Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1310.3041 · Physical Review E

Truncated phase-space approach to polaron response

Dries Sels, F. Brosens

Published Jan 17, 2014• 6 citations
arXivHTMLPDF

Abstract

A method is presented to obtain the linear response coefficients of a system coupled to a bath. The method is based on a systematic truncation of the Liouville equation for the reduced distribution function. The first-order truncation results are expected to be accurate in the low-temperature and weak-coupling regime. Explicit expressions for the conductivity of the Fröhlich polaron are obtained, and the discrepancy between the Kadanoff and the Feynman-Hellwarth-Iddings-Platzman mobility is elucidated.

DOI
10.1103/physreve.89.012124

Related papers

All-coupling polaron optical response: Analytic approaches beyond the adiabatic approximation

Serghei N. Klimin, Jacques Tempere, J. T. Devreese

In the present work, the problem of an all-coupling analytic description for the optical conductivity of the Fr\"ohlich polaron is treated, with the goal being to bridge the gap in the validity range that exists between two complementary methods: on the one hand, the memory-function formalism and, on the other hand, the strong-coupling expansion based on the Franck-Condon picture for the polaron response. At intermediate coupling, both methods were found to fail as they do not reproduce diagrammatic quantum Monte Carlo results. To resolve this, we modify the memory-function formalism with respect to the Feynman-Hellwarth-Iddings-Platzman approach in order to take into account a nonquadratic interaction in a model system for the polaron. The strong-coupling expansion is extended beyond the adiabatic approximation by including in the treatment nonadiabatic transitions between excited polaron states. The polaron optical conductivity that we obtain at $T=0$ by combining the two extended methods agrees well, both qualitatively and quantitatively, with the diagrammatic quantum Monte Carlo results in the whole available range of the electron-phonon coupling strength.

arXiv:1606.00605•Physical review. B./Physical review. B•Sep 22, 2016•8 citations

Multiple phonon modes in Feynman path-integral variational polaron mobility

Bradley A. A. Martin, Jarvist Moore Frost

The Feynman path-integral variational approach to the polaron problem, along with the associated Feynman-Hellwarth-Iddings-Platzman (FHIP) linear-response mobility theory, provides a computationally amenable method to predict the frequency-resolved temperature-dependent charge-carrier mobility, and other experimental observables in polar semiconductors. We show that the FHIP mobility theory predicts non-Drude transport behavior, and shows remarkably good agreement with the recent diagrammatic Monte Carlo mobility simulations of Mishchenko et al. [Phys. Rev. Lett. 123, 076601 (2019)] for the abstract Fr\"ohlich Hamiltonian. We extend this method to multiple phonon modes in the Fr\"ohlich model action. This enables a slightly better variational solution, as inferred from the resulting energy. We carry forward this extra complexity into the mobility theory, which shows a richer structure in the frequency and temperature-dependent mobility, due to the different phonon modes activating at different energies. The method provides a computationally efficient and fully quantitative method of predicting polaron mobility and response in real materials.

arXiv:2203.16472•Physical review. B./Physical review. B•Mar 13, 2023•7 citations

Polaron Mobility at Finite Temperature

David C. Langreth

The Kadanoff-Baym transport theory leads to an expression for polaron mobility which becomes exact for low, but finite, temperature, ${e}^{\frac{\ensuremath{\Theta}}{T}}\ensuremath{\gg}1$, but not necessarily $\frac{\ensuremath{\Theta}}{T}\ensuremath{\gg}1$. This expression is evaluated exactly in the weak-coupling limit. Comparison with previous variational calculations shows that the latter have not predicted even qualitatively valid corrections to the known asymptotic zero-temperature result. Simple arguments allow the present weak-coupling expression to be extended to finite coupling. These arguments are verified by a quantitative calculation using the Feynman model. It is found that the corrections due to finite temperature are at least as important as those due to a finite coupling constant.

