2,437 research outputs found
Background Independent Quantum Mechanics, Metric of Quantum States, and Gravity: A Comprehensive Perspective
This paper presents a comprehensive perspective of the metric of quantum
states with a focus on the background independent metric structures. We also
explore the possibilities of geometrical formulations of quantum mechanics
beyond the quantum state space and Kahler manifold. The metric of quantum
states in the classical configuration space with the pseudo-Riemannian
signature and its possible applications are explored. On contrary to the common
perception that a metric for quantum state can yield a natural metric in the
configuration space with the limit when Planck constant vanishes, we obtain the
metric of quantum states in the configuration space without imposing this
limiting condition. Here, Planck constant is absorbed in the quantity like Bohr
radii. While exploring the metric structure associated with Hydrogen like atom,
we witness another interesting finding that the invariant lengths appear in the
multiple of Bohr radii.Comment: 25 Pages;journal reference added:Published in- Int. J. Theor. Phys.
46 (2007) 3216-3229. References revise
Inseparability of Quantum Parameters
In this work, we show that 'splitting of quantum information' [6] is an
impossible task from three different but consistent principles of unitarity of
Quantum Mechanics, no-signalling condition and non increase of entanglement
under Local Operation and Classical Communication.Comment: 9 pages, Presented in Quantum Computing Back Action in IIT Kanpur
(2006). Accepted in International Journal of Theoretical Physic
Minimum cbits for remote preperation and measurement of a qubit
We show that a qubit chosen from equatorial or polar great circles on a Bloch
spehere can be remotely prepared with one cbit from Alice to Bob if they share
one ebit of entanglement. Also we show that any single particle measurement on
an arbitrary qubit can be remotely simulated with one ebit of shared
entanglement and communication of one cbit.Comment: Latex, 7 pages, minor changes, references adde
General impossible operations in quantum information
We prove a general limitation in quantum information that unifies the
impossibility principles such as no-cloning and no-anticloning. Further, we
show that for an unknown qubit one cannot design a universal Hadamard gate for
creating equal superposition of the original and its complement state.
Surprisingly, we find that Hadamard transformations exist for an unknown qubit
chosen either from the polar or equatorial great circles. Also, we show that
for an unknown qubit one cannot design a universal unitary gate for creating
unequal superpositions of the original and its complement state. We discuss why
it is impossible to design a controlled-NOT gate for two unknown qubits and
discuss the implications of these limitations.Comment: 15 pages, no figures, Discussion about personal quantum computer
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Probing Grand Unification Through Neutrino Oscillations, Leptogenesis, and Proton Decay
Evidence in favor of supersymmetric grand unification including that based on
the observed family multiplet-structure, gauge coupling unification, neutrino
oscillations, baryogenesis, and certain intriguing features of quark-lepton
masses and mixings is noted. It is argued that attempts to understand (a) the
tiny neutrino masses (especially Delta m^2 (nu_2 -nu_3)), (b) the baryon
asymmetry of the universe (which seems to need leptogenesis), and (c) the
observed features of fermion masses such as the ratio m_b/m_tau, the smallness
of V_cb and the maximality of theta_{nu_mu-nu_tau}, seem to select out the
route to higher unification based on an effective string-unified G(224) =
SU(2)_L x SU(2)_R x SU(4)^c or SO(10)-symmetry, operative in 4D, as opposed to
other alternatives.
