Energy States and Bloch States for an Accelerated Electron in a Periodic Lattice

Churchill, J.N.; Holmstrom, F.E.

doi:10.1088/0031-8949/27/2/006

Cited by 20 publications

(8 citation statements)

References 34 publications

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“…Early evidence of time‐domain Bloch oscillations (BOs) in superlattices was revealed by transient degenerate four‐wave mixing (DFWM) , yielding results in agreement with the work of Esaki and Tsu . BOs emerge when an electron subject to a perfectly periodic lattice potential executes periodic motion in the presence of an external electric field . In recent decades, BOs were found in various physical systems.…”

Section: Introductionsupporting

confidence: 67%

Transient dynamics of a one‐dimensional Holstein polaron under the influence of an external electric field

et al. 2017

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Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external electric field is studied by employing the multi-D 2 Ansatz, also known as a superposition of the usual Davydov D 2 trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton-phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non-zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton-phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite-sized ring within the antiadiabatic regime. For strong diagonal coupling, the multi-D 2 Anstaz is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations.

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Section: Introductionsupporting

confidence: 67%

Transient dynamics of a one‐dimensional Holstein polaron under the influence of an external electric field

et al. 2017

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“…known as the Bloch period. There has been a long-standing controversy about the existence of the Wannier-Stark ladder and Bloch oscillations [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], and only recently agreement about the nature of the Wannier-Stark ladder was reached. The history of this discussion is carefully summarized in [12,[20][21][22].…”

Section: Wannier-stark Problemmentioning

confidence: 99%

Wannier–Stark resonances in optical and semiconductor superlattices

2002

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In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices.

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“…In a subsequent paper, 34 they constructed time-dependent Bloch states which were exact solutions of the TDSE by taking linear combinations of the solutions of the TISE with energies corresponding to the WSL. They showed that such solutions of the TDSE remain in a single band and repeat after the period of one Bloch oscillation.…”

Section: Y/(zt) = 1 " (Z) Exp {-Ie"t / R)mentioning

confidence: 99%

Quantum dynamical phenomena of independent electrons in semiconductor superlattices subject to a uniform electric field

Bouchard

1994

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, "Quantum dynamical phenomena of independent electrons in semiconductor superlattices subject to a uniform electric field " (1993 INFORMATION TO USERSThis manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer.The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction.In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book.

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Energy States and Bloch States for an Accelerated Electron in a Periodic Lattice

Cited by 20 publications

References 34 publications

Transient dynamics of a one‐dimensional Holstein polaron under the influence of an external electric field

Transient dynamics of a one‐dimensional Holstein polaron under the influence of an external electric field

Wannier–Stark resonances in optical and semiconductor superlattices

Quantum dynamical phenomena of independent electrons in semiconductor superlattices subject to a uniform electric field

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