scholarly journals Hilbert Bimodules with Involution

2001 ◽  
Vol 44 (3) ◽  
pp. 355-369 ◽  
Author(s):  
Nik Weaver

AbstractWe examine Hilbert bimodules which possess a (generally unbounded) involution. Topics considered include a linking algebra representation, duality, locality, and the role of these bimodules in noncommutative differential geometry

2020 ◽  
Vol 75 (5) ◽  
pp. 381-391 ◽  
Author(s):  
Heinz-Jürgen Schmidt

AbstractWe investigate the motion of a classical spin processing around a periodic magnetic field using Floquet theory, as well as elementary differential geometry and considering a couple of examples. Under certain conditions, the role of spin and magnetic field can be interchanged, leading to the notion of “duality of loops” on the Bloch sphere.


2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Zhan Chen

AbstractDifferential geometry (DG) based solvation models have shown their great success in solvation analysis by avoiding the use of ad hoc surface definitions, coupling the polar and nonpolar free energies, and generating solvent-solute boundary in a physically self-consistent fashion. Parameter optimization is a key factor for their accuracy, predictive ability of solvation free energies, and other applications. Recently, a series of efforts have been made to improve the parameterization of these new implicit solvent models. In thiswork, we aim at studying the role of dispersion attraction in the parameterization of our DG based solvation models. To this end, we first investigate the necessity of van derWaals (vdW) dispersion interactions in the model and then carry out systematic parameterization for the model in the absence of electrostatic interactions. In particular, we explore how the changes in Lennard-Jones (L-J) potential expression, its decomposition scheme, and choices of some fixed parameter values affect the optimal values of other parameters as well as the overall modeling error. Our study on nonpolar solvation analysis offers insights into the parameterization of nonpolar components for the full DG based models by eliminating uncertainties from the electrostatic polar component. Therefore, it can be regarded as a step towards better parameterization for the full DG based model.


2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040011
Author(s):  
Giacomo Rosati

For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group.


K-Theory ◽  
1990 ◽  
Vol 4 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Tetsuya Masuda ◽  
Yoshiomi Nakagami ◽  
Junsei Watanabe

K-Theory ◽  
1991 ◽  
Vol 5 (2) ◽  
pp. 151-175 ◽  
Author(s):  
Tetsuya Masuda ◽  
Yoshiomi Nakagami ◽  
Junsei Watanabe

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