1,084 research outputs found
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 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 . 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, where is the
stationary wave function and the transient time constant 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
- …