A model of interband radiative transition

 Dittrich Jaroslav DITTRICH Jaroslav
 Department of Theoretical Physics Nuclear Physics Institute Academy of Sciences

 Exner Pavel EXNER Pavel
 Department of Theoretical Physics Nuclear Physics Institute Academy of Sciences

 Hirokawa Masao HIROKAWA Masao
 Department of Mathematics, Faculty of Science Okayama University
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Author(s)

 Dittrich Jaroslav DITTRICH Jaroslav
 Department of Theoretical Physics Nuclear Physics Institute Academy of Sciences

 Exner Pavel EXNER Pavel
 Department of Theoretical Physics Nuclear Physics Institute Academy of Sciences

 Hirokawa Masao HIROKAWA Masao
 Department of Mathematics, Faculty of Science Okayama University
Abstract
We consider a simple model which is a caricature of a crystal interacting with a radiation field. The model has two bands of continuous spectrum and the particle can pass from the upper one to the lower by radiating a photon, the coupling between the excited and deexcited states being of a Friedrichs type. Under suitable regularity and analyticity assumptions we find the continued resolvent and show that for weak enough coupling it has a curvetype singularity in the lower halfplane which is a deformation of the upperband spectral cut. We then find a formula for the decay amplitude and show that for a fixed energy it is approximately exponential at intermediate times, while the tail has a powerlike behaviour.
Journal

 Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 56(3), 753786, 20040701
The Mathematical Society of Japan
References: 25

1
 Puiseux series for resonances at an embedded eigenvalue

HOWLAND J. S.
Pacific J. Math. 55, 157176, 1974
Cited by (1)

2
 A class of analytic perturbations for onebody Schrodinger Hamiltonians

AGUILAR J.
Commun. Math. Phys. 22, 269279, 1971
Cited by (1)

3
 <no title>

REED M.
Functional Analysis, 1972
Cited by (1)

4
 <no title>

JARNIK V.
Differential Calculus II, 1956
Cited by (1)

5
 <no title>

CERNY I.
Foundations of Analysis in the Complex Domain, 1967
Cited by (1)

6
 <no title>

RUDIN W.
Real and Complex Analysis, 1974
Cited by (5)

7
 On the perturbation of continuous spectra

FRIEDRICHS K. O.
Comm. Pure Appl. Math. 1, 361406, 1948
DOI Cited by (2)

8
 A nonrelativistic model of twoparticle decay

DITTRICH J.
Czechoslovak J. Phys., B 37, 503515, 10281034, 1987
DOI Cited by (1)

9
 A nonrelativistic model of twoparticle decay

DITTRICH J.
Czechoslovak J. Phys., B 38, 591610, 1988
Cited by (1)

10
 A nonrelativistic model of twoparticle decay

DITTRICH J.
Czechoslovak J. Phys., B 39, 121138, 1989
Cited by (1)

11
 The Livsic matrix in perturbation theory

HOWLAND J. S.
J. Math. Anal. Appl. 50, 415437, 1975
DOI Cited by (1)

12
 Perturbation of unstable eigenvalues of finite multiplicity

BAUMGARTEL H.
J. Funct. Anal. 22, 187203, 1976
DOI Cited by (1)

13
 On the equality of resonances (poles of scattering amplitude) and virtual poles

BAUMGARTEL H.
Math. Nachr. 86, 167174, 1978
DOI Cited by (1)

14
 Quantum theory of the damped harmonic oscillator

GRABERT H.
Z. Phys. B 55, 8794, 1984
Cited by (2)

15
 Time behavior of the correlation functions in a simple dissipative quantum model

ASLANGUL C.
J. Statist. Phys. 40, 167189, 1985
Cited by (1)

16
 Longtime tails in quantum Brownian motion

JUNG R.
Phys. Rev. A 32, 25102512, 1985
Cited by (1)

17
 The correlation function for a quantum oscillator in a lowtemperature heat bath

BRAUN E.
Physica A 143, 547567, 1987
Cited by (1)

18
 An inverse problem in quantum field theory and canonical correlation functions

HIROKAWA Masao
Journal of the Mathematical Society of Japan 51(2), 337369, 199904
JSTAGE References (35) Cited by (1)

19
 Spectral analysis of a quantum harmonic oscillator coupled to infinitely many scalar bosons

ARAI A.
J. Math. Anal. Appl. 140, 270288, 1989
DOI Cited by (2)

20
 Friedrichs model with virtual transitions, Exact solution and indirect spectroscopy

KARPOV E.
J. Math. Phys. 41, 118131, 2000
Cited by (1)

21
 Renormalization group analysis of spectral problems in quantum field theory

BACH V.
Adv. Math. 137, 205298, 1998
DOI Cited by (2)

22
 Return to equilibrium

BACH V.
J. Math. Phys. 41, 39854060, 2000
Cited by (2)

23
 Scattering in periodic systems : from resonances to band structure

BARRA F.
J. Phys. A 32, 33573375, 1999
Cited by (1)

24
 Quantum field theory of unstable particles

ARAKI H. , Yasuo MUNAKATA , Masaaki KAWAGUCHI , Tetsuo GOTO , Department of Physics Kyoto University , Department of Physics Kyoto University , Research Institute for Fundamental Physics Kyoto University , Department of Physics Osaka University
Progr. Theoret. Phys. 17, 419442, 1957
DOI Cited by (2)

25
 Longtime behavior of twopoint functions of a quantum harmonic oscillator interacting with bosons

Arai Asao
Journal of Mathematical Physics 30(6), 12771288, 198906
IR Cited by (2)