84 results found
Stedman ML, Foulkes WMC, Nekovee M, 1998, An accelerated Metropolis method, JOURNAL OF CHEMICAL PHYSICS, Vol: 109, Pages: 2630-2634, ISSN: 0021-9606
Hood RQ, Chou MY, Williamson AJ, et al., 1997, Quantum Monte Carlo investigation of exchange and correlation in silicon, PHYSICAL REVIEW LETTERS, Vol: 78, Pages: 3350-3353, ISSN: 0031-9007
Foulkes WMC, Nekovee M, Hood RQ, et al., 1997, Quantum Monte Carlo studies of exchange and correlation in solids., ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, Vol: 213, Pages: 125-COMP, ISSN: 0065-7727
Williamson AJ, Rajagopal G, Needs RJ, et al., 1997, Elimination of Coulomb finite-size effects in quantum many-body simulations, PHYSICAL REVIEW B, Vol: 55, Pages: R4851-R4854, ISSN: 0163-1829
Kenny SD, Rajagopal G, Needs RJ, et al., 1996, Quantum Monte Carlo calculations of the energy of the relativistic homogeneous electron gas, PHYSICAL REVIEW LETTERS, Vol: 77, Pages: 1099-1102, ISSN: 0031-9007
Needs RJ, Rajagopal G, Williamson AJ, et al., 1996, Quantum Monte Carlo studies of electronic systems, Pacific Conference on Condensed Matter Theory - Complex Materials and Strongly Correlated Systems, Publisher: KOREAN PHYSICAL SOC, Pages: S116-S120, ISSN: 0374-4884
Williamson AJ, Kenny SD, Rajagopal G, et al., 1996, Optimized wave functions for quantum Monte Carlo studies of atoms and solids, Physical Review B, Vol: 53, Pages: 9640-9648, ISSN: 1550-235X
Wave functions for the homogeneous electron gas, a germanium pseudosolid, and a germanium pseudoatom are optimized using the method of variance minimization. Forms for the Jastrow factor which are convenient to optimize and may be evaluated rapidly are devised and tested and we stress the advantages of using expressions which are linear in the variable parameters. For each system studied we have performed variational and diffusion quantum Monte Carlo calculations to test the accuracy of the optimized wave functions. The results of our study are very promising for future applications of quantum Monte Carlo methods to real materials.
Fraser LM, Foulkes WMC, Rajagopal G, et al., 1996, Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions, PHYSICAL REVIEW B, Vol: 53, Pages: 1814-1832, ISSN: 0163-1829
RAJAGOPAL G, NEEDS RJ, JAMES A, et al., 1995, VARIATIONAL AND DIFFUSION QUANTUM MONTE-CARLO CALCULATIONS AT NONZERO WAVE VECTORS - THEORY AND APPLICATION TO DIAMOND-STRUCTURE GERMANIUM, PHYSICAL REVIEW B, Vol: 51, Pages: 10591-10600, ISSN: 0163-1829
Rajagopal G, Needs RJ, Kenny S, et al., 1994, Quantum Monte Carlo calculations for solids using special k points methods., Phys Rev Lett, Vol: 73, Pages: 1959-1962
ANNETT JF, MATTHEW W, FOULKES C, et al., 1994, A recursive solution of Heisenberg's equation and its interpretation, J PHYS-CONDENS MAT, Vol: 6, Pages: 6455-6475, ISSN: 0953-8984
We present the generalization of the recursion method of Haydock and co-workers to systems of many interacting particles. This new method has close similarities to the memory function or Mori formalism, but with some important differences. Heisenberg's equation for the time evolution of a microscopic operator is recursively transformed into a tridiagonal matrix equation. This equation resolves the operator into components corresponding to transitions of different energies. The projected spectrum of transitions has a continued fraction expansion given by the elements of the tridiagonal matrix, We show that for an appropriate choice of inner product this density of transitions obeys a generalization of the black body theorem of electromagnetism, in that it is exponentially insensitive to distant parts of the system. This implies that the projected density of transitions is computationally stable and can be calculated even in macroscopic many-body systems. We argue that the physical content of the density of transitions is determined by the nature of its singular points, such as discrete transitions, continuous spectrum, band edges and van Hove singularities.
