Difference Hierarchies for nT τ-functions

2018 ◽  
Vol 29 (13) ◽  
pp. 1850090
Author(s):  
Darlayne Addabbo ◽  
Maarten Bergvelt
Keyword(s):  
Fock Space ◽  
Loop Group ◽  
Matrix Group ◽  
Infinite Matrix ◽  
Matrix Elements ◽  
Type Formula ◽  
Change Of Variables ◽  
Usual Formula ◽  
Bilinear Equations ◽  
Text Component

We introduce hierarchies of difference equations (referred to as [Formula: see text]-systems) associated to the action of a (centrally extended, completed) infinite matrix group [Formula: see text] on [Formula: see text]-component fermionic Fock space. The solutions are given by matrix elements ([Formula: see text]-functions) for this action. We show that the [Formula: see text]-functions of type [Formula: see text] satisfy bilinear equations of length [Formula: see text]. The [Formula: see text]-system is, after a change of variables, the usual [Formula: see text] term [Formula: see text]-system of type [Formula: see text]. Restriction from [Formula: see text] to a subgroup isomorphic to the loop group [Formula: see text], defines [Formula: see text]-systems, studied earlier in [1] by the present authors for [Formula: see text].

scholarly journals Hardy-Type Space Associated with an Infinite-Dimensional Unitary Matrix Group

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Oleh Lopushansky
Keyword(s):  
Fock Space ◽  
Matrix Group ◽  
Unitary Matrix ◽  
Type Space ◽  
Infinite Dimensional ◽  
System A ◽  
Hardy Type ◽  
Complex Functions ◽  
Hardy Type Space ◽  
The Right

We investigate an orthogonal system of the homogenous Hilbert-Schmidt polynomials with respect to a probability measure which is invariant under the right action of an infinite-dimensional unitary matrix group. With the help of this system, a corresponding Hardy-type space of square-integrable complex functions is described. An antilinear isomorphism between the Hardy-type space and an associated symmetric Fock space is established.

scholarly journals Noncommutative probability of type D

2017 ◽  
Vol 28 (02) ◽  
pp. 1750010 ◽  
Author(s):  
Marek Bożejko ◽  
Wiktor Ejsmont ◽  
Takahiro Hasebe
Keyword(s):  
Brownian Motion ◽  
Coxeter Groups ◽  
Fock Space ◽  
Noncommutative Probability ◽  
Type Formula ◽  
Type D

We construct a deformed Fock space and a Brownian motion coming from Coxeter groups of type [Formula: see text]. The construction is analogous to that of the [Formula: see text]-Fock space (of type [Formula: see text]) and the [Formula: see text]-Fock space (of type [Formula: see text]).

scholarly journals Finite-Field Calculations of Transition Properties by the Fock Space Relativistic Coupled Cluster Method: Transitions between Different Fock Space Sectors

2020 ◽  
Author(s):  
Andrei Zaitsevskii ◽  
Alexander Oleynichenko ◽  
Ephraim Eliav
Keyword(s):  
Finite Field ◽  
Transition Matrix ◽  
Fock Space ◽  
Electronic States ◽  
Radiative Properties ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Matrix Elements ◽  
Transition Dipole ◽  
Transition Matrix Elements

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the $1h1p$ sector) in heavy atoms (Xe, Hg) and simple molecules of heavy element compounds (I${}_2$, TlF) are reported.

scholarly journals Finite-Field Calculations of Transition Properties by the Fock Space Relativistic Coupled Cluster Method: Transitions between Different Fock Space Sectors

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1845
Author(s):  
Andréi Zaitsevskii ◽  
Alexander V. Oleynichenko ◽  
Ephraim Eliav
Keyword(s):  
Finite Field ◽  
Transition Matrix ◽  
Fock Space ◽  
Electronic States ◽  
Radiative Properties ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Matrix Elements ◽  
Transition Dipole ◽  
Transition Matrix Elements

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the 1h1p sector) in heavy atoms (Xe and Hg) and simple molecules of heavy element compounds (I2 and TlF) are reported.

scholarly journals Diagonal and off-diagonal hyperfine structure matrix elements in KCs within the relativistic Fock space coupled cluster theory

2020 ◽  
Vol 756 ◽  
pp. 137825 ◽  
Author(s):  
Alexander V. Oleynichenko ◽  
Leonid V. Skripnikov ◽  
Andréi Zaitsevskii ◽  
Ephraim Eliav ◽  
Vladimir M. Shabaev
Keyword(s):  
Hyperfine Structure ◽  
Fock Space ◽  
Coupled Cluster ◽  
Matrix Elements ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Structure Matrix

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

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