The DOI matches its Crossref record; 57 of the 57 references it cites were found in a registry or an index.
Numerical path integral techniques for long time dynamics of quantum dissipative systems
Abstract
Recent progress in numerical methods for evaluating the real-time path integral in dissipative harmonic environments is reviewed. Quasi-adiabatic propagators constructed numerically allow convergence of the path integral with large time increments. Integration of the harmonic bath leads to path integral expressions that incorporate the exact dynamics of the quantum particle along the adiabatic path, with an influence functional that describes nonadiabatic corrections. The resulting quasi-adiabatic propagator path integral is evaluated by efficient system-specific quadratures in most regimes of parameter space, although some cases are handled by grid Monte Carlo sampling. Exploiting the finite span of nonlocal influence functional interactions characteristic of broad condensed phase spectra leads to an iterative scheme for calculating the path integral over arbitrary time lengths. No uncontrolled approximations are introduced, and the resulting methodology converges to the exact quantum result with modest amounts of computational power. Applications to tunneling dynamics in the condensed phase are described.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Quantum Mechanics and Path Integrals
(1966) · Students Quarterly Journal · doi:10.1049/sqj.1966.0063 · Cited by 9,537
Brownian motion in a field of force and the diffusion model of chemical reactions
Kramers, H. A. (1940) · Physica · doi:10.1016/s0031-8914(40)90098-2 · Cited by 8,625
Reaction-rate theory: fifty years after Kramers
Hänggi, P., Talkner, P., & Borkovec, M. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.251 · Cited by 6,154
Dynamics of the dissipative two-state system
Leggett, A. J., Chakravarty, S., Dorsey, A. T., Fisher, M. P. A., Garg, A., & Zwerger, W. (1987) · Reviews of Modern Physics · doi:10.1103/revmodphys.59.1 · Cited by 5,109
Space-Time Approach to Non-Relativistic Quantum Mechanics
Feynman, R. P. (1948) · Reviews of Modern Physics · doi:10.1103/revmodphys.20.367 · Cited by 4,271
Quantum tunnelling in a dissipative system
Caldeira, A. O., & Leggett, A. J. (1983) · Annals of Physics · doi:10.1016/0003-4916(83)90202-6 · Cited by 3,647
Holstein, T. (1959) · Annals of Physics · doi:10.1016/0003-4916(59)90002-8 · Cited by 3,273
The theory of a general quantum system interacting with a linear dissipative system
Feynman, R. P., & Vernon, F. L. (1963) · Annals of Physics · doi:10.1016/0003-4916(63)90068-x · Cited by 2,887
Path integral approach to quantum Brownian motion
Caldeira, A. O., & Leggett, A. J. (1983) · Physica A: Statistical Mechanics and its Applications · doi:10.1016/0378-4371(83)90013-4 · Cited by 2,772
Cited by
Coherence in Energy Transfer and Photosynthesis
Chenu, A., & Scholes, G. D. (2015) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-040214-121713 · Cited by 420
Iterative real-time path integral approach to nonequilibrium quantum transport
Weiss, S., Eckel, J., Thorwart, M., & Egger, R. (2008) · Physical Review B · doi:10.1103/physrevb.77.195316 · Cited by 211
Quantum dynamics of a qubit coupled with a structured bath
Huang, P., & Zheng, H. (2008) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/20/39/395233 · Cited by 10
Metadata
- Authors
- Makri, N.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1995-05-01
- Volume
- 36
- Issue
- 5
- Pages
- 2430-2457
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1988719923
- Cited by
- 377
- References
- 57
- FWCI
- 7.57
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Numerical path integral techniques for long time dynamics of quantum dissipative systems. https://app.cochat.ai/papers/10.1063/1.531046
- The paper
- Makri, N. (1995). Numerical path integral techniques for long time dynamics of quantum dissipative systems. Journal of Mathematical Physics. https://doi.org/10.1063/1.531046
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
