메뉴 건너뛰기




Volumn 23, Issue 1, 2011, Pages 83-125

Perturbation of near threshold eigenvalues: Crossover from exponential to non-exponential decay laws

Author keywords

Decay laws; exponential decay; Fermi Golden Rule; non exponential decay

Indexed keywords


EID: 79952058978     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X11004230     Document Type: Article
Times cited : (11)

References (33)
  • 2
    • 0030371071 scopus 로고    scopus 로고
    • Interchannel resonances at a threshold
    • B. Baumgartner, Interchannel resonances at a threshold, J. Math. Phys. 37 (1996) 5928-5938.
    • (1996) J. Math. Phys. , vol.37 , pp. 5928-5938
    • Baumgartner, B.1
  • 3
    • 33646469595 scopus 로고    scopus 로고
    • A general resonance theory based on Mourre's inequality
    • L. Cattaneo, G. M. Graf and W. Hunziker, A general resonance theory based on Mourre's inequality, Ann. H. Poincaŕe 7 (2006) 583-614.
    • (2006) Ann. H. Poincaŕe , vol.7 , pp. 583-614
    • Cattaneo, L.1    Graf, G.M.2    Hunziker, W.3
  • 4
    • 0000428387 scopus 로고
    • The evolution of unstable quantum states and a resolution of Zeno's paradox
    • C. B. Chiu, E. C. G. Sudarshan and B. Misra, The evolution of unstable quantum states and a resolution of Zeno's paradox, Phys. Rev. D 16 (1976) 520-529.
    • (1976) Phys. Rev. D , vol.16 , pp. 520-529
    • Chiu, C.B.1    Sudarshan, E.C.G.2    Misra, B.3
  • 5
    • 0035539930 scopus 로고    scopus 로고
    • Resonance theory for Schrödinger operators
    • O. Costin and A. Soffer, Resonance theory for Schrödinger operators, Comm. Math. Phys. 224 (2001) 133-152.
    • (2001) Comm. Math. Phys. , vol.224 , pp. 133-152
    • Costin, O.1    Soffer, A.2
  • 6
    • 0002480621 scopus 로고
    • Resonances, spectral concentration and exponential decay
    • E. B. Davies, Resonances, spectral concentration and exponential decay, Lett. Math. Phys. 1 (1975) 31-35.
    • (1975) Lett. Math. Phys. , vol.1 , pp. 31-35
    • Davies, E.B.1
  • 7
    • 4444320940 scopus 로고
    • Pole approximation and spectral concentration
    • M. Demuth, Pole approximation and spectral concentration, Math. Nachr. 73 (1976) 65-72.
    • (1976) Math. Nachr. , vol.73 , pp. 65-72
    • Demuth, M.1
  • 8
    • 59349090312 scopus 로고    scopus 로고
    • Non-exponential decay laws in perturbation theory of near threshold eigenvalues
    • 013516
    • V. Dinu, A. Jensen and G. Nenciu, Non-exponential decay laws in perturbation theory of near threshold eigenvalues, J. Math. Phys. 50 (2009) 013516, 20 pp.
    • (2009) J. Math. Phys. , vol.50 , pp. 20
    • Dinu, V.1    Jensen, A.2    Nenciu, G.3
  • 10
    • 7644232309 scopus 로고
    • Decay theory of unstable quantum systems
    • L. Fonda, G. C. Ghirardi and A. Rimini, Decay theory of unstable quantum systems, Rep. Prog. Phys. 41 (1978) 587-631.
    • (1978) Rep. Prog. Phys. , vol.41 , pp. 587-631
    • Fonda, L.1    Ghirardi, G.C.2    Rimini, A.3
  • 11
    • 0000727740 scopus 로고
    • Seeking the non-exponential decay
    • P. T. Greenland, Seeking the non-exponential decay, Nature 335 (1988) 298-299.
    • (1988) Nature , vol.335 , pp. 298-299
    • Greenland, P.T.1
  • 12
    • 0000901164 scopus 로고
