  Zbl 0219.47005
[BG] Boutet de Monvel, A., Georgescu, V.: Boundary values of the resolvent of a self-adjoint operator: Higher order estimates, in: Boutet de Monvel, A., Marchenko, V., eds, Algebraic and Geometric Methods in Mathematical Physics, 9-52, Kluwer Academic Publishers 1996.  MR 1385675 |  Zbl 0917.47022
[BR] Bratteli, O., Robinson, D.: Operator algebras and Quantum Statistical Physics 2, 2nd ed. Springer, 1997  MR 1441540
[DJ] Dereziński, J., Jak${\check{\rm s}}$ić, V.: Spectral theory of Pauli-Fierz Hamiltonians I, preprint 1999, MaPhySto
[DJP] Dereziński, J., Jak${\check{\rm s}}$ić, V., Pillet, C.-A.: In preparation.
[He] Heitler, W.: The Quantum Theory of Radiation, Oxford, Oxford University Press (1954).  Zbl 0055.21603
[Ge] Gerard, C.: On the existence of ground states for massless Pauli-Fierz Hamiltonians, preprint  MR 1777307 |  Zbl 1004.81012
[HuSp2] Hübner, M., Spohn, H.: Spectral properties of the spin-boson Hamiltonian, Ann. Inst. H. Poincare 62, 289 (1995). Numdam |  MR 1335060 |  Zbl 0827.47053
[JL] Jak${\check{\rm s}}$ić, V., Last: The structure of the spectrum of the Anderson type Hamiltonians, preprint 1999
[JP1] Jak${\check{\rm s}}$ić, V., Pillet, C.-A.: On a model for quantum friction II: Fermi’s golden rule and dynamics at positive temperature, Commun. Math. Phys. 176, 619 (1996). Article |  Zbl 0852.47038
[JP2] Jak${\check{\rm s}}$ić, V., Pillet, C.-A.: On a model for quantum friction III: Ergodic properties of the spin-boson system, Commun. Math. Phys. 178, 627 (1996). Article |  MR 1395208 |  Zbl 0864.47049
[JMP] Jensen, A., Mourre, E., Perry, P.: Multiple commutator estimates and resolvent smoothness in quantum scattering theory, Ann. Inst. H. Poincare 41, 207 (1984). Numdam |  MR 769156 |  Zbl 0561.47007
[GGK] Gohberg, I., Goldberg, S., Kaashoek, M. A.: Classes of Linear Operators, Vol. 2, Birkhäuser 1993.  MR 1246332 |  Zbl 0789.47001
[Kato] Kato, T.: Perturbation Theory for Linear Operators, second edition, Springer-Verlag, Berlin (1976).  MR 407617 |  Zbl 0148.12601
[MeMo] Mennicken, R., Motovilov, A. K.: Operator interpretation of resonances arising in spectral problems for $2\times 2$ operator matrices, preprint.  MR 1680916
[Mo] Mourre, E.: Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys. 78, 391 (1981). Article |  MR 603501 |  Zbl 0489.47010
[PSS] Perry, P. Sigal, I. M. Simon, B.: Spectral analysis of N-body Schrödinger operators, Ann. Math. 114, 519 (1981).  MR 634428 |  Zbl 0477.35069
[RS4] Reed, M., Simon, B.: Methods of Modern Mathematical Physics, IV. Analysis of Operators, London, Academic Press (1978).  MR 493421 |  Zbl 0401.47001
[Si] Simon, B.: Resonances in N-body quantum systems with dilation analytic potential and foundations of time-dependent perturbation theory, Ann. Math. 97, 247 (1973).  MR 353896 |  Zbl 0252.47009
[Sk] Skibsted, E.: Spectral analysis of $N$-body systems coupled to a bosonic system, preprint.
Copyright Cellule MathDoc 2019 | Crédit | Plan du site