432 research outputs found
Charged particles in a rotating magnetic field
We study the valence electron of an alkaline atom or a general charged
particle with arbitrary spin and with magnetic moment moving in a rotating
magnetic field. By using a time-dependent unitary transformation, the
Schr\"odinger equation with the time-dependent Hamiltonian can be reduced to a
Schr\"odinger-like equation with a time-independent effective Hamiltonian.
Eigenstates of the effective Hamiltonian correspond to cyclic solutions of the
original Schr\"odinger equation. The nonadiabatic geometric phase of a cyclic
solution can be expressed in terms of the expectation value of the component of
the total angular momentum along the rotating axis, regardless of whether the
solution is explicitly available. For the alkaline atomic electron and a strong
magnetic field, the eigenvalue problem of the effective Hamiltonian is
completely solved, and the geometric phase turns out to be a linear combination
of two solid angles. For a weak magnetic field, the same problem is solved
partly. For a general charged particle, the problem is solved approximately in
a slowly rotating magnetic field, and the geometric phases are also calculated.Comment: REVTeX, 13 pages, no figure. There are two minor errors in the
published version due to incorrect editing by the publisher. The "spin-1" in
Sec. I and the "spin 1" in Sec. II below Eq. (2c) should both be changed to
"spin" or "spin angular momentum". The preferred E-mail for correspondence is
[email protected] or [email protected]
Measuring Pancharatnam's relative phase for SO(3) evolutions using spin polarimetry
In polarimetry, a superposition of internal quantal states is exposed to a
single Hamiltonian and information about the evolution of the quantal states is
inferred from projection measurements on the final superposition. In this
framework, we here extend the polarimetric test of Pancharatnam's relative
phase for spin proposed by Wagh and Rakhecha [Phys. Lett. A {\bf 197},
112 (1995)] to spin undergoing noncyclic SO(3) evolution. We
demonstrate that the output intensity for higher spin values is a polynomial
function of the corresponding spin intensity. We further propose a
general method to extract the noncyclic SO(3) phase and visibility by rigid
translation of two spin flippers. Polarimetry on higher spin states
may in practice be done with spin polarized atomic beams.Comment: New title, minor corrections, journal reference adde
Observation of off-diagonal geometric phase in polarized neutron interferometer experiments
Off-diagonal geometric phases acquired in the evolution of a spin-1/2 system
have been investigated by means of a polarized neutron interferometer. Final
counts with and without polarization analysis enable us to observe
simultaneously the off-diagonal and diagonal geometric phases in two detectors.
We have quantitatively measured the off-diagonal geometric phase for noncyclic
evolutions, confirming the theoretical predictions. We discuss the significance
of our experiment in terms of geometric phases (both diagonal and off-diagonal)
and in terms of the quantum erasing phenomenon.Comment: pdf, 22 pages + 8 figures (included in the pdf). In print on Phys.
Rev.
Performance Analysis of MUSIC and Smooth MUSIC Algorithm for DOA Estimation
Smart Antenna Systems is one amongst speedily developing areas of wireless communication. With effective direction of arrival (DOA) and Beam forming techniques Smart Antenna Systems persuade is most effective in terms of quality of signals in wireless communication. This paper analyzed and compares the performance of MUSIC and Smooth MUSIC DOA estimation algorithm on the uniform linear array (ULA) which are used in design of smart antenna system. MUSC algorithm is high resolution subspace based method which is used for DOA estimation of uncorrelated signals while smoothing of MUSIC is introduced for DOA estimation of completely correlated signal. The angular resolution of DOA estimation techniques improves as number of elements in array, snapshots and values of SNR increases.