    • Resonances, metastable states and exponential decay laws in perturbation theory
    • W. Hunziker, Resonances, metastable states and exponential decay laws in perturbation theory, Comm. Math. Phys. 132 (1990) 177-188.
    • (1990) Comm. Math. Phys. , vol.132 , pp. 177-188
    • Hunziker, W.1
  • 13
    • 84972562665 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in L2(Rm), mÝ 5
    • A. Jensen, Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in L2(Rm), mÝ 5, Duke Math. J. 47 (1980) 57-80.
    • (1980) Duke Math. J. , vol.47 , pp. 57-80
    • Jensen, A.1
  • 14
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions
    • A. Jensen and T. Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke Math. J. 46 (1979) 583-611.
    • (1979) Duke Math. J. , vol.46 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 15
    • 0035619840 scopus 로고    scopus 로고
    • A unified approach to resolvent expansions at thresholds
    • A. Jensen and G. Nenciu, A unified approach to resolvent expansions at thresholds, Rev. Math. Phys. 13(6) (2001) 717-754.
    • (2001) Rev. Math. Phys. , vol.13 , Issue.6 , pp. 717-754
    • Jensen, A.1    Nenciu, G.2
  • 16
    • 29144474430 scopus 로고    scopus 로고
    • The fermi golden rule and its form at thresholds in odd dimensions
    • DOI 10.1007/s00220-005-1428-0
    • A. Jensen and G. Nenciu, The Fermi golden rule and its form at thresholds in odd dimensions, Comm. Math. Phys. 261 (2006) 693-727. (Pubitemid 41813079)
    • (2006) Communications in Mathematical Physics , vol.261 , Issue.3 , pp. 693-727
    • Jensen, A.1    Nenciu, G.2
  • 17
    • 33846308507 scopus 로고    scopus 로고
    • Schrödinger operators on the half line: Resolvent expansions and the Fermi golden rule at thresholds
    • A. Jensen and G. Nenciu, Schrödinger operators on the half line: Resolvent expansions and the Fermi golden rule at thresholds, Proc. Indian Acad. Sci. (Math. Sci.) 116 (2006) 375-392. (Pubitemid 46120512)
    • (2006) Proceedings of the Indian Academy of Sciences: Mathematical Sciences , vol.116 , Issue.4 , pp. 375-392
    • Jensen, A.1    Nenciu, G.2
  • 20
    • 18444397747 scopus 로고    scopus 로고
    • Non-exponential decay of an unstable quantum system: Small Q-value s-wave decay
    • 012109
    • T. Jittoh, S. Masumoto, J. Sato, Y. Sato and K. Takeda, Non-exponential decay of an unstable quantum system: Small Q-value s-wave decay, Phys. Rev. A 71 (2005) 012109, 7 pp.
    • (2005) Phys. Rev. A , vol.71 , pp. 7
    • Jittoh, T.1    Masumoto, S.2    Sato, J.3    Sato, Y.4    Takeda, K.5
  • 21
    • 33845202266 scopus 로고    scopus 로고
    • Production of cold molecules via magnetically tunable Feshbach resonances
    • DOI 10.1103/RevModPhys.78.1311
    • T. Köhler, K. G̀oral and P. Julienne, Production of cold molecules via magnetically tunable Feshbach resonances, Rev. Mod. Phys. 78 (2006) 1311-1361. (Pubitemid 44853877)
    • (2006) Reviews of Modern Physics , vol.78 , Issue.4 , pp. 1311-1361
    • Kohler, T.1    Goral, K.2    Julienne, P.S.3
  • 23
    • 19244365258 scopus 로고    scopus 로고
    • Feshbach resonances with large background scattering length: Interplay with open-channel resonances
    • 012701
