The sign problem in full configuration interaction quantum Monte Carlo: Linear and sub-linear representation regimes for the exact wave function

We investigate the sign problem for full configuration interaction quantum Monte Carlo (FCIQMC), a stochastic algorithm for finding the ground state solution of the Schr\"odinger equation with substantially reduced computational cost compared with exact diagonalisation. We find $k$-space Hubbard models for which the solution is yielded with storage that grows sub-linearly in the size of the many-body Hilbert space, in spite of using a wave function that is simply linear combination of states. The FCIQMC algorithm is able to find this sub-linear scaling regime without bias and with only a choice of Hamiltonian basis. By means of a demonstration we solve for the energy of a 70-site half-filled system (with a space of $10^{38}$ determinants) in 250 core hours, substantially quicker than the $\sim$10$^{36}$ core hours that would be required by exact diagonalisation. This is the largest space that has been sampled in an unbiased fashion. The challenge for the recently-developed FCIQMC method is made clear: expand the sub-linear scaling regime whilst retaining exact on average accuracy. This result rationalizes the success of the initiator adaptation (i-FCIQMC) and offers clues to improve it. We argue that our results changes the landscape for development of FCIQMC and related methods.Comment: 6 pages, 4 figures. The mentioned supplementary material is included as "Ancillary files". Comments welcom

Range Separated Brueckner Coupled Cluster Doubles Theory

We introduce a range-separation approximation to coupled cluster doubles (CCD) theory that successfully overcomes limitations of regular CCD when applied to the uniform electron gas. We combine the short-range ladder channel with the long-range ring channel in the presence of a Bruckner renormalized one-body interaction and obtain ground-state energies with an accuracy of 0.001 a.u./electron across a wide range of density regimes. Our scheme is particularly useful in the low-density and strongly-correlated regimes, where regular CCD has serious drawbacks. Moreover, we cure the infamous overcorrelation of approaches based on ring diagrams (i.e. the particle-hole random phase approximation). Our energies are further shown to have appropriate basis set and thermodynamic limit convergence, and overall this scheme promises energetic properties for realistic periodic and extended systems which existing methods do not possess.Comment: 5 pages, 3 figs. Now with supplementary info. Comments welcome: [email protected]

The role of unsteadiness in direct initiation of gaseous detonations

An analytical model is presented for the direct initiation of gaseous detonations by a blast wave. For stable or weakly unstable mixtures, numerical simulations of the spherical direct initiation event and local analysis of the one-dimensional unsteady reaction zone structure identify a competition between heat release, wave front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the wave front. The quasi-steady assumption is thus shown to be incorrect for direct initiation. The numerical simulations also suggest a non-uniqueness of critical energy in some cases, and the model developed here is an attempt to explain the lower critical energy only. A critical shock decay rate is determined in terms of the other fundamental dynamic parameters of the detonation wave, and hence this model is referred to as the critical decay rate (CDR) model. The local analysis is validated by integration of reaction-zone structure equations with real gas kinetics and prescribed unsteadiness. The CDR model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models of the critical energy, this equation is not dependent on other experimentally determined parameters and for evaluation requires only an appropriate reaction mechanism for the given gas mixture. For different fuel–oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude

Structural trends in clusters of quadrupolar spheres

The influence of quadrupolar interactions on the structure of small clusters is investigated by adding a point quadrupole of variable strength to the Lennard-Jones potential. Competition arises between sheet-like arrangements of the particles, favoured by the quadrupoles, and compact structures, favoured by the isotropic Lennard-Jones attraction. Putative global potential energy minima are obtained for clusters of up to 25 particles using the basin-hopping algorithm. A number of structural motifs and growth sequences emerge, including star-like structures, tubes, shells and sheets. The results are discussed in the context of colloidal self-assembly.Comment: 8 pages, 6 figure

A Full Configuration Interaction Perspective on the Homogeneous Electron Gas

Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a newly developed stochastic technique, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which samples the exact wavefunction expanded in plane wave Slater determinants. Despite the introduction of a basis set incompleteness error, we obtain a finite-basis energy which is significantly, and variationally lower than any previously published work for the 54-electron HEG at $r_s$ = 0.5 a.u., in a Hilbert space of $10^{108}$ Slater determinants. At this value of $r_s$, as well as of 1.0 a.u., we remove the remaining basis set incompleteness error by extrapolation, yielding results comparable or better than state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in sizable periodic systems.Comment: 4-page lette

Adaptation from Novels into Films: A Study of Six Examples, with an Accompanying Screenplay and Self-analysis.

This thesis consists of two primary components: a study of six novels and their respective adaptations into popular commercial films, and my attempt at writing a partial screenplay adaptation of my own previously written novel fragment. I have intentionally chosen to focus upon literary works written in English in the latter half of the twentieth century: they range from the middle 1950s (Vladimir Nabokov's Lolita) to the early 1990s (Bret Easton Ellis' American Psycho). Their filmic adaptations range from the late 1960s (John Frankenheimer's The Fixer) to the early twenty first century (Mary Harron's American Psycho). I have specifically focused upon relatively recent works - both literary and filmic - so as to attain some degree of chronological, and thus aesthetic, homogeny in the examples I have studied. Otherwise, the thesis would have been too unwieldy and disparate if I had of included both Classical and Postmodern prose works, or films from both the early twentieth century and early twenty first century. I believe my own screenplay fragment, Eleven A'Bier Place, and the novel fragment from which it is adapted, share some thematic concerns with at least some of the novels and films which I have studied in the thesis. The partial screenplay adaptation I have written references contemporary media in a similar way to American Psycho; it focuses upon drug-crazed criminals as in A Clockwork Orange and Fear and Loathing in Las Vegas; it depicts the descent into insanity like The Shining. However, it is very much my own work. As far as I can recall I had no specific literary or cinematic precursors in mind when I began the project, although undoubtedly there exist texts which have strongly influenced me in this regard