Apoptosis of moving nonorthogonal basis functions in many-particle quantum dynamics

Werther, Michael; Großmann, Frank

doi:10.1103/physrevb.101.174315

Cited by 37 publications

(32 citation statements)

References 39 publications

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“…Until recently, improvements upon harmonic models were limited to fairly expensive, exact quantum methods. [27] To propagate accurate nuclear wavepackets without precomputing potential energy surfaces, a number of direct dynamics or on-the-fly methods [28][29][30][31][32][33][34][35][36][37] were developed, which require only local potential energy information along the trajectories guiding the wavepacket. Most of these employ multiple Gaussian wavepackets, whose propagation can be costly when coupled µ(q) ≈ µ(q 0 ), ( 6)…”

Section: Beyond Global Harmonic Models: Thawed Gaussian Approximationmentioning

confidence: 99%

Efficient Semiclassical Dynamics for Vibronic Spectroscopy beyond Harmonic, Condon, and Zero-Temperature Approximations

Begušić

Vaníček

2021

Chimia

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Understanding light-induced processes in biological and human-made molecular systems is one of the main goals of physical chemistry. It has been known for years that the photoinduced dynamics of atomic nuclei can be studied by looking at the vibrational substructure of electronic absorption and emission spectra. However, theoretical simulation is needed to understand how dynamics translates into the spectral features. Here, we review several recent developments in the computation of vibrationally resolved electronic spectra (sometimes simply called 'vibronic' spectra). We present a theoretical approach for computing such spectra beyond the commonly used zero-temperature, Condon, and harmonic approximations. More specifically, we show how the on-the-fly ab initio thawed Gaussian approximation, which partially includes anharmonicity effects, can be combined with the thermo-field dynamics to treat non-zero temperature and with the Herzberg-Teller correction to include non-Condon effects. The combined method, which can treat all three effects, is applied to compute the S1 ← S0 and S2 ← S0 absorption spectra of azulene.

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Section: Beyond Global Harmonic Models: Thawed Gaussian Approximationmentioning

confidence: 99%

Efficient Semiclassical Dynamics for Vibronic Spectroscopy beyond Harmonic, Condon, and Zero-Temperature Approximations

Begušić

Vaníček

2021

Chimia

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“…where the Lagrangian L is to be found in appendix A. The integration of equations of motion for the variational variables u i can result in numerical instabilities [57]. An apoptosis procedure has been implemented to circumvent the singularity problem of the numerical solver that makes the multi-D2 ansatz a rather stable tool in the study of polaron dynamics [68].…”

Section: Multi-d2 Ansatzmentioning

confidence: 99%

“…In that respect we say that the method is numerically accurate within the theoretical model of the system. The method has been applied to a multitude of systems, including a Holstein model of polaron dynamics in the presence of external fields [54][55][56], phase transitions in the spin-boson model [57] or singlet fission model [58], a dissipative LZ model that is based on QED protocols [41,59] and other investigations in quantum optics [60,61].…”

Section: Introductionmentioning

confidence: 99%

Polaron dynamics of Bloch–Zener oscillations in an extended Holstein model

et al. 2021

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Recent developments in qubit engineering make circuit quantum electrodynamics devices promising candidates for the study of Bloch oscillations (BOs) and Landau–Zener (LZ) transitions. In this work, a hybrid circuit chain with alternating site energies under external electric fields is employed to study Bloch–Zener oscillations (BZOs), i.e. coherent superpositions of BOs and LZ transitions. We couple each of the tunable qubits in the chain to dispersionless optical phonons and build an extended Holstein polaron model with the purpose of investigating vibronic effects in the BZOs. We employ an extension of the Davydov ansatz in combination with the Dirac–Frenkel time-dependent variational principle to simulate the dynamics of the qubit chain under the influence of high-frequency quantum harmonic oscillators. Band gaps emerge due to energy differences in site energies at alternating qubit sites, and are shown to play key roles in tuning band structures and time periodic reconstructions of the wave patterns. In the absence of qubit–phonon interactions, the qubits undergo either standard BZOs or breathing modes, depending on whether the initial wave packet is formed by a broad or narrow Gaussian wave packet, respectively. The BZOs can get localized in space if the band gaps are sufficiently large. In the presence of qubit–phonon coupling, the periodic behavior of BZOs can be washed out and undergo dynamic localization. The influence of an ohmic bath on the dynamics of BZOs is investigated by means of a Markovian master equation approach. Finally, we calculate the von Neumann entropy as a measure of the entanglement between qubits and phonons.

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“…and we have given the fully variational equations of motion in [42]. In the case that the Ansatz ( 9) is restricted to a single term, i.e., M = 1, these equations reduce to…”

Section: B Coupling To a Finite Heat Bathmentioning

confidence: 99%

Quantum approach to the thermalization of the toppling pencil interacting with a finite bath

Choudhury¹,

Großmann²

2021

Preprint

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We investigate the longstanding problem of thermalization of quantum systems coupled to an environment by focusing on a bistable quartic oscillator interacting with a finite number of harmonic oscillators. In order to overcome the exponential wall that one usually encounters in grid based approaches to solve the time-dependent Schrödinger equation of the extended system, methods based on the time-dependent variational principle are best suited. Here we will apply the method of coupled coherent states [D. V. Shalashilin and M. S. Child, J. Chem. Phys. 113, 10028 (2000)].By investigating the dynamics of an initial wavefunction on top of the barrier of the double well, it will be shown that only a handful of oscillators with suitably chosen frequencies, starting in their ground states, is enough to drive the bistable system close to its uncoupled ground state. The long-time average of the double-well energy is found to be a monotonously decaying function of the number of environmental oscillators in the parameter range that was numerically accessible.

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Apoptosis of moving nonorthogonal basis functions in many-particle quantum dynamics

Cited by 37 publications

References 39 publications

Efficient Semiclassical Dynamics for Vibronic Spectroscopy beyond Harmonic, Condon, and Zero-Temperature Approximations

Efficient Semiclassical Dynamics for Vibronic Spectroscopy beyond Harmonic, Condon, and Zero-Temperature Approximations

Polaron dynamics of Bloch–Zener oscillations in an extended Holstein model

Quantum approach to the thermalization of the toppling pencil interacting with a finite bath

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