Jorge Villavicencio

Hermitian and non-Hermitian formulations of the time evolution of quantum decay

This work discusses Hermitian and non-Hermitian formulations for the time evolution of quantum decay, which involve, respectively, continuum wave functions and resonant states, to show that they lead to an identical description for a large class of well-behaved potentials. Our approach is based on the analytical properties of the outgoing Green function to the problem in the complex wave number plane.

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 a regime could be observed in semiconductor double-barrier resonant quantum structures with appropriate parameters.

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 Schrodinger 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 us to manipulate the above frequencies to control the tunneling transient behavior of the probability density in the short-time regime.

Transient time-domain resonances and the time scale for tunneling

Transient time-domain resonances found recently in time-dependent solutions to Schrodingers equation are used to investigate the issue of the tunneling time in rectangular potential barriers. In general, a time-frequencyanalysis shows that these transients have frequencies above the cutoff frequency associated with the barrier height, and hence correspond to nontunneling processes. We find, however, a regime characterized by the barrier opacity, where the peak maximum t m a x of the time-domain resonance corresponds to under-the-barrier tunneling. We argue that t m a x represents the relevant tunneling time scale through the classically forbidden region.

Exact relativistic time evolution for a step potential barrier

We derive an exact analytic solution to a Klein-Gordon equation for a step potential barrier with cutoff plane wave initial conditions, in order to explore wave evolution in a classical forbidden region. We find that the relativistic solution rapidly evanesces within a depth 2xp inside the potential, where xp is the penetration length of the stationary solution. Beyond the characteristic distance 2xp, a Sommerfeld-type precursor travels along the potential at the speed of light, c. However, no spatial propagation of a main wavefront along the structure is observed. We also find a non-causal time evolution of the wavefront peak. The effect is only an apparent violation of Einstein causality.

Quantum-shutter approach to tunneling time scales with wave packets

The quantum-shutter approach to tunneling time scales [G. Garcia-Calderon and A. Rubio, Phys. Rev. A 55, 3361 (1997)], which uses a cutoff plane wave as the initial condition, is extended to consider certain type of wave packet initial conditions. An analytical expression for the time-evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit of the barrier, originally found with the cutoff plane wave initial condition, is studied with the wave packet initial conditions. It is found that the time-domain resonance is not very sensitive to the width of the packet when the transmission process occurs in the tunneling regime.

Role of the buildup oscillations on the speed of resonant tunneling diodes

The fastest tunneling response in double barrier resonant structures is investigated by considering explicit analytic solutions of the time-dependent Schrodinger equation. For cutoff initial plane waves, we find that the earliest tunneling events consist of the emission of a series of propagating pulses of the probability density governed by the buildup oscillations in the quantum well. We show that the fastest tunneling response comes from the contribution of incident carriers at energies different from resonance, and that its relevant time scale is given by τr=πℏ/|E−e|, where e is the resonance energy and E is the incidence energy.

Quasienergy spectrum and tunneling current in ac-driven triple quantum dot shuttles

The dynamics of electrons in ac-driven double quantum dots have been extensively analyzed by means of Floquet theory. In these systems, coherent destruction of tunneling has been shown to occur for certain ac field parameters. In this work we analyze, by means of Floquet theory, the electron dynamics of a triple quantum dot in series attached to electric contacts, where the central dot position oscillates. In particular, we analyze the quasienergy spectrum of this ac-driven nanoelectromechanical system as a function of the intensity and frequency of the ac field and of external dc voltages. For strong driving fields, we derive, by means of perturbation theory, analytical expressions for the quasienergies of the driven oscillator system. From this analysis, we discuss the conditions for coherent destruction of tunneling (CDT) to occur as a function of detuning and field parameters. For zero detuning, and from the invariance of the Floquet Hamiltonian under a generalized parity transformation, we find analytical expressions describing the symmetry properties of the Fourier components of the Floquet states under such a transformation. By using these expressions, we show that in the vicinity of the CDT condition, the quasienergy spectrum exhibits exact crossings which can be characterized by the parity properties of the corresponding eigenvectors.

Hermitian and non-Hermitian description of quantum wave propagation

Two different approaches that provide solutions of the time-dependent Schrodinger equation for the quantum shutter initial condition, are used and compared in the description of transient quantum wave propagation. One of them is a (non-Hermitian) resonance formalism that involves a discrete resonant state expansion of the wavefunction in terms of the resonances of the system, and the other one is a (Hermitian) approach based on a continuum wavefunction expansion of the solution. We investigate the equivalence of these different methods in resonant structures finding that the two approaches lead to results that are numerically indistinguishable from each other. In particular, we verify that the continuum wavefunction expansion predicts the existence of resonance forerunners in the probability density, which are identical to those obtained with the resonance state formalism. We also provide with useful criteria for the numerical evaluation of the solutions obtained with both formulations based on the knowledge of the relevant contributions of the spectrum in momentum k space.