Semiclassical propagation for multidimensional systems by an initial value method

Kay, Kenneth G.

doi:10.1063/1.467665

Cited by 253 publications

(162 citation statements)

References 52 publications

Supporting

Mentioning

156

Contrasting

Unclassified

Order By: Relevance

“…These calculations demonstrated importance of coupling of the reaction modes to the vibrational modes and predicted absorption spectrum. The drawbacks of the semiclassical initial value representation methods are the expensive stability analysis that scales as N 2 , the notorious sign problem of the oscillatory phase space integrals resulting in a very large number of trajectories, [12][13][14] and also difficulties in assessing the semiclassical error and in systematically improving semiclassical description toward full quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Energy conserving approximations to the quantum potential: Dynamics with linearized quantum force

Garashchuk

Rassolov

2004

The Journal of Chemical Physics

View full text Add to dashboard Cite

Solution of the Schrödinger equation within the de Broglie-Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact time-evolution of a correlated Gaussian wave function in a locally quadratic potential. The method is computationally cheap in many dimensions, conserves total energy and satisfies the criterion on the average quantum force. Expectation values are readily found by summing over trajectory weights. Efficient extraction of the phase-dependent quantities is discussed. We illustrate the efficiency and accuracy of the linear quantum force approximation by examining a one-dimensional scattering problem and by computing the wavepacket reaction probability for the hydrogen exchange reaction and the photodissociation spectrum of ICN in two dimensions.

show abstract

Section: Introductionmentioning

confidence: 99%

Energy conserving approximations to the quantum potential: Dynamics with linearized quantum force

Garashchuk

Rassolov

2004

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…(19) takes the form The Ðnal expression for the correlation o J 2 o \ p 2 /(m H /J3). function is C AB (t) \ PP dp 1 dp 2 dq…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Semiclassical approach to the hydrogen-exchange reaction Reactive and transition-state dynamics

Garashchuk¹,

Großmann²,

Tannor³

1997

Faraday Trans.

View full text Add to dashboard Cite

Scattering matrix elements and symmetric transition-state resonances for the collinear reaction are obtainedH 2 using a time-dependent approach. The correlation function between reactant channel wavepackets and product channel wavepackets is used to determine the S-matrix elements. In a similar fashion, autocorrelation functions are used to extract the positions and widths of transition-state resonances. The time propagation of the wavepackets is performed by the improved semiclassical frozen Gaussian method of Herman and Kluk, which is an initial value, uniformly converged method. The agreement between the quantum and semiclassical results is far better than that obtained previously for this system by other semiclassical methods.

show abstract

“…If the typical actions involved in the system are large compared to , the propagator can be approximated semiclassically employing fixed width (so-called frozen) Gaussian wave packets r|z(r, p) , centered around the phase space points r and p. The resulting propagator was developed by Herman and Kluk [21], based on previous work done by Heller [22], and brought back to the center of attention by Kay [23,24]. The so-called Herman-Kluk propagator applied to an initial Gaussian state |z 0 reads [9]…”

Section: The Semiclassical Herman-kluk Propagatormentioning

confidence: 99%

Time-dependent semiclassics for ultracold bosons

Simon

Strunz

2014

Phys. Rev. A

View full text Add to dashboard Cite

We study the out-of-equilibrium dynamics of ultracold bosons in a double-and triple-well potential within the Bose-Hubbard model by means of the semiclassical Herman-Kluk propagator and compare the results to the frequently applied "classical dynamics" calculation in terms of the truncated Wigner approximation (TWA). For the double-well system we find the semiclassical results in excellent agreement with the numerically exact ones, while the TWA is not able to reproduce any revivals of the wave function. The triple-well system turns out to be more difficult to handle due to the irregularity of the corresponding classical phase space. Here, deviations of the TWA from the exact dynamics appear even for short times, while better agreement is obtained using the semiclassical approach presented in this article.

show abstract

Semiclassical propagation for multidimensional systems by an initial value method

Cited by 253 publications

References 52 publications

Energy conserving approximations to the quantum potential: Dynamics with linearized quantum force

Energy conserving approximations to the quantum potential: Dynamics with linearized quantum force

Semiclassical approach to the hydrogen-exchange reaction Reactive and transition-state dynamics

Time-dependent semiclassics for ultracold bosons

Contact Info

Product

Resources

About