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

Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers

Volumn 44, Issue 6 A, 2005, Pages 4252-4268

  Koiso, Takuji ^a   Muraguchi, Masakazu ^a   Takeda, Kyozaburo ^a   Watanabe, Naoki ^b  

^a WASEDA UNIVERSITY   (Japan)

^b Fuji Research Institute Corporation   (Japan)

Author keywords

Ballistic phenomena; Classical arrival time; Cyclotron motion; Half ellipse confined room; Quantum arrival time; Time dependent Schr dinger equation; Wave packet

Indexed keywords

DISPERSIONS; NUMERICAL ANALYSIS; QUANTUM THEORY; WAVE PROPAGATION;

BALLISTIC PHENOMENA; CLASSICAL ARRIVAL TIME; CYCLOTRON MOTION; HALF-ELLIPSE CONFINED ROOM; QUANTUM ARRIVAL TIME; TIME-DEPENDENT SCHRÖDINGER EQUATION; WAVE PACKETS;

ELECTRONS;

EID: 23944451079     PISSN: 00214922     EISSN: None     Source Type: Journal    
DOI: 10.1143/JJAP.44.4252     Document Type: Article

References (17)

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7. In actual calculations, we surrounded the present system with a free space twice as large as that in Fig. 1 in order to avoid the reflection from the potential walls of the emitter and collector rooms. Thus, the resulting system is divided into 1024 × 1024 units in the calculations.
8. sℏ)2 = 5.9 meV. The effective unit of the magnetic field B is also equal to 6.76 T in this work.
9. 8)
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13. Under the Cayley approximation, each operator of eq. (13) is exactly unitary, so the norm is conserved strictly, but the energy is not conserved exactly due to the separation of the incommutable operators. Yet it oscillates near its initial values and never drifts monotonically.
14. The reflection rule of the electron wave packet is almost the same as that of geometrical optics while the refraction rule is completely opposite.
15. x dx′ ie/ℏc By. Because the integrated vector potential Ξ(x, y) is just a local function, the two exponential operators appearing in front of and behind the free kinetic operator change the phase contrarily and mutually. This identity is, then, useful if the exponential operator appearing in eq. (18) is decomposed into the x-part and y-part, individually.
16. We found the discrepancy from the classically predicted n-th cyclotron magnetic field both in Figs. 16(a) and 16(b). The corresponding discrepancy increases with an increase in the magnetic field (n number). Figure 16(c) also reveals that the degree of this discrepancy depends on the strength of the magnetic field but is independent of the existence of the ellipse potential wall. Thus, more accurate calculations are required in the high magnetic fields: At the applied magnetic field B = 0.1563 a.u. for example, which induces the 3rd cyclotron motion (orbital d in Fig. 4), the resulting cyclotron orbital is not closed and causes a deviation of 0.283 a.u. by one cycle in the case of the present spatial 0.25 × 0.25 a.u. unit (division of 512 × 512). However, the use of the four-times accurate division unit (0.125 × 0.125 a.u.) reduces this deviation to 0.175 a.u.
17. 2 is possible if an "infinite" amount of time passes. However, within the arrival time of 100-200 comparable to the others, the electron cannot be injected into the focal point.