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Stuart C Althorpe - One of the best experts on this subject based on the ideXlab platform.
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on the uniqueness of t 0 Quantum transition state theory
Journal of Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C AlthorpeAbstract:It was shown recently that there exists a true Quantum transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) Quantum flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other flux-side time-correlation function gives either non-positive-definite Quantum Statistics or zero. We introduce a generalized flux-side time-correlation function which includes all other (known) flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite Quantum Statistics is RPMD-TST.
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derivation of a true t 0 Quantum transition state theory part i uniqueness and equivalence to ring polymer molecular dynamics transition state theory
arXiv: Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C AlthorpeAbstract:Surprisingly, there exists a Quantum flux-side time-correlation function which has a non-zero short-time (t->0+) limit, and thus yields a rigorous Quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function, and derive its short-time limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this common dividing surface to be a single point gives a short-time limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932, but which does not give positive-definite Quantum Statistics, causing it to fail while still in the shallow-tunnelling regime. Choosing the dividing surface to be invariant to imaginary-time translation gives, uniquely, a short-time limit that gives the correct positive- definite Quantum Statistics at all temperatures, and which is identical to ring-polymer molecular dynamics (RPMD) TST. We find that the RPMD-TST rate is not a strict upper bound to the exact Quantum rate, but a good approximation to one if real-time coherence effects are small. Part II will show that the RPMD-TST rate is equal to the exact Quantum rate in the absence of recrossing.
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derivation of a true t 0 Quantum transition state theory i uniqueness and equivalence to ring polymer molecular dynamics transition state theory
Journal of Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C AlthorpeAbstract:Surprisingly, there exists a Quantum flux-side time-correlation function which has a non-zero t → 0+ limit and thus yields a rigorous Quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function and derive its t → 0+ limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this function to be a single point gives a t → 0+ limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932; however, this expression does not give positive-definite Quantum Statistics, causing it to fail while still in the shallow-tunnelling regime. Positive-definite Quantum Statistics is obtained only if the dividing surface is invariant to imaginary-time translation, in which case the t → 0+ limit is identical to ring-polymer molecular dynamics (RPMD) TST. The RPMD-TST rate is not a strict upper bound to the exa...
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derivation of a true t 0 Quantum transition state theory i uniqueness and equivalence to ring polymer molecular dynamics transition state theory
Journal of Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C AlthorpeAbstract:Surprisingly, there exists a Quantum flux-side time-correlation function which has a non-zero t → 0+ limit and thus yields a rigorous Quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function and derive its t → 0+ limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this function to be a single point gives a t → 0+ limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932; however, this expression does not give positive-definite Quantum Statistics, causing it to fail while still in the shallow-tunnelling regime. Positive-definite Quantum Statistics is obtained only if the dividing surface is invariant to imaginary-time translation, in which case the t → 0+ limit is identical to ring-polymer molecular dynamics (RPMD) TST. The RPMD-TST rate is not a strict upper bound to the exact Quantum rate, but is a good approximation to one if real-time coherence effects are small. Part II will show that the RPMD-TST rate is equal to the exact Quantum rate in the absence of recrossing.
Timothy J H Hele - One of the best experts on this subject based on the ideXlab platform.
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on the uniqueness of t 0 Quantum transition state theory
Journal of Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C AlthorpeAbstract:It was shown recently that there exists a true Quantum transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) Quantum flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other flux-side time-correlation function gives either non-positive-definite Quantum Statistics or zero. We introduce a generalized flux-side time-correlation function which includes all other (known) flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite Quantum Statistics is RPMD-TST.
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derivation of a true t 0 Quantum transition state theory part i uniqueness and equivalence to ring polymer molecular dynamics transition state theory
arXiv: Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C AlthorpeAbstract:Surprisingly, there exists a Quantum flux-side time-correlation function which has a non-zero short-time (t->0+) limit, and thus yields a rigorous Quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function, and derive its short-time limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this common dividing surface to be a single point gives a short-time limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932, but which does not give positive-definite Quantum Statistics, causing it to fail while still in the shallow-tunnelling regime. Choosing the dividing surface to be invariant to imaginary-time translation gives, uniquely, a short-time limit that gives the correct positive- definite Quantum Statistics at all temperatures, and which is identical to ring-polymer molecular dynamics (RPMD) TST. We find that the RPMD-TST rate is not a strict upper bound to the exact Quantum rate, but a good approximation to one if real-time coherence effects are small. Part II will show that the RPMD-TST rate is equal to the exact Quantum rate in the absence of recrossing.
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derivation of a true t 0 Quantum transition state theory i uniqueness and equivalence to ring polymer molecular dynamics transition state theory
Journal of Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C AlthorpeAbstract:Surprisingly, there exists a Quantum flux-side time-correlation function which has a non-zero t → 0+ limit and thus yields a rigorous Quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function and derive its t → 0+ limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this function to be a single point gives a t → 0+ limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932; however, this expression does not give positive-definite Quantum Statistics, causing it to fail while still in the shallow-tunnelling regime. Positive-definite Quantum Statistics is obtained only if the dividing surface is invariant to imaginary-time translation, in which case the t → 0+ limit is identical to ring-polymer molecular dynamics (RPMD) TST. The RPMD-TST rate is not a strict upper bound to the exa...