DOI: 10.17762/ijritcc2321-8169.15071
Geometric Phases and Multiple Degeneracies in Harmonic Resonators
In a recent experiment Lauber et al. have deformed cyclically a microwave
resonator and have measured the adiabatic normal-mode wavefunctions for each
shape along the path of deformation. The nontrivial observed cyclic phases
around a 3-fold degeneracy were accounted for by Manolopoulos and Child within
an approximate theory. However, open-path geometrical phases disagree with
experiment. By solving exactly the problem, we find unsuspected extra
degeneracies around the multiple one that account for the measured phase
changes throughout the path. It turns out that proliferation of additional
degeneracies around a multiple one is a common feature of quantum mechanics.Comment: 4 pages, 4 figures. Accepted in Phys. Rev. Let
Off-Diagonal Geometric Phases
We investigate the adiabatic evolution of a set of non-degenerate eigenstates
of a parameterized Hamiltonian. Their relative phase change can be related to
geometric measurable quantities that extend the familiar concept of Berry phase
to the evolution of more than one state. We present several physical systems
where these concepts can be applied, including an experiment on microwave
cavities for which off-diagonal phases can be determined from published data.Comment: 5 pages 2 figures - RevTeX. Revised version including geometrical
interpretatio
Geometric phases for neutral and charged particles in a time-dependent magnetic field
It is well known that any cyclic solution of a spin 1/2 neutral particle
moving in an arbitrary magnetic field has a nonadiabatic geometric phase
proportional to the solid angle subtended by the trace of the spin. For neutral
particles with higher spin, this is true for cyclic solutions with special
initial conditions. For more general cyclic solutions, however, this does not
hold. As an example, we consider the most general solutions of such particles
moving in a rotating magnetic field. If the parameters of the system are
appropriately chosen, all solutions are cyclic. The nonadiabatic geometric
phase and the solid angle are both calculated explicitly. It turns out that the
nonadiabatic geometric phase contains an extra term in addition to the one
proportional to the solid angle. The extra term vanishes automatically for spin
1/2. For higher spin, however, it depends on the initial condition. We also
consider the valence electron of an alkaline atom. For cyclic solutions with
special initial conditions in an arbitrary strong magnetic field, we prove that
the nonadiabatic geometric phase is a linear combination of the two solid
angles subtended by the traces of the orbit and spin angular momenta. For more
general cyclic solutions in a strong rotating magnetic field, the nonadiabatic
geometric phase also contains extra terms in addition to the linear
combination.Comment: revtex, 18 pages, no figur
Noncyclic geometric phase for neutrino oscillation
We provide explicit formulae for the noncyclic geometric phases or
Pancharatnam phases of neutrino oscillations. Since Pancharatnam phase is a
generalization of the Berry phase, our results generalize the previous findings
for Berry phase in a recent paper [Phys. Lett. B, 466 (1999) 262]. Unlike the
Berry phase, the noncyclic geometric phase offers distinctive advantage in
terms of measurement and prediction. In particular, for three-flavor mixing,
our explicit formula offers an alternative means of determining the
CP-violating phase. Our results can also be extended easily to explore
geometric phase associated with neutron-antineutron oscillations
Comment on "Neutron Interferometric Observation of Noncyclic Phase"
A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep
1998)] to measure the noncyclic phase associated with a precessing neutron spin
in a neutron interferometer, as given by the Pancharatnam criterion, is
presented. It is pointed out that since the experiment measures, not the
noncyclic phase itself, but a quantity derived from it, it misses the most
interesting feature of such a phase, namely the different sign associated with
states lying in the upper and the lower hemispheres, a feature originating in
the existence of a phase singularity. Such effects have earlier been predicted
and seen in optical interference experiments using polarization of light as the
spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].Comment: 5 pages, 0 figures, submitted to Phys.Rev.Let
A clinical study on the effect of Bilvapatra Ghana in the management of Madhumeha with respect to Type II Diabetes Mellitus
In the course of evolution of human life, man has struggled a lot to obtain the best of living standards. Among all necessities, health care is given the best attention because, only healthy individual can enjoy the benefits of beauties of the nature. Positive health doesn’t mean only physical but physiological, mental, social and spiritual wellbeing also. If the principles of Ayurveda are studied in modern scientific way, both in respect of its approach to disease and therapy, especially in relation to Madhumeha. Diabetes results when the body makes too little insulin or does not use insulin properly, allowing sugar levels to build up in the blood stream. The free radicals are one of the important etiological factors for the development of diabetes and its complications. Antioxidants capable of protecting against the damage induced by free radicals and it also have a role in reducing the effects of diabetes. There are many herbal medicinal plants like Babul, Bilva, Davana, Neem, Jambu etc. with proven antidiabetic and related beneficial effects. Bilvapatra is effective in the treatment for diabetes by reducing blood glucose level. So in present study Bilvapatra Ghana is used in the management of Madhumeha
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