2,768 research outputs found
Analysis of the second order exchange self energy of a dense electron gas
We investigate the evaluation of the six-fold integral representation for the
second order exchange contribution to the self energy of a three dimensional
electron gas at the Fermi surface.Comment: 6 page
Quantum transport of Dirac electrons in graphene in the presence of a spatially modulated magnetic field
We have investigated the electrical transport properties of Dirac electrons
in a monolayer graphene sheet in the presence of a perpendicular magnetic field
that is modulated weakly and periodically along one direction.We find that the
Landau levels broaden into bands and their width oscillates as a function of
the band index and the magnetic field.We determine the component
of the magnetoconductivity tensor for this system which is shown to exhibit
Weiss oscillations.We also determine analytically the asymptotic expressions
for .We compare these results with recently obtained results for
electrically modulated graphene as well as those for magnetically modulated
conventional two-dimensional electron gas (2DEG) system.We find that in the
magnetically modulated graphene system cosidered in this work,Weiss
oscillations in have a reduced amplitude compared to the 2DEG but
are less damped by temperature while they have a higher amplitude than in the
electrically modulated graphene system. We also find that these oscillations
are out of phase by with those of the electrically modulated system while
they are in phase with those in the 2DEG system.Comment: Accepted in PRB: 10 pages, 3 figure
Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
A generalized Fermi-Bose mapping method is used to determine the exact ground
states of several models of mixtures of strongly interacting ultracold gases in
tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D
Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D
spin-aligned Fermi gas with infinitely strong zero-range attractions). We
detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and
boson-fermion (BF) interactions. Exact results are given for density profiles
in a harmonic trap, single-particle density matrices, momentum distributions,
and density-density correlations. Since the ground state is highly degenerate,
we analyze the splitting of the ground manifold for large but finite BB and BF
repulsions.Comment: Revised to discuss splitting of degenerate ground manifold for large
but finite BB and BF repulsions; accepted by PR
Effective one-dimensional description of confined diffusion biased by a transverse gravitational force
Diffusion of point-like non interacting particles in a two-dimensional (2D)
channel of varying cross section is considered. The particles are biased by a
constant force in the transverse direction. We apply our recurrence mapping
procedure, which enables us to derive an effective one-dimensional (1D)
evolution equation, governing the 1D density of the particles in the channel.
In the limit of stationary flow, we arrive at an extended Fick-Jacobs equation,
corrected by an effective diffusion coefficient D(x), depending on the
longitudinal coordinate x. Our result is an approximate formula for D(x),
involving also influence of the transverse force. Our calculations are verified
on the stationary diffusion in a linear cone, which is exactly solvable.Comment: 10 pages, 7 figures, submitted in Phys. Rev.
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
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
Time-dependent quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator
We present a theoretical study of time-dependent quantum transport in a
resonant tunnel junction coupled to a nanomechanical oscillator within the
non-equilibrium Green's function technique. An arbitrary voltage is applied to
the tunnel junction and electrons in the leads are considered to be at zero
temperature. The transient and the steady state behavior of the system is
considered here in order to explore the quantum dynamics of the oscillator as a
function of time. The properties of the phonon distribution of the
nanomechnical oscillator strongly coupled to the electrons on the dot are
investigated using a non-perturbative approach. We consider both the energy
transferred from the electrons to the oscillator and the Fano factor as a
function of time. We discuss the quantum dynamics of the nanomechanical
oscillator in terms of pure and mixed states. We have found a significant
difference between a quantum and a classical oscillator. In particular, the
energy of a classical oscillator will always be dissipated by the electrons
whereas the quantum oscillator remains in an excited state. This will provide
useful insight for the design of experiments aimed at studying the quantum
behavior of an oscillator.Comment: 24 pages, 10 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
Nonlinear screening and ballistic transport in a graphene p-n junction
We study the charge density distribution, the electric field profile, and the
resistance of an electrostatically created lateral p-n junction in graphene. We
show that the electric field at the interface of the electron and hole regions
is strongly enhanced due to limited screening capacity of Dirac quasiparticles.
Accordingly, the junction resistance is lower than estimated in previous
literature.Comment: 4 pages, 2 figures. (v1) Original version (v2) Introduction largely
rewritten, minor typos fixed throughou
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