Quantum rates for a double well coupled to a dissipative bath: Accurate path integral results and comparison with approximate theories

A new continuous configuration time-dependent self-consistent field method has been developed to study polyatomic dynamical problems by using the discrete variable representation for the reaction system, and applied to a reaction system coupled to a bath. The method is very efficient because the equations involved are as simple as those in the traditional single configuration approach, and can account for the correlations between the reaction system and bath modes rather well. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1869496͔The last decade has witnessed significant progress in quantum mechanical studies of dynamical chemical processes at the molecular level. The development of the timedependent wave packet ͑TDWP͒ method has made it possible to perform exact quantum mechanical calculations for four-atom systems. [1][2][3][4] The recent report on the state-to-state integral cross sections for the H + H 2 O reaction suggests that we are close to solving four-atom reactive scattering problems completely. 2 The grand challenge in the field of quantum dynamics now is to develop practical yet accurate methods to study polyatomic dynamical problems involving many atoms. However, due to the fact that computational effort grows exponentially with dimensionality, it is impractical at present to study polyatomic dynamical processes exactly in full dimensions although there has been some progress in this direction. 5 Naturally, one has to resort to the reduced dimensionality approach to cut down the number of degrees of freedom included in dynamical studies, or some computational approximate methods to overcome the scaling of effort with dimensionality.A promising approach is the time-dependent selfconsistent field ͑TDSCF͒ method. [6][7][8][9][10][11][12][13][14][15] In the simplest version, i.e., the single configuration time-dependent self-consistent field ͑SC-TDSCF͒ approach, the wave function of the system is written as a direct product of the wave functions for subsystems. [7][8][9][10]12 A principal drawback of SC-TDSCF is that it replaces exact interaction between subsystems by meanfield coupling, resulting in the lack of correlations between subsystems. One way to account for the important correlations neglected in SC-TDSCF is to add wave functions with different configurations to give more flexibility to the wave function of the system, resulting in the so-called multiconfiguration time-dependent self-consistent field ͑MC-TDSCF͒ method. 6,13-15 Wave functions with different configurations are usually constructed by imposing orthogonal condition explicitly, making it hard to use more than a few configurations in numerical implementation. Furthermore, the resulting equations for MC-TDSCF are very complicated compared to those in SC-TDSCF method. For these reasons, MC-TDSCF has only been applied to some model problems. The closely related multiconfiguration time-dependent Hartree method ͑MCTDH͒ generalizes MC-TDSCF in a systematic way, thus eliminating the need for choices of the TDSCF states. 16,17 It ha...

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confidence: 95%

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confidence: 99%

Continuous configuration time-dependent self-consistent field method for polyatomic quantum dynamical problems

Zhang

Bao

Yang

et al. 2005

“…Second, the expression for the rate constant as a time integral over flux-flux auto correlation function has been evaluated earlier both analytically and numerically using path integral approaches. Although for equilibrium properties the imaginary time propagator has proved to be very much successful 23 , particularly for developing quantum transition state theory 35 , it is not easy to extract dynamical information for nonequilibrium problems 22 because of the oscillatory nature of the real time propagator in many situations. The c-number phase space method that we use here, on the other hand, being independent of path integral approach is an alternative for calculation of the rate without these problems.…”

Section: Introductionmentioning

confidence: 99%

“…, extension of Kramers results to non-Markovian regime 4,5,6 , generalizations to higher dimensions 7,8 , inclusion of complex potentials 9,10 , generalization to open systems 11,12,13 , analysis of semiclassical and quantum effects 14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29 , thermal ratchet 30 and molecular motors 31 etc. These developments have been the subject of several reviews and monographs.We refer to 15,16,17,22 .…”

Section: Introductionmentioning

confidence: 99%

Quantum phase-space function formulation of reactive flux theory

Barik

Banik

Ray

2003

On the basis of a coherent state representation of quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee et al, Phys. Rev. E 65, 021109 (2002); 66, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a time dependent quantum transmission coefficient -a quantum analogue of classical Kramers'-Grote-Hynes coefficient in the spirit of Kohen and Tannor's classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the non-Markovian limits have been worked out in detail for intermediate to strong damping regime with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the low temperature regime.

“…To overcome such difficulty, the numerical analytic continuation scheme based on the maximum entropy method has been proposed to be applied to various quantum dynamical problems [7,8,9]. As an alternative approach, one can directly evaluate the real time path integrals, although this suffers from the sign problem; the error grows exponentially with time because of the rapid oscillation which originates from the factor exp(iS[q(t)]/ ) [2, 10,11]. In addition to these approaches, another numerical method has been proposed to evaluate the eigenstates of quantum systems using the path integral and to construct the real time quantum correlation functions [12].…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamical correlations: Effective potential analytic continuation approach

Horikoshi

Kinugawa

2003

We propose a new quantum dynamics method called the effective potential analytic continuation (EPAC) to calculate the real time quantum correlation functions at finite temperature. The method is based on the effective action formalism which includes the standard effective potential. The basic notions of the EPAC are presented for a one-dimensional double well system in comparison with the centroid molecular dynamics (CMD) and the exact real time quantum correlation function. It is shown that both the EPAC and the CMD well reproduce the exact short time behavior, while at longer time their results deviate from the exact one. The CMD correlation function damps rapidly with time because of ensemble dephasing. The EPAC correlation function, however, can reproduce the long time oscillation inherent in the quantum double well systems. It is also shown that the EPAC correlation function can be improved toward the exact correlation function by means of the higher order derivative expansion of the effective action.