Short-time quantum dynamics of sharp boundaries potentials

Granot, Er'el; Marchewka, Avi

doi:10.1016/j.physb.2014.11.010

Cited by 3 publications

(5 citation statements)

References 26 publications

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“…Therefore, in the short-time regime, the effect of the potential term can be ignored in comparison to the kinetic one (for a detailed explanation, see Refs. [20,21] and references therein). Therefore, in the short time that follows the shutter's removal, the wavefunction singularity governs the wavefunction dynamics, and the non-linear electron-electron interaction can be neglected.…”

Section: Quantum Wire In 3dmentioning

confidence: 99%

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Universal Short-Time Conductance Behavior Emerges between Two Adjacent Reservoirs

Granot

2024

Condensed Matter

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When a shutter, which differentiates between two adjacent particles’ reservoirs with a voltage gap, is lifted, a current emerges. In this paper, the temporal dynamics of this emerging current is analyzed. The main results are as follows: (A) the current’s prefactor in the short-time behavior is related to the long-time frequencies, by which the current converges to its equilibrium value (the conductance quantum unit 2e2/h). (B) In the short-time regime, the current is proportional to the square root of the time. (C) The maximum overshoot conductance is bounded by Gmax = ζe2/h, where ζ is a universal value which is very close to Euler’s number. (D) Most of these results are valid for a thin wire in 3D, even in the presence of electron–electron interactions.

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Section: Quantum Wire In 3dmentioning

confidence: 99%

mentioning

confidence: 99%

Universal Short-Time Conductance Behavior Emerges between Two Adjacent Reservoirs

Granot

2024

Condensed Matter

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“…Therefore, it is clear that activation is suppressed when (50) which, in the slowly varying approximation (i.e., large τ), correspond to (see [40]) (51) Therefore, the incoming energies for which Ω act ≅ Ω, and thus no activation occurs, are approximately (see Figures 10 and 11) (52) Therefore, Eq. (42) should be rewritten more accurately as (53) like destructive interference condition in the WKB approximation (see, for example, ref.…”

Section: Selected Elevations and Forbidden Activationsmentioning

confidence: 99%

“…To illustrate this point, we define the mean activated energy (40) where P(ω act Ω) is the probability of an incoming particle with energy Ω to exit the barrier with the energy ω act . In Figure 7 the mean activation energy <ω act > is plotted as a function of the perturbation time scale τ, and in Figure 8, <ω act > is plotted as a function of the incoming particle's energy Ω.…”

Section: Selected Elevations and Forbidden Activationsmentioning

confidence: 99%

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Dynamic Resonant Tunneling

Granot¹,

Zangwill²

2016

Research Advances in Quantum Dynamics

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The physics of dynamic resonant tunneling is investigated.First, the resonant tunneling effect through an opaque barrier via a delta-function well is illustrated. Then, it is shown that, even in the adiabatic regime, where the dynamics can be governed by an analytic solution, the particle can be activated to higher energies. If the well varies quickly enough that the particle cannot escape from the well during the energetic elevation, the activation can be enhanced, as was anticipated by Azbel. However, and this is the main result of this work, the quasi-bound state of the well can even "reduce" the activation. In fact, because the resonant energy of the well matches twice the incoming particle's energy, and if the contribution to the wave function from both parts destructively interferes, then the particle cannot dwell in the well and activation is suppressed.This effect can be utilized in frequency-controlled transistors, and it is even speculated that it may explain the reason that humans can distinguish between tens of thousands of different odors with merely few hundreds of odor receptors.Lastly, the short time dynamics of a very fast perturbative well is also discussed.

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