1,192 research outputs found
Instabilities and Non-Reversibility of Molecular Dynamics Trajectories
The theoretical justification of the Hybrid Monte Carlo algorithm depends
upon the molecular dynamics trajectories within it being exactly reversible. If
computations were carried out with exact arithmetic then it would be easy to
ensure such reversibility, but the use of approximate floating point arithmetic
inevitably introduces violations of reversibility. In the absence of evidence
to the contrary, we are usually prepared to accept that such rounding errors
can be made small enough to be innocuous, but in certain circumstances they are
exponentially amplified and lead to blatantly erroneous results. We show that
there are two types of instability of the molecular dynamics trajectories which
lead to this behavior, instabilities due to insufficiently accurate numerical
integration of Hamilton's equations, and intrinsic chaos in the underlying
continuous fictitious time equations of motion themselves. We analyze the
former for free field theory, and show that it is essentially a finite volume
effect. For the latter we propose a hypothesis as to how the Liapunov exponent
describing the chaotic behavior of the fictitious time equations of motion for
an asymptotically free quantum field theory behaves as the system is taken to
its continuum limit, and explain why this means that instabilities in molecular
dynamics trajectories are not a significant problem for Hybrid Monte Carlo
computations. We present data for pure gauge theory and for QCD with
dynamical fermions on small lattices to illustrate and confirm some of our
results.Comment: 28 pages latex with 19 color postscript figures included by eps
On Gauge Invariance of Breit-Wigner Propagators
We present an approach to bosonic () as well as fermionic
(top-quark) Breit-Wigner propagators which is consistent with gauge invariance
arguments. In particular, for the -boson propagator we extend previous
analyses and show that the part proportional to must be
modified near the resonance. We derive a mass shift which agrees with results
obtained elsewhere by different methods. The modified form of a resonant heavy
fermion propagator is also given.Comment: 16 p., TeX, (final version
Morphologic variation of the diaphragmatic crura: a correlation with pathologic processes of the esophageal hiatus?
The contributions of muscle fibers from the right and left diaphragmatic
crura to the formation of the esophageal hiatus have been documented in
several studies, none coming to a complete consensus on the number of
anatomic variations or the prevalence of these variations in the human population.
These variations may play a role in the pathogenicity of specific
diseases that involve the esophageal hiatus, such as hiatal hernias. We examined
a total of two hundred adult cadavers during 2000-2007. The variations
in the diaphragmatic crura, particularly their muscular contributions
to the formation of the esophageal hiatus, were grossly examined and revealed
a bilateral occurrence of diaphragmatic crura in all 200 specimens.
The results of the various morphological patterns of circumferential muscle
fibers forming the esophageal hiatus were classified into six groups. The
most common type (Type I, 45%) formed the esophageal hiatus from muscular
contributions arising solely from the right crus. In Type II (20%) the
esophageal hiatus was formed by muscular contributions from the right
and left crura. In Type III (15%), the right and left muscular contributions
arose from the right crus with an additional band from the left crus. Type IV
(10%) showed that the right and left muscular contributions arose from the
right crus, with two additional (anterior and posterior) bands arising from
the left crus. Type V (5%) demonstrated the contributions arising solely from
the left crus. In Type VI (5%) the right and left contributions originated from
the left crus with two additional bands, one from the right crus and one
from the left crus.
