4,324 research outputs found
The Leggett-Garg inequality and Page-Wootters mechanism
Violation of the Leggett-Garg inequality (LGI) implies quantum phenomena. In
this light we establish that the Moreva \textit{et al.} \cite{moreva}
experiment demonstrating the Page-Wootter's mechanism \cite{wootters} falls in
the quantum domain. An observer outside a 2-photons world does not detect any
change in the photons state,i.e. there is no time parameter for the outside
observer. But an observer attached to one of the photons sees the other photon
evolving and this means there is an "internal" time. The LGI is violated for
the clock photon whose state evolves with the internal time as measured by the
system photon. Conditional probabilities in this 2-photons system are computed
for both sharp and unsharp measurements. The conditional probability increases
for entangled states as obtained by Page and Wootters for both ideal and also
unsharp measurements. We discuss how the conditional probabilities can be used
to distinguish between massless and massive gravitons. This is important in the
context of gravitational waves.Comment: 5 pages, Late
dimensional Dirac equation with non Hermitian interaction
We study dimensional Dirac equation with non Hermitian interactions,
but real energies. In particular, we analyze the pseudoscalar and scalar
interactions in detail, illustrating our observations with some examples. We
also show that the relevant hidden symmetry of the Dirac equation with such an
interaction is pseudo supersymmetry.Comment: 9 page
Scattering states of a particle, with position-dependent mass, in a symmetric heterojunction
The study of a particle with position-dependent effective mass (pdem), within
a double heterojunction is extended into the complex domain --- when the region
within the heterojunctions is described by a non Hermitian
symmetric potential. After obtaining the exact analytical solutions, the
reflection and transmission coefficients are calculated, and plotted as a
function of the energy. It is observed that at least two of the characteristic
features of non Hermitian symmetric systems --- viz., left / right
asymmetry and anomalous behaviour at spectral singularity, are preserved even
in the presence of pdem. The possibility of charge conservation is also
discussed.Comment: 12 pages, including 6 figures; Journal of Physics A : Math. Theor.
(2012
Scattering states of a particle, with position-dependent mass, in a double heterojunction
In this work we obtain the exact analytical scattering solutions of a
particle (electron or hole) in a semiconductor double heterojunction -
potential well / barrier - where the effective mass of the particle varies with
position inside the heterojunctions. It is observed that the spatial dependence
of mass within the well / barrier introduces a nonlinear component in the plane
wave solutions of the continuum states. Additionally, the transmission
coefficient is found to increase with increasing energy, finally approaching
unity, whereas the reflection coefficient follows the reverse trend and goes to
zero.Comment: 7 pages, 6 figure
symmetric models with nonlinear pseudo supersymmetry
By applying the higher order Darboux algorithm to an exactly solvable non
Hermitian symmetric potential, we obtain a hierarchy of new
exactly solvable non Hermitian symmetric potentials with real
spectra. It is shown that the symmetry underlying the potentials so generated
and the original one is {\it nonlinear pseudo supersymmetry}. We also show that
this formalism can be used to generate a larger class of new solvable
potentials when applied to non Hermitian systems.Comment: 18 page
SWKB Quantization Rules for Bound States in Quantum Wells
In a recent paper by Gomes and Adhikari (J.Phys B30 5987(1997)) a matrix
formulation of the Bohr-Sommerfield quantization rule has been applied to the
study of bound states in one dimension quantum wells. Here we study these
potentials in the frame work of supersymmetric WKB (SWKB) quantization
approximation and find that SWKB quantization rule is superior to the modified
Bohr-Sommerfield or WKB rules as it exactly reproduces the eigenenergies.Comment: 8 page
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