34,266 research outputs found
Bardeen-Cooper-Schrieffer formalism of superconductivity in carbon nanotubes
We develop the Bardeen-Cooper-Schrieffer (BCS) formalism for the
superconductivity of carbon nanotubes. It is found that the superconducting
transition temperature Tc of single-wall carbon nanotubes decreases
exponentially with the increase of the tube diameter because the density of
states near the Fermi energy is inversely proportional to the tube diameter.
For the multi-wall carbon nanotubes, the Cooper paring hopping between layers
enhances the superconducting correlation and increases the superconducting
transition temperature, which is consistent with the experimental observation.Comment: 11 page
Exact Solutions of the two-dimensional Schr\"{o}dinger equation with certain central potentials
By applying an ansatz to the eigenfunction, an exact closed form solution of
the Schr\"{o}dinger equation in 2D is obtained with the potentials,
, and
, respectively. The restrictions on the
parameters of the given potential and the angular momentum are obtained.Comment: Latex files and accepted by Inter. J. Theor. Phys. 39, No.
Nonconvex Demixing From Bilinear Measurements
We consider the problem of demixing a sequence of source signals from the sum
of noisy bilinear measurements. It is a generalized mathematical model for
blind demixing with blind deconvolution, which is prevalent across the areas of
dictionary learning, image processing, and communications. However, state-of-
the-art convex methods for blind demixing via semidefinite programming are
computationally infeasible for large-scale problems. Although the existing
nonconvex algorithms are able to address the scaling issue, they normally
require proper regularization to establish optimality guarantees. The
additional regularization yields tedious algorithmic parameters and pessimistic
convergence rates with conservative step sizes. To address the limitations of
existing methods, we thus develop a provable nonconvex demixing procedure
viaWirtinger flow, much like vanilla gradient descent, to harness the benefits
of regularization-free fast convergence rate with aggressive step size and
computational optimality guarantees. This is achieved by exploiting the benign
geometry of the blind demixing problem, thereby revealing that Wirtinger flow
enforces the regularization-free iterates in the region of strong convexity and
qualified level of smoothness, where the step size can be chosen aggressively.Comment: This paper has been accepted by IEEE Transactions on Signal
Processin
Fault-Tolerant Control of Linear Quantum Stochastic Systems
In quantum engineering, faults may occur in a quantum control system, which
will cause the quantum control system unstable or deteriorate other relevant
performance of the system. This note presents an estimator-based fault-tolerant
control design approach for a class of linear quantum stochastic systems
subject to fault signals. In this approach, the fault signals and some
commutative components of the quantum system observables are estimated, and a
fault-tolerant controller is designed to compensate the effect of the fault
signals. Numerical procedures are developed for controller design and an
example is presented to demonstrate the proposed design approach.Comment: 7 pages, 1 figur
Quantum Szilard engines with arbitrary spin
The quantum Szilard engine (QSZE) is a conceptual quantum engine for
understanding the fundamental physics of quantum thermodynamics and information
physics. We generalize the QSZE to an arbitrary spin case, i.e., a spin QSZE
(SQSZE), and we systematically study the basic physical properties of both
fermion and boson SQSZEs in a low-temperature approximation. We give the
analytic formulation of the total work. For the fermion SQSZE, the work might
be absorbed from the environment, and the change rate of the work with
temperature exhibits periodicity and even-odd oscillation, which is a
generalization of a spinless QSZE. It is interesting that the average absorbed
work oscillates regularly and periodically in a large-number limit, which
implies that the average absorbed work in a fermion SQSZE is neither an
intensive quantity nor an extensive quantity. The phase diagrams of both
fermion and boson SQSZEs give the SQSZE doing positive or negative work in the
parameter space of the temperature and the particle number of the system, but
they have different behaviors because the spin degrees of the fermion and the
boson play different roles in their configuration states and corresponding
statistical properties. The critical temperature of phase transition depends
sensitively on the particle number. By using Landauer's erasure principle, we
give the erasure work in a thermodynamic cycle, and we define an efficiency (we
refer to it as information-work efficiency) to measure the engine's ability of
utilizing information to extract work. We also give the conditions under which
the maximum extracted work and highest information-work efficiencies for
fermion and boson SQSZEs can be achieved.Comment: 24 pages, 11 figure
Topological effects of charge transfer in telomere G-quadruplex: Mechanism on telomerase activation and inhibition
We explore charge transfer in the telomere G-Quadruplex (TG4) DNA
theoretically by the nonequilibrium Green's function method, and reveal the
topological effect of charge transport in TG4 DNA. The consecutive TG4(CTG4) is
