2,535 research outputs found
Birefringent Gravitational Waves and the Consistency Check of Inflation
In this work we show that the gravitational Chern-Simons term, aside from
being a key ingredient in inflationary baryogenesis, modifies super-horizon
gravitational waves produced during inflation. We compute the super-Hubble
gravitational power spectrum in the slow-roll approximation and show that its
overall amplitude is modified while its spectral index remains unchanged (at
leading order in the slow-roll parameters). Then, we calculate the correction
to the tensor to scalar ratio, T/S. We find a correction of T/S which is
dependent on (more precisely quadratic in ), the parameter
characterizing the amplitude of the Chern-Simons terms. In a stringy embedding
of the leptogenesis mechanism, is the ratio between the Planck scale
and the fundamental string scale. Thus, in principle, we provide a direct probe
of leptogenesis due to stringy dynamics in the Cosmic Microwave Background
(CMB). However, we demonstrate that the corresponding correction of T/S is in
fact very small and not observable in the regime where our calculations are
valid. To obtain a sizable effect, we argue that a non-linear calculation is
necessary.Comment: 9 pages, 1 figure, RevTe
Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation
We analyze the position and momentum uncertainties of the energy eigenstates
of the harmonic oscillator in the context of a deformed quantum mechanics,
namely, that in which the commutator between the position and momentum
operators is given by [x,p]=i\hbar(1+\beta p^2). This deformed commutation
relation leads to the minimal length uncertainty relation \Delta x >
(\hbar/2)(1/\Delta p +\beta\Delta p), which implies that \Delta x ~ 1/\Delta p
at small \Delta p while \Delta x ~ \Delta p at large \Delta p. We find that the
uncertainties of the energy eigenstates of the normal harmonic oscillator
(m>0), derived in Ref. [1], only populate the \Delta x ~ 1/\Delta p branch. The
other branch, \Delta x ~ \Delta p, is found to be populated by the energy
eigenstates of the `inverted' harmonic oscillator (m<0). The Hilbert space in
the 'inverted' case admits an infinite ladder of positive energy eigenstates
provided that \Delta x_{min} = \hbar\sqrt{\beta} > \sqrt{2}
[\hbar^2/k|m|]^{1/4}. Correspondence with the classical limit is also
discussed.Comment: 16 pages, 31 eps figure
Theory of 4e versus 2e supercurrent in frustrated Josepshon-junction rhombi chain
We consider a chain of Josepshon-junction rhombi (proposed originally in
\cite{Doucot}) in quantum regime, and in the realistic case when charging
effects are determined by junction capacitances. In the maximally frustrated
case when magnetic flux through each rhombi is equal to one half of
superconductive flux quantum , Josepshon current is due to correlated
transport of {\em pairs of Cooper pairs}, i.e. charge is quantized in units of
. Sufficiently strong deviation from the maximally frustrated point brings the system back to
usual -quantized supercurrent. We present detailed analysis of Josepshon
current in the fluctuation-dominated regime (sufficiently long chains) as
function of the chain length, ratio and flux deviation .
We provide estimates for the set of parameters optimized for the observation of
-supercurrent.Comment: 23 pages, 9 figure
Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term
We give the approximate analytic solutions of the Dirac equations for the
Rosen-Morse potential including the spin-orbit centrifugal term. In the
framework of the spin and pseudospin symmetry concept, we obtain the analytic
bound state energy spectra and corresponding two-component upper- and
lower-spinors of the two Dirac particles, in closed form, by means of the
Nikiforov-Uvarov method. The special cases of the s-wave kappa=1,-1 (l=l bar=0)
Rosen-Morse potential, the Eckart-type potential, the PT-symmetric Rosen-Morse
potential and non-relativistic limits are briefly studied.Comment: 23 page
The role of interactions, tunneling and harmonic confinement on the adiabatic loading of bosons in an optical lattice
We calculate entropy-temperature curves for interacting bosons in unit filled
optical lattices for both homogeneous and harmonically trapped situations, and
use them to understand how adiabatic changes in the lattice depth affect the
temperature of the system. In a translationally invariant lattice, the zero
tunneling limit facilitates a rather detailed analytic description. Unlike the
non-interacting bosonic system which is always cooled upon adiabatic loading
for low enough initial temperature, the change in the excitation spectrum
induced by interactions can lead to heating. Finite tunneling helps to reduce
this heating. Finally, we study the spatially inhomogeneous system confined in
a parabolic potential and show that the presence of the trap can significantly
reduce the final available temperature, due to the non-vanishing superfluid
component at the edge of the cloud which is present in trapped systems.Comment: 9 pages and 6 figures. Two typos in Sec.IIIA were corrected and some
references were update
Traveling waves and Compactons in Phase Oscillator Lattices
We study waves in a chain of dispersively coupled phase oscillators. Two
approaches -- a quasi-continuous approximation and an iterative numerical
solution of the lattice equation -- allow us to characterize different types of
traveling waves: compactons, kovatons, solitary waves with exponential tails as
well as a novel type of semi-compact waves that are compact from one side.
Stability of these waves is studied using numerical simulations of the initial
value problem.Comment: 22 pages, 25 figure
RKKY Interaction in Graphene from Lattice Green's Function
We study the exchange interaction between two magnetic impurities in
graphene (the RKKY interaction) by directly computing the lattice Green's
function for the tight-binding band structure for the honeycomb lattice. The
method allows us to compute numerically for much larger distances than can
be handled by finite-lattice calculations as well as for small distances. %
avoids the use of a cutoff function often invoked in the literature to curtail
the diverging contributions from the linear bands and yields results that are
valid for all distances. In addition, we rederive the analytical long-distance
behavior of for linearly dispersive bands and find corrections to the
oscillatory factor that were previously missed in the literature. The main
features of the RKKY interaction in graphene are that unlike the behavior of an ordinary 2D metal in the
long-distance limit, in graphene falls off as , shows the -type oscillations with additional phase factors depending on the
direction, and exhibits a ferromagnetic interaction for moments on the same
sublattice and an antiferromagnetic interaction for moments on the opposite
sublattices as required by particle-hole symmetry. The computed with the
full band structure agrees with our analytical results in the long-distance
limit including the oscillatory factors with the additional phases.Comment: 8 pages, 11 figure
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