Electronic States in Crystals under Large Over-All Perturbations

Abstract

points the spike rarely settles, but oscillates about the surface with great rapidity. With steel points, on the other hand, the discharge frequently anchors itself to one spot, and there remains quite steady, only moving about when the field is increased almost to Qashover. It is not unusual for the stem to take up a position off, and inclined to, the axis of symmetry. When the point is subsequently examined under the microscope it is usually found that the spot favored by the root of the discharge, coincides with a small crater on the surface. These form more readily on steel than on platinum, the process no doubt being assisted by chemical action, and this may account for the effect referred to.Discourse on the mechanism of the transition from the Trichel pulse regime to the pulse-free discharge would be little more than speculation at this stage, comment is therefore reserved until a more thorough investigation of the phenomenon has been made. It is perhaps worth stating that too much importance should not be attached to the changes in shape of the induced Trichel pulses as the transition is approached, since these are largely conditioned by the circuit. PH YSICAL REVIEWSolutions of the three-dimensional Schrodinger equation are discussed for a potential which is the sum of a potential with the periodicity of the crystal lattice plus a perturbing potential. A general theory of large over-all perturbations, such that the energy lies close to one permitted band in one region of the crystal and close to a second permitted band in another, is developed. The theory is then applied to a one-dimensional crystal in a uniform electric field, using the narrow band approximation; the probability for an electron to cross a forbidden energy band is calculated. These results are considered in connection with the interpretation of the current-voltage characteristic of an N -P junction of germanium at high electric fields.

Entanglement in spin chains with gradients

“…dq 2π e −iτ sin(q−ϕ)+iqn = e iϕn J n (τ ). (19) with ϕ = arctan(t/λ). Thus, up to phase factors the quantities F n are Bessel functions with argument τ , a fact which was not realized in [13].…”

On the existence of Stark ladders in finite crystals

“…Zak (1968) has further stated that even in the most favourable case for the existence of a ladder, a one-band linear tight-binding chain, none could result. Other workers, such as Feuer (1952) and Hacker and Obermair (1970), have examined the infinite linear chain and find ladder-like behaviour, and Shockley (1972) suggested that, under certain conditions, this may be true even for finite crystals.…”

“…have been discussed for an infinite chain by Feuer (1952) and Hacker and Obermair (1970). In this case.…”

Intraband polarization as the source of degenerate four-wave mixing signals in asymmetric semiconductor quantum well structures

“…The electronic stationary states in a periodic potential with period d in the presence of an external dc electric field E dc are localized in a one-band approximation and have energies E n ϭE 0 ϩenE dc d, where n is an integer. 25 These equally spaced states form the so-called Wannier Stark ladder ͑WSL͒ in the BSSL; they were first evidenced experimentally by Mendez et al, 26 and have been theoretically treated with the inclusion of excitonic effects by a number of authors. [27][28][29][30] Shortly after the experimental observation of the WSL states, the dynamical behavior of excitons in BSSL's were investigated both theoretically 31 and experimentally.…”