9,316 research outputs found
Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model
We derive the effective potentials for composite operators in a
Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in
each case they are equivalent to the corresponding effective potentials based
on an auxiliary scalar field. The both effective potentials could lead to the
same possible spontaneous breaking and restoration of symmetries including
chiral symmetry if the momentum cutoff in the loop integrals is large enough,
and can be transformed to each other when the Schwinger-Dyson (SD) equation of
the dynamical fermion mass from the fermion-antifermion vacuum (or thermal)
condensates is used. The results also generally indicate that two effective
potentials with the same single order parameter but rather different
mathematical expressions can still be considered physically equivalent if the
SD equation corresponding to the extreme value conditions of the two potentials
have the same form.Comment: 7 pages, no figur
On Distance-Regular Graphs with Smallest Eigenvalue at Least
A non-complete geometric distance-regular graph is the point graph of a
partial geometry in which the set of lines is a set of Delsarte cliques. In
this paper, we prove that for fixed integer , there are only finitely
many non-geometric distance-regular graphs with smallest eigenvalue at least
, diameter at least three and intersection number
Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression
We study soliton pulse compression in materials with cascaded quadratic
nonlinearities, and show that the group-velocity mismatch creates two different
temporally nonlocal regimes. They correspond to what is known as the stationary
and nonstationary regimes. The theory accurately predicts the transition to the
stationary regime, where highly efficient pulse compression is possible.Comment: 3 pages, 2 figures, published verison in Optics Letters. Contains
revised equations, including an updated mode
Limits to compression with cascaded quadratic soliton compressors
We study cascaded quadratic soliton compressors and address the physical
mechanisms that limit the compression. A nonlocal model is derived, and the
nonlocal response is shown to have an additional oscillatory component in the
nonstationary regime when the group-velocity mismatch (GVM) is strong. This
inhibits efficient compression. Raman-like perturbations from the cascaded
nonlinearity, competing cubic nonlinearities, higher-order dispersion, and
soliton energy may also limit compression, and through realistic numerical
simulations we point out when each factor becomes important. We find that it is
theoretically possible to reach the single-cycle regime by compressing
high-energy fs pulses for wavelengths in a
-barium-borate crystal, and it requires that the system is in the
stationary regime, where the phase mismatch is large enough to overcome the
detrimental GVM effects. However, the simulations show that reaching
single-cycle duration is ultimately inhibited by competing cubic nonlinearities
as well as dispersive waves, that only show up when taking higher-order
dispersion into account.Comment: 16 pages, 5 figures, submitted to Optics Expres
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