Density functional theory of superconductivity in doped tungsten oxides

We apply density functional theory for superconductors (SCDFT) to doped tungsten oxide in three forms: electrostatically doped WO3, perovskite WO3−xFx, and hexagonal CsxWO3. We achieve a consistent picture in which the experimental superconducting transition temperature Tc is reproduced, and superconductivity is understood as a weak-coupling state sustained by soft vibrational modes of the WO6 octahedra. SCDFT simulations of CsxWO3 allow us to explain the anomalous Tc behavior observed in most tungsten bronzes, where Tc decreases with increasing carrier density. Here, the opening of structural channels to host Cs atoms induces a softening of strongly coupled W-O modes. By increasing the Cs content, these modes are screened and Tc is strongly reduced

Stochastic Schr\"odinger equations with coloured noise

A natural non-Markovian extension of the theory of white noise quantum trajectories is presented. In order to introduce memory effects in the formalism an Ornstein-Uhlenbeck coloured noise is considered as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, non-Markovian stochastic Schr\"odinger equations which unravel non-Markovian master equations are derived.Comment: 4pages, revte

On the (2,3)-generation of the finite symplectic groups

This paper is a new important step towards the complete classification of the finite simple groups which are $(2,3)$-generated. In fact, we prove that the symplectic groups $Sp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 4$. Because of the existing literature, this result implies that the groups $PSp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 2$, with the exception of $PSp_4(2^f)$ and $PSp_4(3^f)$

More on regular subgroups of the affine group

This paper is a new contribution to the study of regular subgroups of the affine group $AGL_n(F)$, for any field $F$. In particular we associate to any partition $\lambda\neq (1^{n+1})$ of $n+1$ abelian regular subgroups in such a way that different partitions define non-conjugate subgroups. Moreover, we classify the regular subgroups of certain natural types for $n\leq 4$. Our classification is equivalent to the classification of split local algebras of dimension $n+1$ over $F$. Our methods, based on classical results of linear algebra, are computer free

The simple classical groups of dimension less than 6 which are (2,3)-generated

In this paper we determine the classical simple groups of dimension r=3,5 which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are PSL_3(q), q 4, and PSU_3(q^2), q^2 9, 25. If r = 5 they are PSL_5(q), for all q, and PSU_5(q^2), q^2 >= 9. Also, the soluble group PSU_3(4) is not (2,3)-generated. We give explicit (2,3)-generators of the linear preimages, in the special linear groups, of the (2,3)-generated simple groups.Comment: 12 page

The (2,3)(2,3)-generation of the finite unitary groups

In this paper we prove that the unitary groups $SU_n(q^2)$ are $(2,3)$-generated for any prime power $q$ and any integer $n\geq 8$. By previous results this implies that, if $n\geq 3$, the groups $SU_n(q^2)$ and $PSU_n(q^2)$ are $(2,3)$-generated, except when $(n,q)\in\{(3,2),(3,3),(3,5),(4,2), (4,3),(5,2)\}$.Comment: In this version, we obtained a complete classification of the finite simple unitary groups which are (2,3)-generated; some proofs have been semplifie

Scott's formula and Hurwitz groups

This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in $PGL_n(F)$ for $n\leq 7$ which are Hurwitz, where $F$ is an algebraically closed field. For the groups $G_2(q)$, $q\geq 5$, and the Janko groups $J_1$ and $J_2$ it provides explicit $(2,3,7)$-generators

Non Markovian Quantum Repeated Interactions and Measurements

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions of the integro-differential and time-convolutioness Master equations for the reduced system are derived. Next, an intuitive and rigorous description of the indirect quantum measurement principle is developed and a discrete non Markovian stochastic Master equation for the open system is obtained. Finally, the question of unravelling in a particular model of non-Markovian quantum interactions is discussed.Comment: 22 page

The (2,3)-generation of the special unitary groups of dimension 6

In this paper we give explicit (2,3)-generators of the unitary groups SU_6(q^ 2), for all q. They fit into a uniform sequence of likely (2,3)-generators for all n>= 6