Physical Review•Jul 15, 1967•79 citations

Impedance function of large polarons: An alternative derivation of the Feynman-Hellwarth-Iddings-Platzman theory

François Maria Peeters, J. T. Devreese

An alternative derivation is presented of the Feynman-Hellwarth-Iddings-Platzman (FHIP) result for the impedance function of a polaron. In the present calculation only simple operator techniques are used. The FHIP result is worked out in such a way that we are able to identify which scattering processes are incorporated. The inverse problem is also solved.

Physical review. B, Condensed matter•Nov 15, 1983•59 citations

Correlation and response functions with non-Markovian dissipation: A reduced Liouville-space theory

Yan Mo, Rui‐Xue Xu, Ping Cui +1 more

Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime.

The Journal of Chemical Physics•Feb 16, 2005•24 citations

Accuracy of second order perturbation theory in the polaron and variational polaron frames

Chee‐Kong Lee, Jeremy M. Moix, Jianshu Cao

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.

arXiv:1201.2436•The Journal of Chemical Physics•May 28, 2012•120 citations
A method is presented to obtain the linear response coefficients of a system coupled to a bath. The method is based on a systematic truncation of the Liouville equation for the reduced distribution function. The first-order truncation results are expected to be accurate in the low-temperature and weak-coupling regime. Explicit expressions for the conductivity of the Fröhlich polaron are obtained, and the discrepancy between the Kadanoff and the Feynman-Hellwarth-Iddings-Platzman mobility is elucidated.
In the present work, the problem of an all-coupling analytic description for the optical conductivity of the Fr\"ohlich polaron is treated, with the goal being to bridge the gap in the validity range that exists between two complementary methods: on the one hand, the memory-function formalism and, on the other hand, the strong-coupling expansion based on the Franck-Condon picture for the polaron response. At intermediate coupling, both methods were found to fail as they do not reproduce diagrammatic quantum Monte Carlo results. To resolve this, we modify the memory-function formalism with respect to the Feynman-Hellwarth-Iddings-Platzman approach in order to take into account a nonquadratic interaction in a model system for the polaron. The strong-coupling expansion is extended beyond the adiabatic approximation by including in the treatment nonadiabatic transitions between excited polaron states. The polaron optical conductivity that we obtain at T=0T=0T=0 by combining the two extended methods agrees well, both qualitatively and quantitatively, with the diagrammatic quantum Monte Carlo results in the whole available range of the electron-phonon coupling strength.
The Feynman path-integral variational approach to the polaron problem, along with the associated Feynman-Hellwarth-Iddings-Platzman (FHIP) linear-response mobility theory, provides a computationally amenable method to predict the frequency-resolved temperature-dependent charge-carrier mobility, and other experimental observables in polar semiconductors. We show that the FHIP mobility theory predicts non-Drude transport behavior, and shows remarkably good agreement with the recent diagrammatic Monte Carlo mobility simulations of Mishchenko et al. [Phys. Rev. Lett. 123, 076601 (2019)] for the abstract Fr\"ohlich Hamiltonian. We extend this method to multiple phonon modes in the Fr\"ohlich model action. This enables a slightly better variational solution, as inferred from the resulting energy. We carry forward this extra complexity into the mobility theory, which shows a richer structure in the frequency and temperature-dependent mobility, due to the different phonon modes activating at different energies. The method provides a computationally efficient and fully quantitative method of predicting polaron mobility and response in real materials.
The Kadanoff-Baym transport theory leads to an expression for polaron mobility which becomes exact for low, but finite, temperature, ${e}^{\frac{\ensuremath{\Theta}}{T}}\ensuremath{\gg}1$, but not necessarily $\frac{\ensuremath{\Theta}}{T}\ensuremath{\gg}1$. This expression is evaluated exactly in the weak-coupling limit. Comparison with previous variational calculations shows that the latter have not predicted even qualitatively valid corrections to the known asymptotic zero-temperature result. Simple arguments allow the present weak-coupling expression to be extended to finite coupling. These arguments are verified by a quantitative calculation using the Feynman model. It is found that the corrections due to finite temperature are at least as important as those due to a finite coupling constant.
Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime.
In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.