91 research outputs found
Recovering the stationary phase condition for accurately obtaining scattering and tunneling times
The stationary phase method is often employed for computing tunneling {\em
phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth
step pulses which collide with a potential barrier. The indiscriminate
utilization of this method without considering the barrier boundary effects
leads to some misconceptions in the interpretation of the phase times. After
reexamining the above barrier diffusion problem where we notice the wave packet
collision necessarily leads to the possibility of multiple reflected and
transmitted wave packets, we study the phase times for tunneling/reflecting
particles in a framework where an idea of multiple wave packet decomposition is
recovered. To partially overcome the analytical incongruities which rise up
when tunneling phase time expressions are obtained, we present a theoretical
exercise involving a symmetrical collision between two identical wave packets
and a one dimensional squared potential barrier where the scattered wave
packets can be recomposed by summing the amplitudes of simultaneously reflected
and transmitted waves.Comment: 32 pages, 5 figures, 1 tabl
Limitations on the principle of stationary phase when it is applied to tunneling analysis
Using a recently developed procedure - multiple wave packet decomposition -
here we study the phase time formulation for tunneling/reflecting particles
colliding with a potential barrier. To partially overcome the analytical
difficulties which frequently arise when the stationary phase method is
employed for deriving phase (tunneling) time expressions, we present a
theoretical exercise involving a symmetrical collision between two identical
wave packets and an one-dimensional rectangular potential barrier. Summing the
amplitudes of the reflected and transmitted waves - using a method we call
multiple peak decomposition - is shown to allow reconstruction of the scattered
wave packets in a way which allows the stationary phase principle to be
recovered.Comment: 17 pages, 2 figure
Topological Insulators with Inversion Symmetry
Topological insulators are materials with a bulk excitation gap generated by
the spin orbit interaction, and which are different from conventional
insulators. This distinction is characterized by Z_2 topological invariants,
which characterize the groundstate. In two dimensions there is a single Z_2
invariant which distinguishes the ordinary insulator from the quantum spin Hall
phase. In three dimensions there are four Z_2 invariants, which distinguish the
ordinary insulator from "weak" and "strong" topological insulators. These
phases are characterized by the presence of gapless surface (or edge) states.
In the 2D quantum spin Hall phase and the 3D strong topological insulator these
states are robust and are insensitive to weak disorder and interactions. In
this paper we show that the presence of inversion symmetry greatly simplifies
the problem of evaluating the Z_2 invariants. We show that the invariants can
be determined from the knowledge of the parity of the occupied Bloch
wavefunctions at the time reversal invariant points in the Brillouin zone.
Using this approach, we predict a number of specific materials are strong
topological insulators, including the semiconducting alloy Bi_{1-x} Sb_x as
well as \alpha-Sn and HgTe under uniaxial strain. This paper also includes an
expanded discussion of our formulation of the topological insulators in both
two and three dimensions, as well as implications for experiments.Comment: 16 pages, 7 figures; published versio
Negative phase time for Scattering at Quantum Wells: A Microwave Analogy Experiment
If a quantum mechanical particle is scattered by a potential well, the wave
function of the particle can propagate with negative phase time. Due to the
analogy of the Schr\"odinger and the Helmholtz equation this phenomenon is
expected to be observable for electromagnetic wave propagation. Experimental
data of electromagnetic wells realized by wave guides filled with different
dielectrics confirm this conjecture now.Comment: 10 pages, 6 figure
Sub-femtosecond determination of transmission delay times for a dielectric mirror (photonic bandgap) as a function of angle of incidence
Using a two-photon interference technique, we measure the delay for
single-photon wavepackets to be transmitted through a multilayer dielectric
mirror, which functions as a ``photonic bandgap'' medium. By varying the angle
of incidence, we are able to confirm the behavior predicted by the group delay
(stationary phase approximation), including a variation of the delay time from
superluminal to subluminal as the band edge is tuned towards to the wavelength
of our photons. The agreement with theory is better than 0.5 femtoseconds (less
than one quarter of an optical period) except at large angles of incidence. The
source of the remaining discrepancy is not yet fully understood.Comment: 5 pages and 5 figure
Conditional probabilities in quantum theory, and the tunneling time controversy
It is argued that there is a sensible way to define conditional probabilities
in quantum mechanics, assuming only Bayes's theorem and standard quantum
theory. These probabilities are equivalent to the ``weak measurement''
predictions due to Aharonov {\it et al.}, and hence describe the outcomes of
real measurements made on subensembles. In particular, this approach is used to
address the question of the history of a particle which has tunnelled across a
barrier. A {\it gedankenexperiment} is presented to demonstrate the physically
testable implications of the results of these calculations, along with graphs
of the time-evolution of the conditional probability distribution for a
tunneling particle and for one undergoing allowed transmission. Numerical
results are also presented for the effects of loss in a bandgap medium on
transmission and on reflection, as a function of the position of the lossy
region; such loss should provide a feasible, though indirect, test of the
present conclusions. It is argued that the effects of loss on the pulse {\it
delay time} are related to the imaginary value of the momentum of a tunneling
particle, and it is suggested that this might help explain a small discrepancy
in an earlier experiment.Comment: 11 pages, latex, 4 postscript figures separate (one w/ 3 parts
Negative group delay for Dirac particles traveling through a potential well
The properties of group delay for Dirac particles traveling through a
potential well are investigated. A necessary condition is put forward for the
group delay to be negative. It is shown that this negative group delay is
closely related to its anomalous dependence on the width of the potential well.
