Generic short-time propagation of sharp-boundaries wave packets

Granot, Er'el; Marchewka, Avi

doi:10.1209/epl/i2005-10264-2

Cited by 40 publications

(48 citation statements)

References 18 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In quantum matter waves, the Moshinsky shutter or the sudden release of rectangular wave packet is also an example of sharp boundaries. The effects arising in the diffraction patterns due to non-sharp boundaries have been investigated recently [5,50,[70][71][72][73].…”

Section: Diffraction In Timementioning

confidence: 99%

Single-slit focusing and its representations

et al. 2017

View full text Add to dashboard Cite

theory of light. Three years later he participated with his Mémoire sur la Diffraction de la Lumière in the Grand Prix of the French Academy of Sciences [2]. It was on this occasion that Siméon Poisson predicted that an opaque disc illuminated by parallel light would create a bright spot in the center of a shadow. This phenomenon was experimentally confirmed by Francois Arago and led to the victory of the wave over the particle theory. In the present article we discuss an effect related to the Poisson spot which is the onedimensional analogue of the camera obscura [3,4].Indeed, we have recently found [5] that a rectangular matter wave packet which undergoes free time evolution according to the Schrödinger equation focuses before it spreads. This phenomenon has been confirmed for light [6], water and surface plasmon waves [7]. In the present article we illustrate this effect in Wigner phase space and verify it using classical light in real space.Our article is organized as follows: in Sect. 2 we first give a brief history of the diffraction of waves, and then review several focusing effects especially those associated with the phenomenon of diffraction in time introduced in Moshinsky [8].We dedicate Sect. 3 to the discussion of the focusing of a rectangular wave packet from the point of view of the timedependent wave function. In particular, we show this effect Abstract We illustrate the phenomenon of the focusing of a freely propagating rectangular wave packet using three different tools: (1) the time-dependent wave function in position space, (2) the Wigner phase-space approach, and (3) an experiment using laser light.

show abstract

Section: Diffraction In Timementioning

confidence: 99%

Single-slit focusing and its representations

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Note that the contribution of the left boundary to the escape probability on the right is O(∆t 3/2 ), (see, e.g., [2], [7], [10]), which is negligible. Adding to (8) the escape probability into the ray x < −1, we obtain the total escape probability…”

Section: Short-time Escape Probabilitymentioning

confidence: 99%

“…Indeed, the short-time escape probability of an initially non-smooth wave function has been discussed several times in the literature [1], [2], [6], [7], [8]. Specifically, it has been shown that in the above mentioned cases the type of discontinuity of the initial wave function determines its escape probability.…”

Section: Introductionmentioning

confidence: 99%

The case of escape probability as linear in short time

Marchewka

Schuss

2018

Physics Letters A

View full text Add to dashboard Cite

We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behaviour, quantum absorption, time of arrival, quantum measurements, and more.

show abstract

“…However, because the quasi-bound state evolves in time, it gains the integral (41) When the incoming energy is above the minimum eigenenergy (i.e., Ω>Ω min *=U−λ 0 2 /4τ 2 ), there are two times, in which Ω=Ω*(t 1 )=Ω*(t 2 ) (see Figure 9), and due to the temporal symmetry of the perturbation t 1 =−t 2 . Therefore, the particle has two options to be temporally bounded to the quasi-eigenstate: it can either begin at t 1 [33], i.e., (42) the particle cannot survive within the well, and activation is frustrated.…”

Section: Selected Elevations and Forbidden Activationsmentioning

confidence: 99%

Dynamic Resonant Tunneling

Granot¹,

Zangwill²

2016

Research Advances in Quantum Dynamics

View full text Add to dashboard Cite

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.

show abstract

Generic short-time propagation of sharp-boundaries wave packets

Cited by 40 publications

References 18 publications

Single-slit focusing and its representations

Single-slit focusing and its representations

The case of escape probability as linear in short time

Dynamic Resonant Tunneling

Contact Info

Product

Resources

About