Foulkes WMC, 1993, Accuracy of the chemical-pseudopotential method for tetrahedral semiconductors., Phys Rev B, Vol: 48, Pages: 14216-14225, ISSN: 0163-1829
FOULKES WMC, 1993, FEYNMAN-KAC PATH-INTEGRAL CALCULATION OF THE GROUND-STATE ENERGIES OF ATOMS - COMMENT, PHYSICAL REVIEW LETTERS, Vol: 71, Pages: 2158-2158, ISSN: 0031-9007
Foulkes WMC, Edwards DM, 1993, Perfect localized basis functions for solids: chemical pseudopotentials and the Kronig-Penney model, J. Phys. Condensed Matter, Vol: 5, Pages: 7987-8004
Hybertsen MS, Stechel EB, Foulkes WM, et al., 1992, Model for low-energy electronic states probed by x-ray absorption in high-Tc cuprates., Phys Rev B, Vol: 45, Pages: 10032-10050, ISSN: 0163-1829
CHEN CT, SETTE F, MA Y, et al., 1991, ELECTRONIC STATES IN LA2-XSRXCUO4+GAMMA PROBED BY SOFT-X-RAY ABSORPTION, PHYSICAL REVIEW LETTERS, Vol: 66, Pages: 104-107, ISSN: 0031-9007
Foulkes WM, Schluter M, 1990, Pseudopotentials with position-dependent electron masses., Phys Rev B, Vol: 42, Pages: 11505-11529, ISSN: 0163-1829
Foulkes WMC, Haydock R, 1989, Tight-binding models and density-functional theory., Phys Rev B, Vol: 39, Pages: 12520-12536, ISSN: 0163-1829
Foulkes WMC, 1989, Transferable tight-binding models from density functional theory, Atomistic Simulation of Materials - Beyond Pair Potentials, Editors: Vitek, Srolovitz, New York, Publisher: Plenum, Pages: 353-359
Foulkes WMC, 1988, Basis functions for tight-binding models, Paris, France, CECAM Workshop in Interatomic Forces, Publisher: C.E.C.A.M., Pages: 81-83
Foulkes M, Haydock R, 1986, The recursion method and expectation values, J. Phys C: Solid State Phys., Vol: 19, Pages: 6573-6587
Fagerholm ED, Foulkes WMC, Gallero-Salas Y, et al., Estimating quantities conserved by virtue of scale invariance in timeseries
In contrast to the symmetries of translation in space, rotation in space, andtranslation in time, the known laws of physics are not universally invariantunder transformation of scale. However, the action can be invariant underchange of scale in the special case of a scale free dynamical system that canbe described in terms of a Lagrangian, that itself scales inversely with time.Crucially, this means symmetries under change of scale can exist in dynamicalsystems under certain constraints. Our contribution lies in the derivation of ageneralised scale invariant Lagrangian - in the form of a power seriesexpansion - that satisfies these constraints. This generalised Lagrangianfurnishes a normal form for dynamic causal models (i.e., state space modelsbased upon differential equations) that can be used to distinguish scaleinvariance (scale symmetry) from scale freeness in empirical data. We establishface validity with an analysis of simulated data and then show how scaleinvariance can be identified - and how the associated conserved quantities canbe estimated - in neuronal timeseries.
Fagerholm ED, Foulkes WMC, Gallero-Salas Y, et al., Network constraints in scale free dynamical systems
Scale free dynamics are observed in a variety of physical and biologicalsystems. These include neural activity in which evidence for scale freeness hasbeen reported using a range of imaging modalities. Here, we derive the ways inwhich connections within a network must transform - relative to system size -in order to maintain scale freeness and test these theoretical transformationsvia simulations. First, we explore the known invariance of planetary motion fororbits varying in size. Using parametric empirical Bayesian modelling and ageneric dynamical systems model, we show that we recover Kepler's third lawfrom orbital timeseries, using our proposed transformations; thereby providingconstruct validation. We then demonstrate that the dynamical critical exponentis inversely proportional to the time rescaling exponent, in the context ofcoarse graining operations. Using murine calcium imaging data, we then showthat the dynamical critical exponent can be estimated in an empiricalbiological setting. Specifically, we compare dynamical critical exponents -associated with spontaneous and task states in two regions of imaged cortex -that are classified as task-relevant and task-irrelevant. We find, consistentlyacross animals, that the task-irrelevant region exhibits higher dynamicalcritical exponents during spontaneous activity than during task performance.Conversely, the task-relevant region is associated with higher dynamicalcritical exponents in task vs. spontaneous states. These data support the ideathat higher dynamical critical exponents, within relevant cortical structures,underwrite neuronal processing due to the implicit increase in cross-scaleinformation transmission.
Pfau D, Spencer JS, Matthews AGDG, et al., Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
Given access to accurate solutions of the many-electron Schr\"odingerequation, nearly all chemistry could be derived from first principles. Exactwavefunctions of interesting chemical systems are out of reach because they areNP-hard to compute in general, but approximations can be found usingpolynomially-scaling algorithms. The key challenge for many of these algorithmsis the choice of wavefunction approximation, or Ansatz, which must trade offbetween efficiency and accuracy. Neural networks have shown impressive power asaccurate practical function approximators and promise as a compact wavefunctionAnsatz for spin systems, but problems in electronic structure requirewavefunctions that obey Fermi-Dirac statistics. Here we introduce a novel deeplearning architecture, the Fermionic Neural Network, as a powerful wavefunctionAnsatz for many-electron systems. The Fermionic Neural Network is able toachieve accuracy beyond other variational quantum Monte Carlo Ans\"atze on avariety of atoms and small molecules. Using no data other than atomic positionsand charges, we predict the dissociation curves of the nitrogen molecule andhydrogen chain, two challenging strongly-correlated systems, to significantlyhigher accuracy than the coupled cluster method, widely considered the mostaccurate scalable method for quantum chemistry at equilibrium geometry. Thisdemonstrates that deep neural networks can improve the accuracy of variationalquantum Monte Carlo to the point where it outperforms other ab-initio quantumchemistry methods, opening the possibility of accurate direct optimisation ofwavefunctions for previously intractable molecules and solids.
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