45,161 research outputs found
Wave function optimization in the variational Monte Carlo method
An appropriate iterative scheme for the minimization of the energy, based on
the variational Monte Carlo (VMC) technique, is introduced and compared with
existing stochastic schemes. We test the various methods for the 1D Heisenberg
ring and the 2D t-J model and show that, with the present scheme, very accurate
and efficient calculations are possible, even for several variational
parameters. Indeed, by using a very efficient statistical evaluation of the
first and the second energy derivatives, it is possible to define a very
rapidly converging iterative scheme that, within VMC, is much more convenient
than the standard Newton method. It is also shown how to optimize
simultaneously both the Jastrow and the determinantal part of the wave
function.Comment: 5 pages, 3 figures, to be published in Phys. Rev B (Rapid Comm.
Angular distribution and rotations of frame in vector meson decays into lepton pairs
We discuss how the angular distribution of lepton pairs from decays of vector
mesons depends on the choice of reference frame, and provide a geometrical
description of the transformations of the coefficients of the angular
distribution. Invariant expressions involving all coefficients are discussed,
together with bounds and consistency relations.Comment: 7 pages, 3 figure
The orders of nonsingular derivations of Lie algebras of characteristic two
Nonsingular derivations of modular Lie algebras which have finite
multiplicative order play a role in the coclass theory for pro- groups and
Lie algebras. A study of the set N_p of positive integers which occur as orders
of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of
positive characteristic p was initiated by Shalev and continued by the present
author. In this paper we continue this study in the case of characteristic two.
Among other results, we prove that any divisor n of 2^k-1 with
belongs to N_2. Our methods consist of elementary arguments
with polynomials over finite fields and a little character theory of finite
groups.Comment: 11 page
Exponential functions in prime characteristic
In this note we determine all power series F(X)\in 1+X\F_p[[X]] such that
has only terms of total degree a multiple of . Up
to a scalar factor, they are all the series of the form for some c\in\F_p and G(X)\in 1+X\F_p[[X]], where
is the Artin-Hasse
exponential.Comment: 6 pages, to be published in Aequationes Mat
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