The Split-Operator Technique for the Study of Spinorial Wavepacket Dynamics

Chaves, Andrey; Farias, G. A.; Peeters, F. M.; Ferreira, Rogelma M. S.

doi:10.4208/cicp.110914.281014a

Cited by 36 publications

(35 citation statements)

References 38 publications

(46 reference statements)

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“…Alternatively, as we are interested only in the trion ground state, we obtain it by evolving an arbitrary initial wave packet in imaginary time τ = it until convergence is reached. The potential and kinetic energy terms in the time evolution operator U (τ + τ, τ ) = exp(−H ± τ/h) are conveniently split into a series of exponentials [51][52][53], where T i is the kinetic energy term in the i direction (for a system with N dimensions). This procedure requires lower computational cost, by paying the price of having a O( τ 3 ) error due to the noncommutativity between kinetic and potential operators, which is controlled here by using a small imaginary time step τ .…”

Section: B Neutral and Charged Excitonsmentioning

confidence: 99%

Ab initio and semiempirical modeling of excitons and trions in monolayer TiS3

et al. 2018

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We explore the electronic and the optical properties of monolayer TiS 3 , which shows in-plane anisotropy and is composed of a chain-like structure along one of the lattice directions. Together with its robust direct band gap, which changes very slightly with stacking order and with the thickness of the sample, the anisotropic physical properties of TiS 3 make the material very attractive for various device applications. In this study, we present a detailed investigation on the effect of the crystal anisotropy on the excitons and the trions of the TiS 3 monolayer. We use many-body perturbation theory to calculate the absorption spectrum of anisotropic TiS 3 monolayer by solving the Bethe-Salpeter equation. In parallel, we implement and use a Wannier-Mott model for the excitons that takes into account the anisotropic effective masses and Coulomb screening, which are obtained from ab initio calculations. This model is then extended for the investigation of trion states of monolayer TiS 3 . Our calculations indicate that the absorption spectrum of monolayer TiS 3 drastically depends on the polarization of the incoming light, which excites different excitons with distinct binding energies. In addition, the binding energies of positively and the negatively charged trions are observed to be distinct and they exhibit an anisotropic probability density distribution.

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Section: B Neutral and Charged Excitonsmentioning

confidence: 99%

Ab initio and semiempirical modeling of excitons and trions in monolayer TiS3

et al. 2018

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“…This approximation, based on the Suzuki-Trotter expansion, has a O(∆τ 3 ) error, which is controlled here by using a small imaginary timestep ∆τ . [29][30][31] By propagating an arbitrary initial wave function in imaginary time, this method directly yields the trion ground state energy E T and the trion wave function, but requires storing a high-dimensional numerical array. In this case, reducing the number of variables of the system is of essence.…”

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confidence: 99%

Theoretical investigation of electron-hole complexes in anisotropic two-dimensional materials

et al. 2016

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“…This value is determined by condition (50), which implies that a typical anomalous velocity induced by SOC, V so ∼ α, exceed the collapse velocity V c , see Eq. (32). If α = α cr , the simulations demonstrate that the BEC starts its evolution by compressing in the beginning, but then slightly expands (not shown in detail).…”

Section: Collapse In the Presence Of The Spin-orbit Coupling And mentioning

confidence: 89%

Coupled density-spin Bose–Einstein condensates dynamics and collapse in systems with quintic nonlinearity

Malomed

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

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We investigate the effects of spin-orbit coupling and Zeeman splitting on the coupled density-spin dynamics and collapse of the Bose-Einstein condensate driven by the quintic self-attraction in the same-and cross-spin channels. The characteristic feature of the collapse is the decrease in the width as given by the participation ratio of the density rather than by the expectation values of the coordinate. Qualitative arguments and numerical simulations reveal the existence of a critical spin-orbit coupling strength which either prohibits or leads to the collapse, and its dependence on other parameters, such as the condensate's norm, spin-dependent nonlinear coupling, and the Zeeman splitting. The entire nonlinear dynamics critically depends on the initial spin sate.

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The Split-Operator Technique for the Study of Spinorial Wavepacket Dynamics

Cited by 36 publications

References 38 publications

Ab initio and semiempirical modeling of excitons and trions in monolayer TiS3

Ab initio and semiempirical modeling of excitons and trions in monolayer TiS3

Theoretical investigation of electron-hole complexes in anisotropic two-dimensional materials

Coupled density-spin Bose–Einstein condensates dynamics and collapse in systems with quintic nonlinearity

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