Time-dependent ballistic phenomena of electron injected into half-ellipse confined room

Takuji Koiso, Masakazu Muraguchi, Kyozaburo Takeda, Naoki Watanabe

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    Abstract

    We theoretically studied the time-developing ballistic phenomena of a single-electron confined in a half-ellipse infinite-potential wall by solving the time-dependent Schrödinger equation numerically. We also solved the corresponding Newton equation in order to compare the classical results with the quantum ones, and extracted the quantum features. The ellipse-shaped potential wall completely reflects an electron and causes the focusing ratio of unity in the classical limit. The dispersion of the wave packet of an electron, however, weakens this characteristic nature, and reduces the focusing ratio from unity. Because the dispersion also lets an electron arrive at the collector indistinctly, we define the effective arrival time by finding inflections in the time-dependent profile of the probability density at the collector. Based on the second-derivation technique, we further determine the quantum arrival time (QAT) at which the intrusion of the wave packet occurs dominantly. The comparison of this QAT with the classical arrival time (CAT) determines whether the corresponding ballistic propagation can be discussed on the basis of the quantum consideration or the classical prediction. We further studied how the change in the half-ellipse potential wall shape affects the ballistic phenomena through the change in the ellipticity γ, the system size L and the dispersion degree σ of the wave packet. Using the ellipse-shaped infinite-potential wall, the application of the magnetic field causes irrational cyclotron motion assisted by the ellipse potential, in addition to the rational cyclotron motions. The numerical solution of the time-dependent Schrödinger equation determines the unique cyclotron motion whose peculiarity is caused by the dispersion of the wave packet and is rarely predicted by the classical limit.

    Original languageEnglish
    Pages (from-to)4252-4268
    Number of pages17
    JournalJapanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers
    Volume44
    Issue number6 A
    DOIs
    Publication statusPublished - 2005 Jun

    Fingerprint

    Wave packets
    ellipses
    Ballistics
    ballistics
    rooms
    Cyclotrons
    Electrons
    wave packets
    arrivals
    electrons
    cyclotrons
    accumulators
    unity
    Magnetic fields
    causes
    ellipticity
    intrusion
    newton
    derivation
    propagation

    Keywords

    • Ballistic phenomena
    • Classical arrival time
    • Cyclotron motion
    • Half-ellipse confined room
    • Quantum arrival time
    • Time-dependent Schrödinger equation
    • Wave packet

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

    Cite this

    Time-dependent ballistic phenomena of electron injected into half-ellipse confined room. / Koiso, Takuji; Muraguchi, Masakazu; Takeda, Kyozaburo; Watanabe, Naoki.

    In: Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers, Vol. 44, No. 6 A, 06.2005, p. 4252-4268.

    Research output: Contribution to journalArticle

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