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.

A bridge too far? : reflections on theory in educational practice

Praxis is a notion underlying several educational theories and it has led to the development of different models of teacher education. Locally, this has also been one of the concepts discussed during the ‘masterisation’ of the teaching profession, by virtue of which pedagogical content knowledge builds on prior-achieved content knowledge. As teacher education in Malta was reformed, a number of unprecedented socio-economic developments created a scenario which, at policy-making level, brought about further educational reforms. These include an outcomes-based model for learning and assessment and a drive towards vocational education. In this presentation, I refer to data regarding teacher-student ratios, as one aspect of the contextualization of education locally, and I proceed to reflect upon two educational documents, using Critical Discourse Analysis. I argue that the cyclical nature of praxis, which requires reflection and action, is somewhat side-lined within the current educational context, possibly because immediate instrumental gains are being prioritized.peer-reviewe

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-$p$ 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 $n^4>(2^k-n)^{3}$ 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 $(F(X+Y))^{-1} F(X)F(Y)$ has only terms of total degree a multiple of $p$. Up to a scalar factor, they are all the series of the form $F(X)=E_p(cX)\cdot G(X^p)$ for some c\in\F_p and G(X)\in 1+X\F_p[[X]], where $E_p(X)=\exp\big(\sum_{i=0}^{\infty}X^{p^i}/p^i\big)$ is the Artin-Hasse exponential.Comment: 6 pages, to be published in Aequationes Mat