A predictive framework based on an effective SO(10) or G(224) symmetry
possessing supersymmetry is presented that successfully describes the masses
and mixings of all fermions including neutrinos. It also accounts for the
observed baryon asymmetry of the universe by utilizing the process of
leptogenesis, which is natural to this framework. It is argued that a
conservative upper limit on the proton lifetime within this
SO(10)/G(224)-framework, which is so far most successful, is given by (1/3-2) x
10^34 years. This in turn strongly suggests that an improvement in the current
sensitivity by a factor of five to ten (compared to SuperK) ought to reveal
proton decay. Implications of this prediction for the next-generation nucleon
decay and neutrino-detector are noted.Comment: 40 page, 3 figures. Conference proceedings from Erice School (Sept
2002), Neutrino Conference (Stony Brook, 2002), PASCOS Conference (Mumbai,
2003) Version 2: New references and some clarifications adde
Geometric Phases for Mixed States during Cyclic Evolutions
The geometric phases of cyclic evolutions for mixed states are discussed in
the framework of unitary evolution. A canonical one-form is defined whose line
integral gives the geometric phase which is gauge invariant. It reduces to the
Aharonov and Anandan phase in the pure state case. Our definition is consistent
with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85},
2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the
parallel transport condition. A comprehensive geometric interpretation is also
given. It shows that the geometric phases for mixed states share the same
geometric sense with the pure states.Comment: 9 pages, 1 figur
Mediation of Long Range Charge Transfer by Kondo Bound States
We present a theory of non-equilibrium long range charge transfer between
donor and acceptor centers in a model polymer mediated by magnetic exciton
(Kondo) bound states. Our model produces electron tunneling lengths easily
exceeding 10, as observed recently in DNA and organic charge transfer
systems. This long ranged tunneling is effective for weak to intermediate
donor-bridge coupling, and is enhanced both by weak to intermediate strength
Coulomb hole-electron attraction (through the orthogonality catastrophe) and by
coupling to local vibrational modes.Comment: Revised content (broadened scope, vibrations added), submitted to
Phys Rev Lett, added autho
Dark matter from SU(4) model
The left-right symmetric Pati-Salam model of the unification of quarks and
leptons is based on SU(4) and SU(2)xSU(2) groups. These groups are naturally
extended to include the classification of families of quarks and leptons. We
assume that the family group (the group which unites the families) is also the
SU(4) group. The properties of the 4-th generation of fermions are the same as
that of the ordinary-matter fermions in first three generations except for the
family charge of the SU(4)_F group: F=(1/3,1/3,1/3,-1), where F=1/3 for
fermions of ordinary matter and F=-1 for the 4-th generation. The difference in
F does not allow the mixing between ordinary and fourth-generation fermions.
Because of the conservation of the F charge, the creation of baryons and
leptons in the process of electroweak baryogenesis must be accompanied by the
creation of fermions of the 4-th generation. As a result the excess n_B of
baryons over antibaryons leads to the excess n_{\nu 4}=N-\bar N=n_B of
neutrinos over antineutrinos in the 4-th generation. This massive
fourth-generation neutrino may form the non-baryonic dark matter. In principle
their mass density n_{\nu 4}m_N in the Universe can give the main contribution
to the dark matter, since the lower bound on neutrino mass m_N from the data on
decay of the Z-bosons is m_N > m_Z/2. The straightforward prediction of this
model leads to the amount of cold dark matter relative to baryons, which is an
order of magnitude bigger than allowed by observations. This inconsistency may
be avoided by non-conservation of the F-charge.Comment: 9 pages, 2 figures, version accepted in JETP Letters, corrected after
referee reports, references are adde
Neutrinoless double beta decay in SO(10) inspired seesaw models
By requiring the lower limit for the lightest right-handed neutrino mass,
obtained in the baryogenesis from leptogenesis scenario, and a Dirac neutrino
mass matrix similar to the up-quark mass matrix we predict small values for the
mass and for the matrix element responsible of the
neutrinoless double beta decay, around eV and
smaller than eV, respectively. The allowed range for the
mass of the heaviest right-handed neutrino is centered around the value of the
scale of B - L breaking in the SO(10) gauge theory with Pati-Salam intermediate
symmetry.Comment: 9 pages, RevTex4. Revised, title change
Observing Nucleon Decay in Lead Perchlorate
Lead perchlorate, part of the OMNIS supernova neutrino detector, contains two
nuclei, 208Pb and 35Cl, that might be used to study nucleon decay. Both would
produce signatures that will make them especially useful for studying
less-well-studied neutron decay modes, e.g., those in which only neutrinos are
emitted.Comment: 6 pages, 2 figure
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