    • B. Marcelis, E. van Kempen, B. Verhaar and J. Kokkelmans, Feshbach resonances with large background scattering length: Interplay with open-channel resonances, Phys. Rev. A 70 (2004) 012701, 15 pp.
    • (2004) Phys. Rev. A , vol.70 , pp. 15
    • Marcelis, B.1    Van Kempen, E.2    Verhaar, B.3    Kokkelmans, J.4
  • 24
    • 0033243768 scopus 로고    scopus 로고
    • A time-dependent theory of quantum resonances
    • M. Merkli and I. M. Sigal, A time-dependent theory of quantum resonances, Comm. Math. Phys. 201 (1999) 549-576.
    • (1999) Comm. Math. Phys. , vol.201 , pp. 549-576
    • Merkli, M.1    Sigal, I.M.2
  • 25
    • 28844460677 scopus 로고    scopus 로고
    • Bound-state eigenenergy outside and inside the
    • continuum for unstable multilevel systems 063405
    • M. Miyamoto, Bound-state eigenenergy outside and inside the continuum for unstable multilevel systems, Phys. Rev. A 72 (2005) 063405, 9 pp.
    • (2005) Phys. Rev. A , vol.72 , pp. 9
    • Miyamoto, M.1
  • 26
    • 0002087150 scopus 로고
    • Asymptotic expansions in time for solutions of Schrödinger-type equations
    • M. Murata, Asymptotic expansions in time for solutions of Schrödinger-type equations, J. Funct. Anal. 49(1) (1982) 10-56.
    • (1982) J. Funct. Anal. , vol.49 , Issue.1 , pp. 10-56
    • Murata, M.1
  • 29
    • 0036702407 scopus 로고    scopus 로고
    • Physical constraints on nonstationary states and nonexponential decay
    • 022118
    • C. Nicolaides, Physical constraints on nonstationary states and nonexponential decay, Phys. Rev. A 66 (2002) 022118, 7 pp.
    • (2002) Phys. Rev. A , vol.66 , pp. 7
    • Nicolaides, C.1
  • 30
    • 33645770880 scopus 로고    scopus 로고
    • Two-channel r-matrix analysis of magnetic-field-induced Feshbach resonances
    • 042705
    • N. Nygaard, B. Schneider and P. Julienne, Two-channel R-matrix analysis of magnetic-field-induced Feshbach resonances, Phys. Rev. A 73 (2006) 042705, 10 pp.
    • (2006) Phys. Rev. A , vol.73 , pp. 10
    • Nygaard, N.1    Schneider, B.2    Julienne, P.3
  • 31
    • 0000978577 scopus 로고
    • Quantum mechanical resonance and limiting absorption: The many body problem
    • A. Orth, Quantum mechanical resonance and limiting absorption: The many body problem, Comm. Math. Phys. 126 (1990) 559-573.
    • (1990) Comm. Math. Phys. , vol.126 , pp. 559-573
    • Orth, A.1
  • 32
    • 59349100272 scopus 로고    scopus 로고
    • Embedded eigenvalues and resonances of Schrödinger operators with two channels
    • X. P. Wang, Embedded eigenvalues and resonances of Schrödinger operators with two channels, Ann. Fac. Sci. Toulouse Math. (6) 16(1) (2007) 179-214.
    • (2007) Ann. Fac. Sci. Toulouse Math. (6) , vol.16 , Issue.1 , pp. 179-214
    • Wang, X.P.1
  • 33
    • 44649156396 scopus 로고    scopus 로고
    • The Lp boundedness of wave operators for Schrödinger operators with threshold singularities I, Odd dimensional case
    • K. Yajima, The Lp boundedness of wave operators for Schrödinger operators with threshold singularities I, Odd dimensional case, J. Math. Sci. Univ. Tokyo 13 (2006) 43-93.
    • (2006) J. Math. Sci. Univ. Tokyo , vol.13 , pp. 43-93
    • Yajima, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.