These variations may play a role in the pathogenicity of specific diseases that
involve the esophageal hiatus such as hiatal hernia, gastroesophageal reflux
disease and Dunbar’s syndrome
Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions
We study a multigrid method for nonabelian lattice gauge theory, the time
slice blocking, in two and four dimensions. For SU(2) gauge fields in two
dimensions, critical slowing down is almost completely eliminated by this
method. This result is in accordance with theoretical arguments based on the
analysis of the scale dependence of acceptance rates for nonlocal Metropolis
updates. The generalization of the time slice blocking to SU(2) in four
dimensions is investigated analytically and by numerical simulations. Compared
to two dimensions, the local disorder in the four dimensional gauge field leads
to kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint
MS-TPI-94-
Quark Mass Textures and sin 2 beta
Recent precise measurements of sin 2 beta from the B-factories (BABAR and
BELLE) and a better known strange quark mass from lattice QCD make precision
tests of predictive texture models possible. The models tested include those
hierarchical N-zero textures classified by Ramond, Roberts and Ross, as well as
any other hierarchical matrix Ansatz with non-zero 12 = 21 and vanishing 11 and
13 elements. We calculate the maximally allowed value for sin 2 beta in these
models and show that all the aforementioned models with vanishing 11 and 13
elements are ruled out at the 3 sigma level. While at present sin 2 beta and
|Vub/Vcb| are equally good for testing N-zero texture models, in the near
future the former will surpass the latter in constraining power.Comment: 1+20 pages, 2 figures, JHEP3 clas
A numerical reinvestigation of the Aoki phase with N_f=2 Wilson fermions at zero temperature
We report on a numerical reinvestigation of the Aoki phase in lattice QCD
with two flavors of Wilson fermions where the parity-flavor symmetry is
spontaneously broken. For this purpose an explicitly symmetry-breaking source
term was added to the fermion action.
The order parameter was computed with
the Hybrid Monte Carlo algorithm at several values of on
lattices of sizes to and extrapolated to . The existence of a
parity-flavor breaking phase can be confirmed at and 4.3, while we
do not find parity-flavor breaking at and 5.0.Comment: 8 pages, 5 figures, Revised version as to be published in Phys.Rev.
Logarithmic Corrections in the 2D XY Model
Using two sets of high-precision Monte Carlo data for the two-dimensional XY
model in the Villain formulation on square lattices, the scaling
behavior of the susceptibility and correlation length at the
Kosterlitz-Thouless phase transition is analyzed with emphasis on
multiplicative logarithmic corrections in the finite-size
scaling region and in the high-temperature phase near
criticality, respectively. By analyzing the susceptibility at criticality on
lattices of size up to we obtain , in agreement with
recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang
zeros in the cosine formulation of the XY model. By studying susceptibilities
and correlation lengths up to in the high-temperature phase,
however, we arrive at quite a different estimate of , which is
in good agreement with recent analyses of thermodynamic Monte Carlo data and
high-temperature series expansions of the cosine formulation.Comment: 13 pages, LaTeX + 8 postscript figures. See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
Electromagnetic vertex function of the pion at T > 0
The matrix element of the electromagnetic current between pion states is
calculated in quenched lattice QCD at a temperature of . The
nonperturbatively improved Sheikholeslami-Wohlert action is used together with
the corresponding improved vector current. The electromagnetic
vertex function is extracted for pion masses down to and
momentum transfers .Comment: 17 pages, 8 figure
Molecular spintronics: Coherent spin transfer in coupled quantum dots
Time-resolved Faraday rotation has recently demonstrated coherent transfer of
electron spin between quantum dots coupled by conjugated molecules. Using a
transfer Hamiltonian ansatz for the coupled quantum dots, we calculate the
Faraday rotation signal as a function of the probe frequency in a pump-probe
setup using neutral quantum dots. Additionally, we study the signal of one
spin-polarized excess electron in the coupled dots. We show that, in both
cases, the Faraday rotation angle is determined by the spin transfer
probabilities and the Heisenberg spin exchange energy. By comparison of our
results with experimental data, we find that the transfer matrix element for
electrons in the conduction band is of order 0.08 eV and the spin transfer
probabilities are of order 10%.Comment: 13 pages, 6 figures; minor change
Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory
We calculate complete spectra of the Kogut-Susskind Dirac operator on the
lattice in quenched SU(3) gauge theory for various values of coupling constant
and lattice size. From these spectra we compute the connected and disconnected
scalar susceptibilities and find agreement with chiral random matrix theory up
to a certain energy scale, the Thouless energy. The dependence of this scale on
the lattice volume is analyzed. In the case of the connected susceptibility
this dependence is anomalous, and we explain the reason for this. We present a
model of chiral perturbation theory that is capable of describing the data
beyond the Thouless energy and that has a common range of applicability with
chiral random matrix theory.Comment: 8 pages, RevTeX, 15 .eps figure
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