484 research outputs found
Equivalence between the real time Feynman histories and the quantum shutter approaches for the "passage time" in tunneling
We show the equivalence of the functions and
for the ``passage time'' in tunneling. The former, obtained within the
framework of the real time Feynman histories approach to the tunneling time
problem, using the Gell-Mann and Hartle's decoherence functional, and the
latter involving an exact analytical solution to the time-dependent
Schr\"{o}dinger equation for cutoff initial waves
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
Quantum shutter approach to tunneling time scales with wave packets
The quantum shutter approach to tunneling time scales (G. Garc\'{\i
}a-Calder\'{o}n and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which
uses a cutoff plane wave as the initial condition, is extended in such a way
that a certain type of wave packet can be used as the initial condition. 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 is in the tunneling
regime.Comment: 6 page
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
Quantum-wave evolution in a step potential barrier
By using an exact solution to the time-dependent Schr\"{o}dinger equation
with a point source initial condition, we investigate both the time and spatial
dependence of quantum waves in a step potential barrier. We find that for a
source with energy below the barrier height, and for distances larger than the
penetration length, the probability density exhibits a {\it forerunner}
associated with a non-tunneling process, which propagates in space at exactly
the semiclassical group velocity. We show that the time of arrival of the
maximum of the {\it forerunner} at a given fixed position inside the potential
is exactly the traversal time, . We also show that the spatial evolution
of this transient pulse exhibits an invariant behavior under a rescaling
process. This analytic property is used to characterize the evolution of the
{\it forerunner}, and to analyze the role played by the time of arrival,
, found recently by Muga and B\"{u}ttiker [Phys. Rev. A {\bf 62},
023808 (2000)].Comment: To be published in Phys. Rev. A (2002
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
Extended WKB method, resonances and supersymmetric radial barriers
Semiclassical approximations are implemented in the calculation of position
and width of low energy resonances for radial barriers. The numerical
integrations are delimited by t/T<<8, with t the period of a classical particle
in the barrier trap and T the resonance lifetime. These energies are used in
the construction of `haired' short range potentials as the supersymmetric
partners of a given radial barrier. The new potentials could be useful in the
study of the transient phenomena which give rise to the Moshinsky's diffraction
in time.Comment: 12 pages, 4 figures, 3 table
Composite Spin Waves, Quasi-Particles and Low Temperature resistivity in Double Exchange Systems
We make a quantum description of the electron low temperature properties of
double exchange materials. In these systems there is a strong coupling between
the core spin and the carriers spin. This large coupling makes the low energy
spin waves to be a combination of ion and electron density spin waves. We study
the form and dispersion of these composite spin wave excitations. We also
analyze the spin up and down spectral functions of the temperature dependent
quasi-particles of this system. Finally we obtain that the thermally activated
composite spin waves renormalize the carriers effective mass and this gives
rise to a low temperature resistivity scaling as T ^{5/2}.Comment: 4 pages, REVTE
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