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Volumn 110, Issue 9, 1999, Pages 4184-4198

Analysis of the Pechukas description of mixed quantum-classical dynamics

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; ELECTRON ENERGY LEVELS; ELECTRON TRANSITIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; VELOCITY;

EID: 0033089771     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.478300     Document Type: Article
Times cited : (5)

References (47)
  • 7
    • 0002627110 scopus 로고
    • Computer Simulation of Nonadiabatic Dynamics in Condensed Systems
    • edited by M. Allen and D. Tildesley Kluwer, Dordrecht
    • D. F. Coker, "Computer Simulation of Nonadiabatic Dynamics in Condensed Systems," in Computer Simulation in Chemical Physics, edited by M. Allen and D. Tildesley (Kluwer, Dordrecht, 1993), pp. 315-377.
    • (1993) Computer Simulation in Chemical Physics , pp. 315-377
    • Coker, D.F.1
  • 15
    • 0042787287 scopus 로고
    • edited by W. E. Parry et al. Benjamin, New York
    • R. Kubo, in Many-Body Problems, edited by W. E. Parry et al. (Benjamin, New York, 1969).
    • (1969) Many-Body Problems
    • Kubo, R.1
  • 20
    • 0346750962 scopus 로고    scopus 로고
    • J. Liam McWhirter, J. Chem. Phys. 108, 8279 (1998). In this letter, we list the typos in Ref. 19 along with their corrections. Given these corrections, Sec. III A of Ref. 19 provides a derivation of the mixed quantum-semiclassical time correlation function which incorporates the initial bath configuration variations presented by Xiao and Coker in Refs. 8 and 13. This derivation, however, avoids Xiao and Coker's ZBR approximation. Xiao and Coker's stationary phase analysis of the initial configuration integrals does not include a normalization integral over the bath momenta near to the bath momenta which dominate these configuration integrals. Consequently, the resulting expressions in Sec. III A for the mixed quantum-semiclassical time correlation functions have the wrong dimensions. This letter corrects the derivation in Sec. III A of Ref. 19 by including this normalization integral.
    • (1998) J. Chem. Phys. , vol.108 , pp. 8279
    • Liam McWhirter, J.1
  • 26
    • 0346750960 scopus 로고    scopus 로고
    • note
    • In most discussions of the reduced propagator, the states | γ′ 〉 and | γ″ 〉 are chosen to be instantaneous adiabatic eigenstates of ĥ(Q,q̂). However, our discussion in this article is completely general, so | γ′ 〉 and | γ″ 〉 can be chosen to be any quantum subsystem state.
  • 27
    • 85086292945 scopus 로고    scopus 로고
    • note
    • j.
  • 29
    • 0347381275 scopus 로고    scopus 로고
    • note
    • In Ref. 25, there are typos in Eq. (33) which describes these jump discontinuities in the bath's velocity. In Eq. (33) the minus sign proceeding the third term should be a positive sign. In addition, in Eq. (B3) of Ref. 25 the third and fourth terms should be positive, the third term including a sum over the quantum numbers ν(j + 1), the fourth term including a sum over the numbers ν(j).
  • 39
    • 0348011819 scopus 로고    scopus 로고
    • note
    • Strictly speaking, since the inequality in Eq. (75) is only approximate, our contradiction implies that the two supposed solutions to the FDE, Eqs. (61) and (62), should be approximately equivalent from t′ to t″ for sufficiently small t″ - t′, becoming increasingly equivalent as t″ - t′ decreases.
  • 40
    • 85086292014 scopus 로고    scopus 로고
    • note
    • t″t′ is not unique. In addition, because any convex subdomain can be divided into an arbitrary number of smaller convex subdomains, the number of convex subdomains in the division of G* is also not unique.
  • 42
    • 0346120320 scopus 로고    scopus 로고
    • note
    • t″t′] given by the right hand side of Eq. (81) does not have bounded, continuous first functional derivatives; therefore, this sample problem does not belong to the class of FDEs to which the theorem of Sec. III A applies.
  • 46
    • 0346120319 scopus 로고    scopus 로고
    • note
    • Even for short time intervals t″ - t′, the Pechukas equation might yield a nonunique solution. As a result, the connected and partially connected classical paths of the coarse grained reduced propagator might not be impervious to this nonuniqueness: specifying the sequence of quantum numbers, γ, and the initial point at t′ (Q′,Q′), might not be sufficient to distinguish one such path from another.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.