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1.
Daniel S. Freed 《Inventiones Mathematicae》1988,92(2):243-254
Summary The index of a family of a family of Dirac operators is aK-Theory element in the parameter space. Sullivan's/k-manifolds are used to detect this index completely. For the first Chern class this gives a topological interpretation of Witten's global anomaly. The relationship with the geometry of the index bundle is considered.To my teacher Isadore M. SingerThe author is partially supported by an NSF Postdoctoral Research Fellowship 相似文献
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Trilisa M. Perrine Rajat K. Chaudhuri Karl F. Freed 《International journal of quantum chemistry》2005,105(1):18-33
Simple and quadratic Padé resummation methods are applied to high‐order series from multireference many‐body perturbation theory (MR‐MBPT) calculations using various partitioning schemes (Møller–Plesset, Epstein–Nesbet, and forced degeneracy) to determine their efficacy in resumming slowly convergent or divergent series. The calculations are performed for the ground and low‐lying excited states of (i) CH2, (ii) BeH2 at three geometries, and (iii) Be, for which full configuration interaction (CI) calculations are available for comparison. The 49 perturbation series that are analyzed include those with oscillatory and monotonic divergence and convergence, including divergences that arise from either frontdoor or backdoor intruder states. Both the simple and quadratic Padé approximations are found to speed the convergence of slowly convergent or divergent series. However, the quadratic Padé method generally outperforms the simple Padé resummation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 相似文献
4.
The influence of monomer structure on the thermodynamic properties of lattice model polymer blends is investigated through Monte Carlo computations. The model of lattice polymers with monomer structure has been used extensively in the context of the lattice cluster theory (LCT), a thermodynamic theory for polymer mixtures in the liquid state. The Monte Carlo computations provide the first unequivocal test of the accuracy of the LCT predictions for binary mixtures of polymers with structured monomers. Four types of monomer structures are analyzed, corresponding to to the monomers of polyethylene, polypropylene, polyethylethylene, and polyisobutylene (PIB). Most computations use chains with M=12 and 24 beads and the total volume fraction of the beads is phi=0.6. Both structurally symmetric and asymmetric blends are investigated. For the symmetric case, the predictions of the LCT for the energies of mixing and the liquid-liquid coexistence curves are in qualitative agreement with the Monte Carlo computations, except for the PIB/PIB symmetric blend. For structurally asymmetric blends, the LCT does not capture contributions to the energy of mixing arising solely from structural differences between the components. Computational estimates of the nonideal entropy of mixing indicate that the LCT also underestimates the entropic cost of mixing chains with different structures, thus explaining some discrepancies between the theoretical and the Monte Carlo liquid--liquid coexistence curves. 相似文献
5.
Some results of approximate ab initio calculations of the “correlation” contribution to the true parameters of the pi electron hamiltonian are presented for the ethylene molecule. In particular, by using sum-of-the-pairs type generalized perturbation theory, it is shown that there is a large core “correlation” contribution to singlet-triplet splittings within pi electron theories that results from the difference in the degree of ionicity of the isoconfigurational states. 相似文献
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We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the Verlinde formula. The careful development may serve as a model for dealing with similar issues in more complicated cases.The first author is supported by NSF grant DMS-8805684, an Alfred P. Sloan Research Fellowship, a Presidential Young Investigators award, and by the O'Donnell Foundation. The second author is supported by NSF grant DMS-9207973 相似文献
8.
A method is presented that can be used (a) to determine the several lowest eigenvalues and eigenvectors of large symmetric matrices, (b) to solve the generalized eigenvalue problem associated with energy-dependent operators, that arises in computations involving energy-dependent many-body Green's functions and in the evaluation of the true parameters of the effective valence shell hamiltonian, and (c) to directly evaluate the matrices associated with resolvent operators. The applicability to large configuration mixing calculations arises when the N-electron basis functions can be easily broken down to a few dominant configurations (the primary block) and their complement. Using the partitioning technique, the effective hamiltonian within the primary block is directly evaluated. The method is extended to evaluation of the dynamical polarizability tensor, which effectively contains the contributions from all of the eigenstates of a hamiltonian matrix, without the necessity of explicitly calculating its eigenvalues and eigenvectors. 相似文献
9.
We report the use of a novel pulsed ESR technique for distance measurement, based on the detection of double quantum coherence (DQC), which yields high quality dipolar spectra, to significantly extend the range of measurable distances in proteins using nitroxide spin-labels. Eight T4 lysozyme (T4L) mutants, doubly labeled with methanethiosulfonate spin-label (MTSSL), have been studied using DQC-ESR at 9 and 17 GHz. The distances span the range from 20 A for the 65/76 mutant to 47 A for the 61/135 mutant. The high quality of the dipolar spectra also allows the determination of the distance distributions, the width of which can be used to set upper and lower bounds in future computational strategy. It is also demonstrated that the shape of these distributions can reveal the presence of multiple conformations of the spin-label, an issue of critical relevance to the structural interpretation of the distances. The distances and distributions found in this study are readily rationalized in terms of the known crystal structure, the characteristic conformers of the nitroxide side chains, and molecular modeling. This study sets the stage for the use of DQC-ESR for determining the tertiary structure of large proteins with just a small number of long-distance constraints. 相似文献
10.
Karl F. Freed 《Chemical physics》1974,4(1):80-95
Open shell generalized perturbation theory (GPT) is a systematic scheme for the improvement of a multi-configurational zeroth order wavefunction that can be chosen so the lowest order corresponds to a sum-of-the-pairs- type theory of electron correlation (with or without pair-pair couplings) in the spirit of the theories of Kelly, Sinano?lu, and Nesbet for the single configurational case. Applications axe presented to the generalized perturbative solution for individual states and for the simultaneous solution for many nondegenerate states. The (2n+ 1)-rule of GPT and the interchange theorems of double Girl' are illustrated. A brief discussion is included concerning the use of GPT in ab initio evaluations of the true parameters that are customarily, only modeled and then fit to experiment in semi-empirical theories of molecular electronic structure. The conceptual value of expressing the results of ab initio calculations in terms of effective hamiltonians is stressed and the relationship between open shell GPT and other theories of electron correlation is also considered. 相似文献