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Frozen Gaussian series representation of the imaginary time propagator theory and numerical tests
Zhang, Dong H.1,2; Shao, Jiushu3; Pollak, Eli4; Eli Pollak
KeywordBoltzmann Equation Convergence Gaussian Processes Iterative Methods Mathematical Operators Matrix Algebra Quantum Theory Tunnelling
Source PublicationJOURNAL OF CHEMICAL PHYSICS
2009-07-28
DOI10.1063/1.3190328
Volume131Issue:4Pages:044116-1-044116-9
Indexed BySCI
SubtypeArticle
Department11
Funding Project1102
Contribution Rank1;1
WOS HeadingsScience & Technology ; Physical Sciences
WOS SubjectPhysics, Atomic, Molecular & Chemical
WOS Research AreaPhysics
WOS KeywordQUANTUM INSTANTON APPROXIMATION ; THERMAL RATE CONSTANTS ; EQUILIBRIUM PROPERTIES ; STATISTICAL-MECHANICS ; SYSTEMS ; DYNAMICS ; MATRIX
AbstractThawed Gaussian wavepackets have been used in recent years to compute approximations to the thermal density matrix. From a numerical point of view, it is cheaper to employ frozen Gaussian wavepackets. In this paper, we provide the formalism for the computation of thermal densities using frozen Gaussian wavepackets. We show that the exact density may be given in terms of a series, in which the zeroth order term is the frozen Gaussian. A numerical test of the methodology is presented for deep tunneling in the quartic double well potential. In all cases, the series is observed to converge. The convergence of the diagonal density matrix element is much faster than that of the antidiagonal one, suggesting that the methodology should be especially useful for the computation of partition functions. As a by product of this study, we find that the density matrix in configuration space can have more than two saddle points at low temperatures. This has implications for the use of the quantum instanton theory.
Language英语
URL查看原文
WOS IDWOS:000268613700017
Citation statistics
Cited Times:9[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://cas-ir.dicp.ac.cn/handle/321008/103191
Collection中国科学院大连化学物理研究所
Corresponding AuthorEli Pollak
Affiliation1.Chinese Acad Sci, Dalian Inst Chem Phys, Ctr Theory & Computat Chem, Dalian 116023, Peoples R China
2.Chinese Acad Sci, Dalian Inst Chem Phys, State Key Lab Mol React Dynam, Dalian 116023, Peoples R China
3.Beijing Normal Univ, Coll Chem, Beijing 100875, Peoples R China
4.Weizmann Inst Sci, Dept Chem Phys, IL-76100 Rehovot, Israel
Recommended Citation
GB/T 7714
Zhang, Dong H.,Shao, Jiushu,Pollak, Eli,et al. Frozen Gaussian series representation of the imaginary time propagator theory and numerical tests[J]. JOURNAL OF CHEMICAL PHYSICS,2009,131(4):044116-1-044116-9.
APA Zhang, Dong H.,Shao, Jiushu,Pollak, Eli,&Eli Pollak.(2009).Frozen Gaussian series representation of the imaginary time propagator theory and numerical tests.JOURNAL OF CHEMICAL PHYSICS,131(4),044116-1-044116-9.
MLA Zhang, Dong H.,et al."Frozen Gaussian series representation of the imaginary time propagator theory and numerical tests".JOURNAL OF CHEMICAL PHYSICS 131.4(2009):044116-1-044116-9.
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