Generalization of the density-matrix method to a non-orthogonal basis

We present a generalization of the Li, Nunes and Vanderbilt density-matrix method to the case of a non-orthogonal set of basis functions. A representation of the real-space density matrix is chosen in such a way that only the overlap matrix, and not its inverse, appears in the energy functional. The generalized energy functional is shown to be variational with respect to the elements of the density matrix, which typically remains well localized.Comment: 11 pages + 2 postcript figures at the end (search for -cut here

An extended space approach for particle Markov chain Monte Carlo methods

In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte Carlo algorithm. This paper describes an approach that also uses sequential Monte Carlo to construct an approximation to the state space, but generates extra states using MCMC runs at each time point. We construct an augmented model for our extended space with the marginal distribution of the sampled states matching the posterior distribution of the state vector. We show how our method may be combined with particle independent Metropolis-Hastings or particle Gibbs steps to obtain a smoothing algorithm. All the Metropolis acceptance probabilities are identical to those obtained in existing approaches, so there is no extra cost in term of Metropolis-Hastings rejections when using our approach. The number of MCMC iterates at each time point is chosen by the used and our augmented model collapses back to the model in Olsson and Ryden (2011) when the number of MCMC iterations reduces. We show empirically that our approach works well on applied examples and can outperform existing methods.Comment: 35 pages, 2 figures, Typos corrected from Version

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve functional tumour-associated blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation medi- ated by vascular targeting agents that induce occlusion/collapse of tumour blood vessels. In contrast, the therapeutic intention of normalising the abnormal structure and function of tumour vascular net- works, e.g. via alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and radiation therapy efficacy. Although both strategies have shown therapeutic potential, it remains unclear why they often fail to control glioma invasion into the surrounding healthy brain tissue. To shed light on this issue, we propose a mathematical model of glioma invasion focusing on the interplay between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells and modulations of the functional tumour vasculature. Vaso-modulatory interventions are modelled by varying the degree of vaso-occlusion. We discovered the existence of a critical cell proliferation/diffusion ratio that separates glioma invasion re- sponses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the tumour front speed and increase the infiltration width, for those in the other regime the invasion speed increases and infiltration width decreases. We show how these in silico findings can be used to guide individualised approaches of vaso-modulatory treatment strategies and thereby improve success rates

Ground-state energy and Wigner crystallization in thick 2D-electron systems

The ground state energy of the 2-D Wigner crystal is determined as a function of the thickness of the electron layer and the crystal structure. The method of evaluating the exchange-correlation energy is tested using known results for the infinitely-thin 2D system. Two methods, one based on the local-density approximation(LDA), and another based on the constant-density approximation (CDA) are established by comparing with quantum Monte-Carlo (QMC) results. The LDA and CDA estimates for the Wigner transition of the perfect 2D fluid are at $r_s=38$ and 32 respectively, compared with $r_s=35\pm5$ from QMC. For thick-2D layers as found in Hetero-junction-insulated-gate field-effect transistors, the LDA and CDA predictions of the Wigner transition are at $r_s=20.5$ and 15.5 respectively. Impurity effects are not considered here.Comment: Last figure and Table are modified in the revised version. Conclusions regarding the Wigner transition in thick layers are modified in the revised version. Latex manuscript, four figure

Quasiparticle Electronic structure of Copper in the GW approximation

We show that the results of photoemission and inverse photoemission experiments on bulk copper can be quantitatively described within band-structure theory, with no evidence of effects beyond the single-quasiparticle approximation. The well known discrepancies between the experimental bandstructure and the Kohn-Sham eigenvalues of Density Functional Theory are almost completely corrected by self-energy effects. Exchange-correlation contributions to the self-energy arising from 3s and 3p core levels are shown to be crucial.Comment: 4 pages, 2 figures embedded in the text. 3 footnotes modified and 1 reference added. Small modifications also in the text. Accepted for publication in PR

Metal-insulator transitions in tetrahedral semiconductors under lattice change

Although most insulators are expected to undergo insulator to metal transition on lattice compression, tetrahedral semiconductors Si, GaAs and InSb can become metallic on compression as well as by expansion. We focus on the transition by expansion which is rather peculiar; in all cases the direct gap at $\Gamma$ point closes on expansion and thereafter a zero-gap state persists over a wide range of lattice constant. The solids become metallic at an expansion of 13 % to 15 % when an electron fermi surface around L-point and a hole fermi surface at $\Gamma$-point develop. We provide an understanding of this behavior in terms of arguments based on symmetry and simple tight-binding considerations. We also report results on the critical behavior of conductivity in the metal phase and the static dielectric constant in the insulating phase and find common behaviour. We consider the possibility of excitonic phases and distortions which might intervene between insulating and metallic phases.Comment: 12 pages, 8 figure

Lower bounds for the conductivities of correlated quantum systems

We show how one can obtain a lower bound for the electrical, spin or heat conductivity of correlated quantum systems described by Hamiltonians of the form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by conservation laws which lead to an infinite conductivity for g=0. The small perturbation g H1, however, renders the conductivity finite at finite temperatures. For example, H0 could be a continuum field theory, where momentum is conserved, or an integrable one-dimensional model while H1 might describe the effects of weak disorder. In the limit g to 0, we derive lower bounds for the relevant conductivities and show how they can be improved systematically using the memory matrix formalism. Furthermore, we discuss various applications and investigate under what conditions our lower bound may become exact.Comment: Title changed; 9 pages, 2 figure