Transient tunneling effects of resonance doublets in triple barrier systems

Transient tunneling effects in triple barrier systems are investigated by considering a time-dependent solution to the Schr\"{o}dinger equation with a cutoff wave initial condition. We derive a two-level formula for incidence energies $E$ near the first resonance doublet of the system. Based on that expression we find that the probability density along the internal region of the potential, is governed by three oscillation frequencies: one of them refers to the well known Bohr frequency, given in terms of the first and second resonance energies of the doublet, and the two others, represent a coupling with the incidence energy $E$. This allows to manipulate the above frequencies to control the tunneling transient behavior of the probability density in the short-time regim

Full time nonexponential decay in double-barrier quantum structures

We examine an analytical expression for the survival probability for the time evolution of quantum decay to discuss a regime where quantum decay is nonexponential at all times. We find that the interference between the exponential and nonexponential terms of the survival amplitude modifies the usual exponential decay regime in systems where the ratio of the resonance energy to the decay width, is less than 0.3. We suggest that such regime could be observed in semiconductor double-barrier resonant quantum structures with appropriate parameters.Comment: 6 pages, 5 figure

Dynamical description of the buildup process in resonant tunneling: Evidence of exponential and non-exponential contributions

The buildup process of the probability density inside the quantum well of a double-barrier resonant structure is studied by considering the analytic solution of the time dependent Schr\"{o}dinger equation with the initial condition of a cutoff plane wave. For one level systems at resonance condition we show that the buildup of the probability density obeys a simple charging up law, $| \Psi (\tau) / \phi | =1-e^{-\tau /\tau_0},$ where $\phi$ is the stationary wave function and the transient time constant $\tau_0$ is exactly two lifetimes. We illustrate that the above formula holds both for symmetrical and asymmetrical potential profiles with typical parameters, and even for incidence at different resonance energies. Theoretical evidence of a crossover to non-exponential buildup is also discussed.Comment: 4 pages, 2 figure

Tunneling dynamics in relativistic and nonrelativistic wave equations

We obtain the solution of a relativistic wave equation and compare it with the solution of the Schroedinger equation for a source with a sharp onset and excitation frequencies below cut-off. A scaling of position and time reduces to a single case all the (below cut-off) nonrelativistic solutions, but no such simplification holds for the relativistic equation, so that qualitatively different ``shallow'' and ``deep'' tunneling regimes may be identified relativistically. The nonrelativistic forerunner at a position beyond the penetration length of the asymptotic stationary wave does not tunnel; nevertheless, it arrives at the traversal (semiclassical or B\"uttiker-Landauer) time "tau". The corresponding relativistic forerunner is more complex: it oscillates due to the interference between two saddle point contributions, and may be characterized by two times for the arrival of the maxima of lower and upper envelops. There is in addition an earlier relativistic forerunner, right after the causal front, which does tunnel. Within the penetration length, tunneling is more robust for the precursors of the relativistic equation

Free initial wave packets and the long-time behavior of the survival and nonescape probabilities

The behavior of both the survival S(t) and nonescape P(t) probabilities at long times for the one-dimensional free particle system is shown to be closely connected to that of the initial wave packet at small momentum. We prove that both S(t) and P(t) asymptotically exhibit the same power-law decrease at long times, when the initial wave packet in momentum representation behaves as O(1) or O(k) at small momentum. On the other hand, if the integer m becomes greater than 1, S(t) and P(t) decrease in different power-laws at long times.Comment: 4 pages, 3 figures, Title and organization changed, however the results not changed, To appear in Phys. Rev.

Time scale of forerunners in quantum tunneling

The forerunners preceding the main tunneling signal of the wave created by a source with a sharp onset or by a quantum shutter, have been generally associated with over-the-barrier (non-tunneling) components. We demonstrate that, while this association is true for distances which are larger than the penetration lenght, for smaller distances the forerunner is dominated by under-the-barrier components. We find that its characteristic arrival time is inversely proportional to the difference between the barrier energy and the incidence energy, a tunneling time scale different from both the phase time and the B\"uttiker-Landauer (BL) time.Comment: Revtex4, 14 eps figure