semiconducting with 0.2 ~ 0.3eV energy gap. Charges transfers favorably in the
consecutive TG4, but are trapped in the non-consecutive TG4 (NCTG4). The global
conductance is inversely proportional to the local conductance for NCTG4. The
topological structure transition from NCTG4 to CTG4 induces abruptly ~ 3nA
charge current, which provide a microscopic clue to understand the telomerase
activated or inhibited by TG4. Our findings reveal the fundamental property of
charge transfer in TG4 and its relationship with the topological structure of
TG4.Comment: 10 pages, 5 figure
Superconducting dark energy
Based on the analogy with superconductor physics we consider a
scalar-vector-tensor gravitational model, in which the dark energy action is
described by a gauge invariant electromagnetic type functional. By assuming
that the ground state of the dark energy is in a form of a condensate with the
U(1) symmetry spontaneously broken, the gauge invariant electromagnetic dark
energy can be described in terms of the combination of a vector and of a scalar
field (corresponding to the Goldstone boson), respectively. The gravitational
field equations are obtained by also assuming the possibility of a non-minimal
coupling between the cosmological mass current and the superconducting dark
energy. The cosmological implications of the dark energy model are investigated
for a Friedmann-Robertson-Walker homogeneous and isotropic geometry for two
particular choices of the electromagnetic type potential, corresponding to a
pure electric type field, and to a pure magnetic field, respectively. The time
evolution of the scale factor, matter energy density and deceleration parameter
are obtained for both cases, and it is shown that in the presence of the
superconducting dark energy the Universe ends its evolution in an exponentially
accelerating vacuum de Sitter state. By using the formalism of the irreversible
thermodynamic processes for open systems we interpret the generalized
conservation equations in the superconducting dark energy model as describing
matter creation. The particle production rates, the creation pressure and the
entropy evolution are explicitly obtained.Comment: 18 pages, 16 figures, accepted for publication in PR
Origin of Cosmic Ray Electrons and Positrons
With experimental results of AMS on the spectra of cosmic ray (CR) ,
, and positron fraction, as well as new measurements of CR
flux by HESS, one can better understand the CR lepton (
and ) spectra and the puzzling electron-positron excess above 10
GeV. In this article, spectra of CR and are fitted with a
physically motivated simple model, and their injection spectra are obtained
with a one-dimensional propagation model including the diffusion and energy
loss processes. Our results show that the electron-positron excess can be
attributed to uniformly distributed sources that continuously inject into the
galactic disk electron-positron with a power-law spectrum cutting off near 1
TeV and a triple power-law model is needed to fit the primary CR electron
spectrum. The lower energy spectral break can be attributed to propagation
effects giving rise to a broken power-law injection spectrum of primary CR
electrons with a spectral hardening above 40 GeV
An Information-Theoretic Analysis for Thompson Sampling with Many Actions
Information-theoretic Bayesian regret bounds of Russo and Van Roy capture the
dependence of regret on prior uncertainty. However, this dependence is through
entropy, which can become arbitrarily large as the number of actions increases.
We establish new bounds that depend instead on a notion of rate-distortion.
Among other things, this allows us to recover through information-theoretic
arguments a near-optimal bound for the linear bandit. We also offer a bound for
the logistic bandit that dramatically improves on the best previously
available, though this bound depends on an information-theoretic statistic that
we have only been able to quantify via computation
Exact solutions of the Li\'enard and generalized Li\'enard type ordinary non-linear differential equations obtained by deforming the phase space coordinates of the linear harmonic oscillator
We investigate the connection between the linear harmonic oscillator equation
and some classes of second order nonlinear ordinary differential equations of
Li\'enard and generalized Li\'enard type, which physically describe important
oscillator systems. By using a method inspired by quantum mechanics, and which
consist on the deformation of the phase space coordinates of the harmonic
oscillator, we generalize the equation of motion of the classical linear
harmonic oscillator to several classes of strongly non-linear differential
equations. The first integrals, and a number of exact solutions of the
corresponding equations are explicitly obtained. The devised method can be
further generalized to derive explicit general solutions of nonlinear second
order differential equations unrelated to the harmonic oscillator. Applications
of the obtained results for the study of the travelling wave solutions of the
reaction-convection-diffusion equations, and of the large amplitude free
vibrations of a uniform cantilever beam are also presented.Comment: 28 pages, no figures; minor modifications, accepted for publication
in Journal of Engineering Mathematic
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