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derivation of a true t 0 Quantum transition state theory i uniqueness and equivalence to ring polymer molecular dynamics transition state theory
Journal of Chemical Physics, 2013Co-Authors: Timothy J H Hele, Stuart C AlthorpeAbstract:Surprisingly, there exists a Quantum flux-side time-correlation function which has a non-zero t → 0+ limit and thus yields a rigorous Quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function and derive its t → 0+ limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this function to be a single point gives a t → 0+ limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932; however, this expression does not give positive-definite Quantum Statistics, causing it to fail while still in the shallow-tunnelling regime. Positive-definite Quantum Statistics is obtained only if the dividing surface is invariant to imaginary-time translation, in which case the t → 0+ limit is identical to ring-polymer molecular dynamics (RPMD) TST. The RPMD-TST rate is not a strict upper bound to the exact Quantum rate, but is a good approximation to one if real-time coherence effects are small. Part II will show that the RPMD-TST rate is equal to the exact Quantum rate in the absence of recrossing.
David E Manolopoulos - One of the best experts on this subject based on the ideXlab platform.
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Quantum Statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics
Journal of Chemical Physics, 2004Co-Authors: Ian R Craig, David E ManolopoulosAbstract:We propose an approximate method for calculating Kubo-transformed real-time correlation functions involving position-dependent operators, based on path integral (Parrinello-Rahman) molecular dynamics. The method gives the exact Quantum mechanical correlation function at time zero, exactly satisfies the Quantum mechanical detailed balance condition, and for correlation functions of the form C(Ax)(t) and C(xB)(t) it gives the exact result for a harmonic potential. It also works reasonably well at short times for more general potentials and correlation functions, as we illustrate with some example calculations. The method provides a consistent improvement over purely classical molecular dynamics that is most apparent in the low-temperature regime.
Mark Tame - One of the best experts on this subject based on the ideXlab platform.
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Quantum Statistics of surface plasmon polaritons in metallic stripe waveguides
arXiv: Quantum Physics, 2012Co-Authors: Giuliana Di Martino, Mark Tame, Yannick Sonnefraud, Stephane Kenacohen, şahin Kaya Ozdemir, M S Kim, Stefan A MaierAbstract:Single surface plasmon polaritons are excited using photons generated via spontaneous parametric down-conversion. The mean excitation rates, intensity correlations and Fock state populations are studied. The observed dependence of the second order coherence in our experiment is consistent with a linear uncorrelated Markovian environment in the Quantum regime. Our results provide important information about the effect of loss for assessing the potential of plasmonic waveguides for future nanophotonic circuitry in the Quantum regime.
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Quantum Statistics of surface plasmon polaritons in metallic stripe waveguides
Nano Letters, 2012Co-Authors: Giuliana Di Martino, Mark Tame, Yannick Sonnefraud, Stephane Kenacohen, şahin Kaya Ozdemir, M S Kim, Stefan A MaierAbstract:Heralded single surface plasmon polaritons are excited using photons generated via spontaneous parametric down conversion. The mean excitation rates, intensity correlations, and Fock state populations are studied. The observed dependence of the second-order coherence in our experiment is consistent with a linear uncorrelated Markovian environment in the Quantum regime. Our results provide important information about the effect of loss for assessing the potential of plasmonic waveguides for future nanophotonic circuitry in the Quantum regime.
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single photon excitation of surface plasmon polaritons
Physical Review Letters, 2008Co-Authors: Mark Tame, D Ballester, Mauro Paternostro, Anatoly V ZayatsAbstract:We provide the Quantum-mechanical description of the excitation of surface plasmon polaritons on metal surfaces by single photons. An attenuated-reflection setup is described for the Quantum excitation process in which we find remarkably efficient photon-to-surface plasmon wave-packet transfer. Using a fully quantized treatment of the fields, we introduce the Hamiltonian for their interaction and study the Quantum Statistics during transfer with and without losses in the metal.
Stefan A Maier - One of the best experts on this subject based on the ideXlab platform.
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Quantum Statistics of surface plasmon polaritons in metallic stripe waveguides
arXiv: Quantum Physics, 2012Co-Authors: Giuliana Di Martino, Mark Tame, Yannick Sonnefraud, Stephane Kenacohen, şahin Kaya Ozdemir, M S Kim, Stefan A MaierAbstract:Single surface plasmon polaritons are excited using photons generated via spontaneous parametric down-conversion. The mean excitation rates, intensity correlations and Fock state populations are studied. The observed dependence of the second order coherence in our experiment is consistent with a linear uncorrelated Markovian environment in the Quantum regime. Our results provide important information about the effect of loss for assessing the potential of plasmonic waveguides for future nanophotonic circuitry in the Quantum regime.
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Quantum Statistics of surface plasmon polaritons in metallic stripe waveguides
Nano Letters, 2012Co-Authors: Giuliana Di Martino, Mark Tame, Yannick Sonnefraud, Stephane Kenacohen, şahin Kaya Ozdemir, M S Kim, Stefan A MaierAbstract:Heralded single surface plasmon polaritons are excited using photons generated via spontaneous parametric down conversion. The mean excitation rates, intensity correlations, and Fock state populations are studied. The observed dependence of the second-order coherence in our experiment is consistent with a linear uncorrelated Markovian environment in the Quantum regime. Our results provide important information about the effect of loss for assessing the potential of plasmonic waveguides for future nanophotonic circuitry in the Quantum regime.
