Transient and asymptotic effects in tunneling

Brouard, S.; Muga, J. G.

doi:10.1103/physreva.54.3055

Cited by 57 publications

(59 citation statements)

References 31 publications

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“…Here it is relevant to note that there is an absence of a propagating wave. This agrees with the criticisms to Moretti's approximate analysis [17,18] who claimed that a velocity analogous to the group velocity could be identified along the classically forbidden region [16]. In fact the absence of a propagating wave along the tunneling region can be also inferred from the analytical solution given by Eq.…”

Section: Resonant Statessupporting

confidence: 78%

Transient Effects in Time-Dependent Tunneling

García–Calderón

2002

phys. stat. sol. (b)

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An exact analytic solution of the time-dependent Schrö dinger equation with cutoff wave initial conditions, that goes into the stationary solution at asymptotically long times, is used to investigate the transient behavior in the time evolution of the probability density along the internal and transmitted regions of a potential barrier. The approach involves the complex poles and residues (resonant states) of the outgoing Green's function of the problem. The solution exhibits absence of propagation along the classically forbidden internal region of the potential, and along the transmitted region it splits into two propagating structures. One of them is a transient effect describing the earliest response of the system to the initial condition whereas the other structure evolves towards the stationary solution.Introduction Quantum tunneling, that refers to the possibility that a particle traverses a classical forbidden region, constitutes one of the paradigms of quantum mechanics. In the energy domain, where the stationary Schrö dinger equation at a fixed energy E is solved, tunneling is a well understood process. A simple example is tunneling through a square barrier appearing in most textbooks. In the time domain, however, there are still aspects open to investigation. In fact, recent technological achievements as the possibility of constructing artificial quantum structures at nanometric scales [1] or the manipulation of individual atoms [2] have stimulated work on time-dependent tunneling both at applied and fundamental levels.In a recent paper García-Calderó n and Rubio [3] discussed the time-dependent solution of the Schrö dinger equation for tunneling through an arbitrary potential with the cutoff initial condition of a plane wave of momentum k and applied it to study the dynamics of tunneling in a double-barrier resonant tunneling system. More recently García-Calderó n and Villavicencio [4] studied the time dependence of the probability density at the barrier edge of a rectangular potential barrier as a function of time. At short times they found a time domain resonance that describes the early time response of the system to the initial condition. They also studied the properties of the time domain resonance peak t p as a function of the barrier width and the potential height and compared it with other tunneling time scales.In this work we extend our investigation of the behaviour of the time-dependent solution of the Schrö dinger equation using cutoff wave initial conditions to the internal and transmitted regions of a rectangular potential barrier. In particular we address the issue of the possible particle propagation along the classically forbidden internal region of the potential and analyze the propagation of the probability density along the corresponding transmitted region.

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Section: Resonant Statessupporting

confidence: 78%

Transient Effects in Time-Dependent Tunneling

García–Calderón

2002

phys. stat. sol. (b)

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“…Other works had already pointed out the dominance of non-tunneling components in the forerunner [218,219,171,59,60] but had not characterized its time dependence.…”

Section: Muga-büttiker Analysis Of Evanescent Wavesmentioning

confidence: 98%

Quantum transients

2009

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Quantum transients are temporary features of matter waves before they reach a stationary regime. Transients may arise after the preparation of an unstable initial state or due to a sudden interaction or a change in the boundary conditions. Examples are diffraction in time, buildup processes, decay, trapping, forerunners or pulse formation, as well as other phenomena recently discovered, such as the simultaneous arrival of a wave peak at arbitrarily distant observers. The interest on these transients is nowadays enhanced by new technological possibilities to control, manipulate and measure matter waves.Comment: review article, 76 pp, 36 figures, more content, typos correcte

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“…On the theoretical side the above achievements have stimulated work on the issue of time-dependent tunneling. In particular, one finds a number of works that deal with the solution to the time-dependent Schrödinger's equation for cutoff wave initial states [3,4,5,6]. One interesting feature of these approaches is that at asymptotically long times the time-dependent solution goes into the well known stationary solution.…”

Section: Introductionmentioning

confidence: 99%

Delay time and tunneling transient phenomena

García–Calderón

Villavicencio

2002

Phys. Rev. A

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Analytic solutions to the time-dependent Schrödinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential barrier opacity α, we find that the probability density exhibits two evolving structures. One refers to the propagation of a forerunner related to a time domain resonance [Phys. Rev. A 64, 0121907 (2001)], while the other consists of a semiclassical propagating wavefront. We find a regime where the forerunners are absent, corresponding to positive time delays, and show that this regime is characterized by opacities α < αc. The critical opacity αc is derived from the analytical expression for the delay time, that reflects a link between transient effects in tunneling and the delay time.

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Transient and asymptotic effects in tunneling

Cited by 57 publications

References 31 publications

Transient Effects in Time-Dependent Tunneling

Transient Effects in Time-Dependent Tunneling

Quantum transients

Delay time and tunneling transient phenomena

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