The exact propagator for an electron in a uniform electric field and its application to Stark effect calculations

Lukes, Timothy J.; Somaratna, K.T.S.

doi:10.1088/0022-3719/2/4/303

Cited by 29 publications

(8 citation statements)

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“…It translates as a Dirac potential V (η) ∼ δ(η) in Eq.20. It is known that a particle in such a narrow potential, and also submitted to an electric field, has no bound state, even for γ infinitesimally small (see [49] and Appendix C for more details). Therefore the resolvent has no simple pole, and the expansions presented in Section II are not valid anymore.…”

Section: Discussionmentioning

confidence: 99%

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Growth over time-correlated disorder: a spectral approach to Mean-field

Gueudré

2016

Preprint

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We generalize a model of growth over a disordered environment, to a large class of Itō processes.In particular, we study how the microscopic properties of the noise influence the macroscopic growth rate. The present model can account for growth processes in large dimensions, and provides a bed to understand better the trade-off between exploration and exploitation. An additional mapping to the Schrördinger equation readily provides a set of disorders for which this model can be solved exactly. This mean-field approach exhibits interesting features, such as a freezing transition and an optimal point of growth, that can be studied in details, and gives yet another explanation for the occurrence of the Zipf law in complex, well-connected systems.

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Section: Discussionmentioning

confidence: 99%

“…For δ potentials, the Dyson equation can be solved exactly in coordinate representation, and gives the Green function G γ as a function of the well-known Green function, noted G 0 , for the free particle under an electric field [49]:…”

Section: Appendix B: Monotonous Decay Of the Annealed Branchmentioning

confidence: 99%

Growth over time-correlated disorder: a spectral approach to Mean-field

Gueudré

2016

Preprint

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“…Therefore, after the electron kinetic energies reach 100 eV, we used a propagator under constant DC fields. For the case of solving the TDSE under constant DC fields, an analytical formula can be obtained, and one can simulate wave functions after any time interval 36 . This allowed us to obtain the far-field wave functions.…”

Section: Methodsmentioning

confidence: 99%

Optical Control of Young’s Type Double-slit Interferometer for Laser-induced Electron Emission from a Nano-tip

Yanagisawa

Ciappina

Hafner³

et al. 2017

Sci Rep

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Interference experiments with electrons in a vacuum can illuminate both the quantum and the nanoscale nature of the underlying physics. An interference experiment requires two coherent waves, which can be generated by splitting a single coherent wave using a double slit. If the slit-edge separation is larger than the coherence width at the slit, no interference appears. Here we employed variations in surface barrier at the apex of a tungsten nano-tip as slits and achieved an optically controlled double slit, where the separation and opening-and-closing of the two slits can be controlled by respectively adjusting the intensity and polarization of ultrashort laser pulses. Using this technique, we have demonstrated interference between two electron waves emitted from the tip apex, where interference has never been observed prior to this technique because of the large slit-edge separation. Our findings pave the way towards simple time-resolved electron holography on e.g. molecular adsorbates employing just a nano-tip and a screen.

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“…The wave functions in this area were in a vacuum-namely, they were the emitted electrons. The extracted wave functions were then propagated onto a screen using the formula provided in reference [33]. The emission pattern is thus a map of the intensities of the far-eld wave function integrated along the perpendicular axis to the screen.…”

Section: Full Textmentioning

confidence: 99%

Subnanometeric optical modulation of a single-molecule electron source

Yanagisawa

Bohn

Kitoh-Nishioka

et al. 2022

Preprint

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The irradiation of femtosecond light pulses onto nano-objects creates localised optical fields on the nanostructure surfaces. Plasmonic effects spatially modulate the local-field distribution, achieving optical control of an ultrafast electron source on a scale of approximately 10 nm. Further miniaturisation of such an electron source down to an atomistically small scale is technically difficult by modulating the local-field distribution via plasmonic effects. Here, by illuminating recently identified single-molecule electron sources with femtosecond light pulses, we discovered that largely modulated emission patterns appeared from single C60 molecules, approximately one nanometre in size. Our simulations revealed that the emission patterns represented the single-molecule molecular orbitals (MOs), and the observed modulations originated from the variations of the single-molecule MOs, practically achieving subnanometric optical modulation of an electron source. Our work has thus demonstrated a simple way to continue miniaturising the spatially-controlled electron source down to an atomistic scale using quantum effects.

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The exact propagator for an electron in a uniform electric field and its application to Stark effect calculations

Cited by 29 publications

References 1 publication

Growth over time-correlated disorder: a spectral approach to Mean-field

Growth over time-correlated disorder: a spectral approach to Mean-field

Optical Control of Young’s Type Double-slit Interferometer for Laser-induced Electron Emission from a Nano-tip

Subnanometeric optical modulation of a single-molecule electron source

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