# Symmetry and Topology in Quantum Logic

## Related Articles

- Quantum Computational Semantics on Fock Space. Chiara, M.; Giuntini, R.; Gudder, S.; Leporini, R. // International Journal of Theoretical Physics;Dec2005, Vol. 44 Issue 12, p2219
In the Fock space semantics, meanings of sentences are identified with density operators of the (unsymmetrized) Fock space $${\cal F}$$ based on the Hilbert space â„‚2. Generally, the meaning of a sentence is smeared over different sectors of $${\cal F}$$ . The standard quantum...

- A fundamental connection between symmetry and spatial localization properties of basis sets. Zicovich-Wilson, Claudio M.; Erba, Alessandro // Theoretical Chemistry Accounts: Theory, Computation, & Modeling;Jun2010, Vol. 126 Issue 3/4, p165
The problem of the compatibility between symmetry and localization properties of basis sets is addressed here. It is shown that both concepts are closely related from a fundamental point of view through the notion of invariance extent. This quantity is a functional that depends on the symmetry...

- Basis set approach to the quantum dissipative dynamics: Application of the multiconfiguration time-dependent Hartree method to the spin-boson problem. Wang, Haobin; Haobin Wang // Journal of Chemical Physics;12/8/2000, Vol. 113 Issue 22
The feasibility of using a basis set approach to the study of quantum dissipative dynamics is investigated for the spin-boson model, a system of two discrete states linearly coupled to a harmonic bath. The infinite Hamiltonian is discretized to a finite number of degrees of freedom. Traditional...

- Unitary quantum time evolution by iterative Lanczos reduction. Park, Tae Jun; Light, J. C. // Journal of Chemical Physics;11/15/1986, Vol. 85 Issue 10, p5870
A general unitary time evolution method for wave packets defined on a fixed L2 basis is developed. It is based on the Lanczos reduction of the full NÃ—N Hamiltonian to a p-dimensional subspace defined by the application of H p-1 times to the initial vector. Unitary time evolution in the...

- Basis set methods for describing the quantum mechanics of a â€˜â€˜systemâ€™â€™ interacting with a harmonic bath. Makri, Nancy; Miller, William H. // Journal of Chemical Physics;2/1/1987, Vol. 86 Issue 3, p1451
The case of a system (e.g., a one-dimensional reaction coordinate) coupled to a â€˜â€˜bathâ€™â€™ of many harmonic oscillators is treated by quantum mechanical basis set methods. By choosing the basis set for the bath to incorporate the coupling explicitly, it is shown how the...

- Gaussian-like quadrature rules for quantum mechanical calculations. Linderberg, Jan; Öhrn, Yngve; Padkjær, So\ren B. // Journal of Chemical Physics;10/15/1989, Vol. 91 Issue 8, p4793
Quadrature rules for the evaluation of matrix elements relevant for one-dimensional quantum mechanical problems are developed and tested. Nodes and weights are determined from a related problem and the general transformation between localized and delocalized basis representations is discussed.

- Time-dependent quantum dynamics in a Gauss-Hermite basis. Billing, Gert D. // Journal of Chemical Physics;3/22/1999, Vol. 110 Issue 12, p5526
Reports on the formulation of time-dependent quantum dynamics in a Gauss-Hermite basis set. Multi-dimensional Hamiltonians; Second order quantum dynamics; Scattering of He atoms on a Cu(001) surface including phonon excitation of the Cu-crystal phonons; Convenience of using the Gauss-Hermite basis.

- Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters. Bubin, Sergiy; Adamowicz, Ludwik // Journal of Chemical Physics;6/14/2006, Vol. 124 Issue 22, p224317
In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix...

- A global ab initio potential energy surface for the X 2Aâ€² ground state of the Si + OH â†’ SiO + H reaction. Dayou, Fabrice; Duflot, Denis; Rivero-Santamaría, Alejandro; Monnerville, Maurice // Journal of Chemical Physics;Nov2013, Vol. 139 Issue 20, p204305
We report the first global potential energy surface (PES) for the X 2Aâ€² ground electronic state of the Si(3P) + OH(X2Î ) â†’ SiO(X1Î£g+) + H(2S) reaction. The PES is based on a large number of ab initio energies obtained from multireference configuration interaction calculations...