相关论文: Quantum Algebraic Symmetries in Nuclei, Molecules …
Adaptive quantum design identifies the best broken-symmetry configurations of atoms and molecules that enable a desired target function response. In this work, numerical optimization is used to design atomic clusters with specified…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
In this paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with "complex Poincar\'e group" ISO(4,C).
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
In this paper, the application of quantum simulations and quantum machine learning to solve low-energy nuclear physics problems is explored. The use of quantum computing to deal with nuclear physics problems is, in general, in its infancy…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative…
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.
We examine several types of symmetries which are relevant to quantum phase transitions in nuclei. These include: critical-point, quasidynamical, and partial dynamical symmetries.
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
We demonstrate how NMR can in principle be used to implement all the elements required to build quantum computers, and briefly discuss the potential applications of insights from quantum logic to the development of novel pulse sequences…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.
Symmetry techniques based on group theory play a prominent role in the analysis of nuclear phenomena, and in particular in the understanding of observed regular patterns in nuclear spectra and selection rules for electromagnetic…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
We motivate the use of quantum algorithms in particle physics and provide a brief overview of the most recent applications at high-energy colliders. In particular, we discuss in detail how a quantum approach reduces the complexity of jet…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…