8,641 research outputs found
Improved variational description of the Wick-Cutkosky model with the most general quadratic trial action
We generalize the worldline variational approach to field theory by
introducing a trial action which allows for anisotropic terms to be induced by
external 4-momenta of Green's functions. By solving the ensuing variational
equations numerically we demonstrate that within the (quenched) scalar
Wick-Cutkosky model considerable improvement can be achieved over results
obtained previously with isotropic actions. In particular, the critical
coupling associated with the instability of the model is lowered, in accordance
with expectations from Baym's proof of the instability in the unquenched
theory. The physical picture associated with a different quantum mechanical
motion of the dressed particle along and perpendicular to its classical
momentum is discussed. Indeed, we find that for large couplings the dressed
particle is strongly distorted in the direction of its four-momentum. In
addition, we obtain an exact relation between the renormalized coupling of the
theory and the propagator. Along the way we introduce new and efficient methods
to evaluate the averages needed in the variational approach and apply them to
the calculation of the 2-point function.Comment: 32 pages, 4 figures, Latex. Some typos corrected and expanded
discussion of the instability of the model provided. Accepted in Eur. Phys.
J.
Mapping unstructured grid problems to the connection machine
We present a highly parallel graph mapping technique that enables one to solve unstructured grid problems on massively parallel computers. Many implicit and explicit methods for solving discretizated partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The time spent communicating can limit the high performance promised by massively parallel computing. To eliminate this bottleneck, we map the graph of the irregular problem to the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. We show that, in comparison to a naive assignment of processors, our heuristic mapping algorithm significantly reduces the communication time on the Connection Machine, CM-2
The influence of self-citation corrections on Egghe's g index
The g index was introduced by Leo Egghe as an improvement of Hirsch's index h
for measuring the overall citation record of a set of articles. It better takes
into account the highly skewed frequency distribution of citations than the h
index. I propose to sharpen this g index by excluding the self-citations. I
have worked out nine practical cases in physics and compare the h and g values
with and without self-citations. As expected, the g index characterizes the
data set better than the h index. The influence of the self-citations appears
to be more significant for the g index than for the h index.Comment: 9 pages, 2 figures, submitted to Scientometric
Integrable impurities for an open fermion chain
Employing the graded versions of the Yang-Baxter equation and the reflection
equations, we construct two kinds of integrable impurities for a small-polaron
model with general open boundary conditions: (a) we shift the spectral
parameter of the local Lax operator at arbitrary sites in the bulk, and (b) we
embed the impurity fermion vertex at each boundary of the chain. The
Hamiltonians with different types of impurity terms are given explicitly. The
Bethe ansatz equations, as well as the eigenvalues of the Hamiltonians, are
constructed by means of the quantum inverse scattering method. In addition, we
discuss the ground-state properties in the thermodynamic limit.Comment: 20 pages, 4 figure
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