Coherent state based solutions of the time-dependent Schrödinger equation: hierarchy of approximations to the variational principle

Werther, Michael; Choudhury, Sreeja Loho; Großmann, Frank

doi:10.1080/0144235x.2020.1823168

Cited by 37 publications

(36 citation statements)

References 188 publications

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“…For key references see, e.g. [39][40][41][42][43] and the reviews [33,44]. However, there has been considerable debate whether these approaches can be used to model tunnel ionisation, as they employ ensembles of real classical trajectories to construct wave packets [141][142][143][144].Tunnelling may manifest itself in position space, as transmission, or in momentum space, as above-the-barrier reflection, and it not being accounted correctly will cause semiclassical IVRs to degrade for longer times [144].…”

Section: Tunnellingmentioning

confidence: 99%

“…Coherent states have also been widely used to construct IVRs guided by Gaussians in phase space, such as the HK propagator [42], the CCS representation [43], the linearised semiclassical IVRs [40] and the Frozen Gaussian Approximation [41]. For a detailed discussion and more coherent-state based IVRS see the recent review [44]. 3 For the Herman-Kluk propagator, we consider a state vector…”

Section: Initial Value Representations (Ivrs)mentioning

confidence: 99%

“…Alternatively, one may develop semiclassical methods, in which swarms of classical trajectories are employed to construct quantum propagators (see, e.g. [39][40][41][42][43] and the reviews [33,44]). Further approximations may then be applied, such as the smoothening of highly oscillatory terms [7], and linearised semiclassical approximations, in which the main contributions stem from trajectories whose phase space coordinates are close enough [40].…”

Section: Introductionmentioning

confidence: 99%

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Attoscience in phase space

Chomet

Faria

2021

Eur. Phys. J. D

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We provide a brief review of how phase space techniques are explored within strong-field and attosecond science. This includes a broad overview of the existing landscape, with focus on strong-field ionisation and rescattering, high-order harmonic generation, stabilisation and free-electron lasers. Furthermore, using our work on the subject, which deals with ionisation dynamics in atoms and diatomic molecules as well as high-order harmonic generation in inhomogeneous fields, we exemplify how such tools can be employed. One may for instance determine qualitatively different phase space dynamics, explore how bifurcations influence ionisation and high-harmonic generation, establish for which regimes classical and quantum correspondence works or fails, and what role different timescales play. Finally, we conclude the review highlighting the importance of the tools available in quantum optics, quantum information and physical chemistry to strong-field laser–matter interaction. Graphic Abstract

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Section: Tunnellingmentioning

confidence: 99%

Section: Initial Value Representations (Ivrs)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Attoscience in phase space

Chomet

Faria

2021

Eur. Phys. J. D

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“…CS have been implementing during the last two decades as an advantageous basis set for solving 3D TDSE for high dimensional quantum systems in the presence of an ultra-short intense laser field. 45,[49][50][51][52][53][54][55][56] One of their beneficial characteristics is that their grid can be generated randomly. The major problem which other basis sets involves Coulombic potential singularities.…”

Section: Introductionmentioning

confidence: 99%

“…SCS method solves the 3D TDSE on the base of a static grid of coherent states (CS). CS have been implementing during the last two decades as an advantageous basis set for solving 3D TDSE for high dimensional quantum systems in the presence of an ultra‐short intense laser field 45,49–56 . One of their beneficial characteristics is that their grid can be generated randomly.…”

Section: Introductionmentioning

confidence: 99%

High‐order harmonic generation by static coherent states method in single‐electron atomic and molecular systems

et al. 2021

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We solve the time-dependent Schrodinger equation using the coherent states as basis sets for computing high harmonic generation (HHG) in a full-dimensional singleelectron "realistic" system. We apply the static coherent states (SCS) method to investigate HHG in the hydrogen molecular ion induced by a linearly polarized laser field. We show that SCS gives reasonable agreement compared to the three dimensional unitary split-operator approach. Next, we study isolated attosecond pulse gen-To do so, we employ the well-known polarization gating technique, which combines two delayed counter-rotating circular laser pulses, and opens up a gate at the central portion of the superposed pulse. Our results suggest that the SCS method can be used for full-dimensional quantum simulation of higher dimensional systems such as the hydrogen molecule in the presence of an external laser field.

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The hierarchy of Davydov's Ansätze and its applications

Zhao

Sun

Chen

et al. 2021

WIREs Comput Mol Sci

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This review provides a bird's eye view over the development of the hierarchy of Davydov's Ansätze and its applications in a variety of problems in computational physical chemistry. Davydov's original solitons appeared in the 1970s as a candidate for vibrational energy carriers in proteins, thanks to their association with the Fröhlich Hamiltonian and the Holstein molecular crystal model.Momentum-space projection of those solitary waves emerged to be great approximations to the ground-state wave functions of the extended Holstein Hamiltonian, lending unambiguous evidence to the absence of formal quantum phase transitions in those systems. The multiple Davydov Ansätze are introduced, with increasing multiplicity, as incremental improvements of their corresponding single-Ansatz parents. The time-dependent variational formalism of Davydov's Ansätze is discussed in great detail, and the relative deviation of the Ansätze is constructed to quantify how faithfully they follow the Schrödinger equation, a quantity that is shown to vanish in the limit of large multiplicities. Three approaches to finite-temperature variational dynamics of Davydov's Ansätze are demonstrated, namely, the Monte Carlo importance sampling, the method of thermo-field dynamics, and the method of displaced number states. Applications of Davydov's Ansätze are given to variants of the spin-boson model, the Landau-Zener transition, the Holstein Hamiltonian, energy transfer in light-harvesting, and singlet fission in organic photovoltaics.As an example, simulation of multidimensional spectroscopic signals via Davydov's Ansätze is fully implemented for the finite-temperature fission process in crystalline rubrene.

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Coherent state based solutions of the time-dependent Schrödinger equation: hierarchy of approximations to the variational principle

Cited by 37 publications

References 188 publications

Attoscience in phase space

Attoscience in phase space

High‐order harmonic generation by static coherent states method in single‐electron atomic and molecular systems

The hierarchy of Davydov's Ansätze and its applications

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