1,673 research outputs found
Bound States and Power Counting in Effective Field Theories
The problem of bound states in effective field theories is studied. A
rescaled version of nonrelativistic effective field theory is formulated which
makes the velocity power counting of operators manifest. Results obtained using
the rescaled theory are compared with known results from NRQCD. The same ideas
are then applied to study Yukawa bound states in 1+1 and 3+1 dimensions, and to
analyze when the Yukawa potential can be replaced by a delta-function
potential. The implications of these results for the study of nucleon-nucleon
scattering in chiral perturbation theory is discussed.Comment: 23 pages, eps figures, uses revte
Evaluation of Seismic Response of a Site Class F Site Using Equivalent Linear and Nonlinear Computer Codes
Evaluation of seismic site response and development of site-specific surface response spectra has evolved in recent years through the use of both equivalent linear (EQL) and nonlinear (NL) computer codes. Before the nonlinear computer codes become popular among practitioners, equivalent linear site response analysis programs were used to develop site-specific design spectra for both soft and stiff sites. Nonlinear site response analysis is now used more routinely for projects planned on Site Class F sites. This paper presents the results of seismic response analyses completed for a Site Class F site at Grays Harbor, Washington. Both the equivalent linear (SHAKE2000) and nonlinear (D-MOD2000) computer codes were used to evaluate the site response under the maximum considered earthquake (MCE) using the guidelines set forth in 2006 International Building Code (IBC) and American Society of Civil Engineers (ASCE) 7-05 code. Comparison of surface response spectra, soil shear stress and strain at various soil layers computed using both the equivalent linear and nonlinear computer program. Conclusions regarding the limitations of the equivalent linear code and presents recommendations on the use of the nonlinear computer code in site response analysis for practitioners
Renormalization schemes and the range of two-nucleon effective field theory
The OS and PDS renormalization schemes for the effective field theory with
nucleons and pions are investigated. We explain in detail how the
renormalization is implemented using local counterterms. Fits to the NN
scattering data are performed in the 1S0 and 3S1 channels for different values
of mu_R. An error analysis indicates that the range of the theory with
perturbative pions is consistent with 500 MeV.Comment: 40 pages, typos corrected, journal version. Discussion of the range
in section VII clarified, conclusions unchange
Exact Markovian kinetic equation for a quantum Brownian oscillator
We derive an exact Markovian kinetic equation for an oscillator linearly
coupled to a heat bath, describing quantum Brownian motion. Our work is based
on the subdynamics formulation developed by Prigogine and collaborators. The
space of distribution functions is decomposed into independent subspaces that
remain invariant under Liouville dynamics. For integrable systems in
Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled,
renormalized particles. In contrast for non-integrable systems, the invariant
subspaces follow a dynamics with broken-time symmetry, involving generalized
functions. This result indicates that irreversibility and stochasticity are
exact properties of dynamics in generalized function spaces. We comment on the
relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.Comment: A few typos in the published version are correcte
The Long and Short of Nuclear Effective Field Theory Expansions
Nonperturbative effective field theory calculations for NN scattering seem to
break down at rather low momenta. By examining several toy models, we clarify
how effective field theory expansions can in general be used to properly
separate long- and short-range effects. We find that one-pion exchange has a
large effect on the scattering phase shift near poles in the amplitude, but
otherwise can be treated perturbatively. Analysis of a toy model that
reproduces 1S0 NN scattering data rather well suggests that failures of
effective field theories for momenta above the pion mass can be due to
short-range physics rather than the treatment of pion exchange. We discuss the
implications this has for extending the applicability of effective field
theories.Comment: 22 pages, 9 figures, references corrected, minor modification
The NN scattering 3S1-3D1 mixing angle at NNLO
The 3S1-3D1 mixing angle for nucleon-nucleon scattering, epsilon_1, is
calculated to next-to-next-to-leading order in an effective field theory with
perturbative pions. Without pions, the low energy theory fits the observed
epsilon_1 well for momenta less than MeV. Including pions
perturbatively significantly improves the agreement with data for momenta up to
MeV with one less parameter. Furthermore, for these momenta the
accuracy of our calculation is similar to an effective field theory calculation
in which the pion is treated non-perturbatively. This gives phenomenological
support for a perturbative treatment of pions in low energy two-nucleon
processes. We explain why it is necessary to perform spin and isospin traces in
d dimensions when regulating divergences with dimensional regularization in
higher partial wave amplitudes.Comment: 17 pages, journal versio
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