In order to demonstrate the validity of stationary-phase approach, numerical
simulations are made for Gaussian-shaped temporal wave packets. A restriction
to the potential-well's width is obtained that is necessary for the wave packet
to remain distortionless in the travelling. Numerical comparison shows that the
relativistic group delay is larger than its corresponding non-relativistic one.Comment: 10 pages, 5 figure
Tin telluride: a weakly co-elastic metal
We report resonant ultrasound spectroscopy (RUS),
dilatometry/magnetostriction, magnetotransport, magnetization, specific heat,
and Sn M\"ossbauer spectroscopy measurements on SnTe and
SnCrTe. Hall measurements at K indicate that our
Bridgman-grown single crystals have a -type carrier concentration of cm and that our Cr-doped crystals have an -type
concentration of cm. Although our SnTe crystals are
diamagnetic over the temperature range , the Cr-doped crystals are room temperature ferromagnets with a Curie
temperature of 294 K. For each sample type, three-terminal capacitive
dilatometry measurements detect a subtle 0.5 micron distortion at K. Whereas our RUS measurements on SnTe show elastic hardening near the
structural transition, pointing to co-elastic behavior, similar measurements on
SnCrTe show a pronounced softening, pointing to
ferroelastic behavior. Effective Debye temperature, , values of SnTe
obtained from Sn M\"ossbauer studies show a hardening of phonons in the
range 60--115K ( = 162K) as compared with the 100--300K range
( = 150K). In addition, a precursor softening extending over
approximately 100 K anticipates this collapse at the critical temperature, and
quantitative analysis over three decades of its reduced modulus finds with , a value
indicating a three-dimensional softening of phonon branches at a temperature
K, considerably below . We suggest that the differences in
these two types of elastic behaviors lie in the absence of elastic domain wall
motion in the one case and their nucleation in the other
On a universal photonic tunnelling time
We consider photonic tunnelling through evanescent regions and obtain general
analytic expressions for the transit (phase) time (in the opaque barrier
limit) in order to study the recently proposed ``universality'' property
according to which is given by the reciprocal of the photon frequency.
We consider different physical phenomena (corresponding to performed
experiments) and show that such a property is only an approximation. In
particular we find that the ``correction'' factor is a constant term for total
internal reflection and quarter-wave photonic bandgap, while it is
frequency-dependent in the case of undersized waveguide and distributed Bragg
reflector. The comparison of our predictions with the experimental results
shows quite a good agreement with observations and reveals the range of
applicability of the approximated ``universality'' property.Comment: RevTeX, 8 pages, 4 figures, 1 table; subsection added with a new
experiment analyzed, some other minor change
Superluminal Localized Solutions to Maxwell Equations propagating along a waveguide: The finite-energy case
In a previous paper of ours [Phys. Rev. E64 (2001) 066603, e-print
physics/0001039] we have shown localized (non-evanescent) solutions to Maxwell
equations to exist, which propagate without distortion with Superluminal speed
along normal-sized waveguides, and consist in trains of "X-shaped" beams. Those
solutions possessed therefore infinite energy. In this note we show how to
obtain, by contrast, finite-energy solutions, with the same localization and
Superluminality properties. [PACS nos.: 41.20.Jb; 03.50.De; 03.30.+p; 84.40.Az;
42.82.Et. Keywords: Wave-guides; Localized solutions to Maxwell equations;
Superluminal waves; Bessel beams; Limited-dispersion beams; Finite-energy
waves; Electromagnetic wavelets; X-shaped waves; Evanescent waves;
Electromagnetism; Microwaves; Optics; Special relativity; Localized acoustic
waves; Seismic waves; Mechanical waves; Elastic waves; Guided gravitational
waves.]Comment: plain LaTeX file (12 pages), plus 10 figure
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