13,129 research outputs found
Relativistic Quantum Transport Theory for Electrodynamics
We investigate the relationship between the covariant and the
three-dimensional (equal-time) formulations of quantum kinetic theory. We show
that the three-dimensional approach can be obtained as the energy average of
the covariant formulation. We illustrate this statement in scalar and spinor
QED. For scalar QED we derive Lorentz covariant transport and constraint
equations directly from the Klein-Gordon equation rather than through the
previously used Feshbach-Villars representation. We then consider pair
production in a spatially homogeneous but time-dependent electric field and
show that the pair density is derived much more easily via the energy averaging
method than in the equal-time representation. Proceeding to spinor QED, we
derive the covariant version of the equal-time equation derived by
Bialynicki-Birula et al. We show that it must be supplemented by another
self-adjoint equation to obtain a complete description of the covariant spinor
Wigner operator. After spinor decomposition and energy average we study the
classical limit of the resulting three-dimensional kinetic equations. There are
only two independent spinor components in this limit, the mass density and the
spin density, and we derive also their covariant equations of motion. We then
show that the equal-time kinetic equation provides a complete description only
for constant external electromagnetic fields, but is in general incomplete. It
must be supplemented by additional constraints which we derive explicitly from
the covariant formulation.Comment: 32 pages, no figures, standard Late
Nucleon Mass Splitting at Finite Isospin Chemical Potential
We investigate nucleon mass splitting at finite isospin chemical potential in
the frame of two flavor Nambu--Jona-Lasinio model. It is analytically proved
that, in the phase with explicit isospin symmetry breaking the proton mass
decreases and the neutron mass increases linearly in the isospin chemical
potential.Comment: 3 pages and no figure
Shattering Thresholds for Random Systems of Sets, Words, and Permutations
This paper considers a problem that relates to the theories of covering
arrays, permutation patterns, Vapnik-Chervonenkis (VC) classes, and probability
thresholds. Specifically, we want to find the number of subsets of
[n]:={1,2,....,n} we need to randomly select, in a certain probability space,
so as to respectively "shatter" all t-subsets of [n]. Moving from subsets to
words, we ask for the number of n-letter words on a q-letter alphabet that are
needed to shatter all t-subwords of the q^n words of length n. Finally, we
explore the number of random permutations of [n] needed to shatter
(specializing to t=3), all length 3 permutation patterns in specified
positions. We uncover a very sharp zero-one probability threshold for the
emergence of such shattering; Talagrand's isoperimetric inequality in product
spaces is used as a key tool.Comment: 25 page
Low-momentum Pion Enhancement Induced by Chiral Symmetry Restoration
The thermal and nonthermal pion production by sigma decay and its relation
with chiral symmetry restoration in a hot and dense matter are investigated.
The nonthermal decay into pions of sigma mesons which are popularly produced in
chiral symmetric phase leads to a low-momentum pion enhancement as a possible
signature of chiral phase transition at finite temperature and density.Comment: 3 pages, 2 figure
Comment on ``Relativistic kinetic equations for electromagnetic, scalar and pseudoscalar interactions''
It is found that the extra quantum constraints to the spinor components of
the equal-time Wigner function given in a recent paper by Zhuang and Heinz
should vanish identically. We point out here the origin of the error and give
an interpretation of the result. However, the principal idea of obtaining a
complete equal-time transport theory by energy averaging the covariant theory
remains valid. The classical transport equation for the spin density is also
found to be incorrect. We give here the correct form of that equation and
discuss briefly its structure.Comment: 5 pages LaTe
Turbulent shear-layer mixing: growth-rate compressibility scaling
A new shear-layer growth-rate compressibility-scaling parameter is proposed as an alternative to the total convective Mach number, Mc. This parameter derives from considerations of compressibility as a means of kinetic-to-thermal-energy conversion and can be significantly different from Mc for flows with far-from-unity free-stream-density and speed-of-sound ratios. Experimentally observed growth rates are well-represented by the new scaling
Numerical Simulation for Solute Transport in Fractal Porous Media
A modified Fokker-Planck equation with continuous source for solute transport in fractal porous media is considered. The dispersion term of the governing equation uses a fractional-order derivative and the diffusion coefficient can be time and scale dependent. In this paper, numerical solution of the modified Fokker-Planck equation is proposed. The effects of different fractional orders and fractional power functions of time and distance are numerically investigated. The results show that motions with a heavy tailed marginal distribution can be modelled by equations that use fractional-order derivatives and/or time and scale dependent dispersivity
Logarithmic Representability of Integers as k-Sums
A set A=A_{k,n} in [n]\cup{0} is said to be an additive k-basis if each
element in {0,1,...,kn} can be written as a k-sum of elements of A in at least
one way. Seeking multiple representations as k-sums, and given any function
phi(n), with lim(phi(n))=infinity, we say that A is a truncated
phi(n)-representative k-basis for [n] if for each j in [alpha n, (k-alpha)n]
the number of ways that j can be represented as a k-sum of elements of A_{k,n}
is Theta(phi(n)). In this paper, we follow tradition and focus on the case
phi(n)=log n, and show that a randomly selected set in an appropriate
probability space is a truncated log-representative basis with probability that
tends to one as n tends to infinity. This result is a finite version of a
result proved by Erdos (1956) and extended by Erdos and Tetali (1990).Comment: 18 page
Thermal and Nonthermal Pion Enhancements with Chiral Symmetry Restoration
The pion production by sigma decay and its relation with chiral symmetry
restoration in a hot and dense matter are investigated in the framework of the
Nambu-Jona-Lasinio model. The decay rate for the process sigma -> 2pion to the
lowest order in a 1/N_c expansion is calculated as a function of temperature T
and chemical potential mu. The thermal and nonthermal enhancements of pions
generated by the decay before and after the freeze-out present only in the
crossover region of the chiral symmetry transition. The strongest nonthermal
enhancement is located in the vicinity of the endpoint of the first-order
transition.Comment: Latex2e, 12 pages, 8 Postscript figures, submitted to Phys. Rev.
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