Related papers: Electronic Fock space as associative superalgebra
We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete…
Recent results, extending the Schmidt decomposition theorem to wavefunctions of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is…
An approximate but straight forward projection method to molecular many alpha-particle states is proposed and the overlap to the shell model space is determined. The resulting space is in accordance with the shell model, but still contains…
An efficient approach to calculate approximate pure-state and transition reduced density matrices in the framework of the multireference relativistic Fock-space coupled cluster (FS CC) theory is proposed. The method is based on the…
A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…
We introduce a complex-valued counterpart of the representer theorem in machine learning. We study several learning and minimization problems in reproducing kernel Hilbert spaces (RKHSs), with the aim of identifying appropriate input-output…
Hamiltonian of a parametric process describing the interaction of a finite number of optical cavity modes, with the microwave field is proposed. Three-boson interaction is due to electro-optical effect. Analysis of the model is based on the…
We define a class of deformed multimode oscillator algebras which possess number operators and can be mapped to multimode Bose algebra.We construct and discuss the states in the Fock space and the corresponding number operators.
A new, very fast, implementation of the exact (Fock) exchange operator for electronic structure calculations within the plane-wave pseudopotential method is described in detail for both molecular and periodic systems, and carefully…
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly…
In this article we introduce a generalization of the Khovanov--Lauda Rouquier algebras, the electric KLR algebras. These are superalgebras which connect to super Brauer algebras in the same way as ordinary KLR-algebras of type $A$ connect…
Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of…
The Fock expansion [1] describes the $S$-state wave function of the two-electron atomic system in the vicinity of the triple coalescence point. The present work constitutes the additional appendix to our paper [2] devoted to refinement and…
We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in…
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive…
Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…
Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems. Despite a great deal of general methodological developments, representing fermionic matter is however still early…
The modular operator approach of Tomita-Takesaki to von Neumann algebras is elucidated in the algebraic structure of certain supersymmetric quantum mechanical systems. A von Neumann algebra is constructed from the operators of the system.…
The Fock-like representations of the Relative Parabose Set (\textsc{Rpbs}) algebra in a single parabosonic and a single parafermionic degree of freedom are investigated. It is shown that there is an infinite family (parametrized by the…