2,897 research outputs found
Chiral Symmetry Restoration and Quark Deconfinement beyond Mean Field in a Magnetized PNJL Model
We study chiral symmetry restoration and quark deconfinement beyond mean
field approximation in a magnetized PNJL model. The feedback from mesons to
quarks modifies the quark coupling constant and Polyakov potential. As a
result, the separate critical temperatures for the two phase transitions at
mean field level coincide and the magnetic catalysis becomes inverse magnetic
catalysis, when the meson contribution is included.Comment: 5 pages,3 figure
A representation formula related to Schrodinger operators
Let H be a Schrodinger operator on the real line, where the potential is in
L^1 and L^2. We define the perturbed Fourier transform F for H and show that F
is an isometry from the absolute continuous subspace onto L^2. This property
allows us to construct a kernel formula for spectral operators. The main
theorem improves the author's previous result for certain short-range
potentials.Comment: four pages, to appear in Anal. Theo. App
From Inverse to Delayed Magnetic Catalysis in Strong Magnetic Field
We study magnetic field effect on chiral phase transition in a
Nambu--Jona-Lasinio model. In comparison with mean field approximation
containing quarks only, including mesons as quantum fluctuations in the model
leads to a transition from inverse to delayed magnetic catalysis at finite
temperature and delays the transition at finite baryon chemical potential. The
location of the critical end point depends on the the magnetic field
non-monotonously.Comment: 5 pages, 5 fig
Two new standing solitary waves in shallow water
In this paper, the closed-form analytic solutions of two new Faraday's
standing solitary waves due to the parametric resonance of liquid in a vessel
vibrating vertically with a constant frequency are given for the first time.
Using a model based on the symmetry of wave elevation and the linearized
Boussinesq equation, we gain the closed-form wave elevations of the two kinds
of non-monotonically decaying standing solitary waves with smooth crest and the
even or odd symmetry. All of them have never been reported, to the best of our
knowledge. Besides, they can well explain some experimental phenomena. All of
these are helpful to deepen and enrich our understandings about standing
solitary waves and Faraday's wave.Comment: 12 pages, 4 figures, accepted by Wave Motio
A new non-perturbative approach in quantum mechanics for time-independent Schr\"{o}dinger equations
A new non-perturbative approach is proposed to solve time-independent
Schr\"{o}dinger equations in quantum mechanics and chromodynamics (QCD). It is
based on the homotopy analysis method (HAM), which was developed by the author
for highly nonlinear equations since 1992 and has been widely applied in many
fields. Unlike perturbative methods, this HAM-based approach has nothing to do
with small/large physical parameters. Besides, convergent series solution can
be obtained even if the disturbance is far from the known status. A nonlinear
harmonic oscillator is used as an example to illustrate the validity of this
approach for disturbances that might be more than hundreds larger than the
possible superior limit of the perturbative approach. This HAM-based approach
could provide us rigorous theoretical results in quantum mechanics and
chromodynamics (QCD), which can be directly compared with experimental data.
Obviously, this is of great benefit not only for improving the accuracy of
experimental measurements but also for validating physical theories.Comment: 26 pages, 12 figures, 9 table
Spectral multipliers for Schroedinger operators with Poeschl-Teller potential
We prove a sharp Mihlin-Hormander multiplier theorem for Schroedinger
operators on . The method, which allows us to deal with general
potentials, improves Hebisch's method relying on heat kernel estimates for
positive potentials. Our result applies to, in particular, the negative
Poeschl-Teller potential V(x)= -\nu(\nu+1) \sech^2 x , , for which
has a resonance at zero.Comment: 23 page
Structure of Compact Stars in Pion Superfluid Phase
The gross structure of compact stars composed of pion superfluid quark matter
is investigated in the frame of Nambu-Jona-Lasinio model. Under the
Pauli-Villars regularization scheme, the uncertainty of the thermodynamic
functions for inhomogeneous states is cured, and the LOFF state appeared in the
hard cutoff scheme is removed from the phase diagram of pion superfluid.
Different from the unpaired quark matter and color superconductor, the strongly
coupled pion superfluid in the state close to the BCS limit is a possible
candidate of compact stars with mass and radius km.Comment: 5 pages, 5 figure
On peaked solitary waves of Camassa-Holm equation
Unlike the Boussinesq, KdV and BBM equations, the celebrated Casamma-Holm
(CH) equation can model both phenomena of soliton interaction and wave
breaking. Especially, it has peaked solitary waves in case of omega=0. Besides,
in case of omega > 0, its solitary wave "becomes and there is no
derivative discontinuity at its peak", as mentioned by Camassa and Holm in 1993
(PRL). However, it is found in this article that the CH equation has peaked
solitary waves even in case of omega > 0. Especially, all of these peaked
solitary waves have an unusual property: their phase speeds have nothing to do
with the height of peakons or anti-peakons. Therefore, in contrast to the
traditional view-points, the peaked solitary waves are a common property of the
CH equation: in fact, all mainstream models of shallow water waves admit such
kind of peaked solitary wavesComment: 11 pages, 4 figures, 2 table
On cusped solitary waves in finite water depth
It is well-known that the Camassa-Holm (CH) equation admits both of the
peaked and cusped solitary waves in shallow water. However, it was an open
question whether or not the exact wave equations can admit them in finite water
depth. Besides, it was traditionally believed that cusped solitary waves, whose
1st-derivative tends to infinity at crest, are essentially different from
peaked solitary ones with finite 1st-derivative. Currently, based on the
symmetry and the exact water wave equations, Liao [1] proposed a unified wave
model (UWM) for progressive gravity waves in finite water depth. The UWM admits
not only all traditional smooth progressive waves but also the peaked solitary
waves in finite water depth: in other words, the peaked solitary progressive
waves are consistent with the traditional smooth ones. In this paper, in the
frame of the linearized UWM, we further give, for the first time, the cusped
solitary waves in finite water depth, and besides reveal a close relationship
between the cusped and peaked solitary waves: a cusped solitary wave is consist
of an infinite number of peaked solitary ones with the same phase speed, so
that it can be regarded as a special peaked solitary wave. This also well
explains why and how a cuspon has an infinite 1st-derivative at crest. It is
found that, like peaked solitary waves, the vertical velocity of a cusped
solitary wave in finite water depth is also discontinuous at crest (x=0), and
especially its phase speed has nothing to do with wave height, too. In
addition, it is unnecessary to consider whether the peaked/cusped solitary
waves given by the UWM are weak solution or not, since the governing equation
is not necessary to be satisfied at crest. All of these would deepen and enrich
our understandings about the cusped solitary waves.Comment: 9 pages, 2 figure
Littlewood-Paley theorem for Schroedinger operators
Let be a Schr\"odinger operator on . Under a polynomial decay
condition for the kernel of its spectral operator, we show that the Besov
spaces and Triebel-Lizorkin spaces associated with are well defined. We
further give a Littlewood-Paley characterization of spaces as well as
Sobolev spaces in terms of dyadic functions of . This generalizes and
strengthens the previous result when the heat kernel of satisfies certain
upper Gaussian bound.Comment: eight pages. submitte
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