24,061 research outputs found
Effect of Resonant Continuum on Pairing Correlations in the Relativistic Approach
A proper treatment of the resonant continuum is to take account of not only
the energy of the resonant state, but also its width. The effect of the
resonant states on pairing correlations is presented based on the relativistic
mean field theory plus Bardeen-Cooper-Schrieffer(BCS) approximation with a
constant pairing strength. The study is performed in an effective Lagrangian
with the parameter set NL3 for neutron rich even-even Ni isotopes. The results
show that the contribution of the proper treatment of the resonant continuum to
pairing correlations for those nuclei close to neutron drip line is important.
The pairing gaps, Fermi energies, pairing correlation energies, and binding
energies are considerably affected with a proper consideration of the width of
resonant states. The problem of an unphysical particle gas, which may appear in
the calculation of the traditional mean field plus BCS method for nuclei in the
vicinity of drip line could be well overcome when the pairing correlation is
performed by using the resonant states instead of the discretized states in the
continuum.Comment: 19 pages, 8 Postscript figur
Indirect unitarity violation entangled with matter effects in reactor antineutrino oscillations
If finite but tiny masses of the three active neutrinos are generated via the
canonical seesaw mechanism with three heavy sterile neutrinos, the 3\times 3
Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing matrix V will not be exactly
unitary. This kind of indirect unitarity violation can be probed in a precision
reactor antineutrino oscillation experiment, but it may be entangled with
terrestrial matter effects as both of them are very small. We calculate the
probability of \overline{\nu}_e \to \overline{\nu}_e oscillations in a good
analytical approximation, and find that, besides the zero-distance effect, the
effect of unitarity violation is always smaller than matter effects, and their
entanglement does not appear until the next-to-leading-order oscillating terms
are taken into account. Given a 20-kiloton JUNO-like liquid scintillator
detector, we reaffirm that terrestrial matter effects should not be neglected
but indirect unitarity violation makes no difference, and demonstrate that the
experimental sensitivities to the neutrino mass ordering and a precision
measurement of \theta_{12} and \Delta_{21} \equiv m^2_2 - m^2_1 are robust.Comment: 21 pages, 6 figures, version to be published in PLB, more discussions
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Strong stability of Nash equilibria in load balancing games
We study strong stability of Nash equilibria in the load balancing games of m (m >= 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the
workload of the server it chooses.
A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is not stable against coordinated deviations of several jobs, while a strong Nash equilibrium (SNE) is. We study how well an
NE approximates an SNE.
Given any job assignment in a load balancing game, the improvement ratio (IR) of a deviation of a job is defined as the ratio between the pre-and post-deviation costs. An NE is said to be a ρ-approximate SNE (ρ >= 1) if there is no coalition of jobs such that each job of the coalition
will have an IR more than ρ from coordinated deviations of the coalition.
While it is already known that NEs are the same as SNEs in the 2-server load balancing game, we prove that, in the m-server load balancing game for any given m >= 3, any NE is a (5=4)-approximate SNE, which together with the lower bound already established in the literature implies that the approximation bound is tight. This closes the final gap in the literature on the study of approximation of general NEs to SNEs in the load balancing games. To establish our upper bound, we apply with novelty a powerful graph-theoretic tool
Exploration of Resonant Continuum and Giant Resonance in the Relativistic Approach
Single-particle resonant-states in the continuum are determined by solving
scattering states of the Dirac equation with proper asymptotic conditions in
the relativistic mean field theory (RMF). The regular and irregular solutions
of the Dirac equation at a large radius where the nuclear potentials vanish are
relativistic Coulomb wave functions, which are calculated numerically.
Energies, widths and wave functions of single-particle resonance states in the
continuum for ^{120}Sn are studied in the RMF with the parameter set of NL3.
The isoscalar giant octupole resonance of ^{120}Sn is investigated in a fully
consistent relativistic random phase approximation. Comparing the results with
including full continuum states and only those single-particle resonances we
find that the contributions from those resonant-states dominate in the nuclear
giant resonant processes.Comment: 16 pages, 2 figure
On the exactness of soft theorems
Soft behaviours of S-matrix for massless theories reflect the underlying
symmetry principle that enforces its masslessness. As an expansion in soft
momenta, sub-leading soft theorems can arise either due to (I) unique structure
of the fundamental vertex or (II) presence of enhanced broken-symmetries. While
the former is expected to be modified by infrared or ultraviolet divergences,
the latter should remain exact to all orders in perturbation theory. Using
current algebra, we clarify such distinction for spontaneously broken (super)
Poincar\'e and (super) conformal symmetry. We compute the UV divergences of
DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft
theorems, while type (I) are shown to be broken and the soft-modifying
higher-dimensional operators are identified. As further evidence for the
exactness of type (II) soft theorems, we consider the alpha' expansion of both
super and bosonic open strings amplitudes, and verify the validity of the
translation symmetry breaking soft-theorems up to O(alpha'^6). Thus the
massless S-matrix of string theory "knows" about the presence of D-branes.Comment: 35 pages. Additional mathematica note book with the UV-divergenece of
the 6-point amplitude in AV/KS theor
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