Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the Russian Academy of Sciences Physics

Describing Statistical Processes in a Nuclear Reactor in the Formalism of the Theory of Coherent States

Maksim Kravchenko, Ed. A. Rudak, Т. Н. Корбут, Michaela Bobková

Published Oct 1, 2021• 0 citations
Publisher

Abstract

Abstract A study is performed of the theory of coherent states’ applicability to solving statistical problems in the reactor physics. A mathematical description of the theory is provided in the formalism of both overlap integrals and operators of the creation and annihilation of phonons. The Poisson distribution is compared to coherent states, and the applicability of the formalism of the theory of coherent states to the physics of reactors is analyzed.

DOI
10.3103/s1062873821100208

Related papers

Statistical Description for the Decay of an Ensemble of Emitter Nuclei in the Context of a Sub-Poisson Distribution

Т. Н. Корбут, Ed. A. Rudak, A. M. Petrovskiy

Abstract A new formalism that combines the simplicity of the mathematical apparatus of the Poisson distribution and a correct description of the decay of the last nucleus of a system in a binomial distribution is proposed, based on Poisson and binomial distributions. The mathematical apparatus of the model for the creation and death of particles in a sub-Poisson distribution is presented, along with the results from comparing descriptions of the radioactive decay of nuclei using Poisson, binomial, and sub-Poisson distributions for a medium based on uranium-235.

Bulletin of the Russian Academy of Sciences Physics•Oct 1, 2018•5 citations

Coherent states

J. C. Garrison, R. Y. Chiao

The elementary quantum theory of quasi-classical states for mechanical harmonic oscillators is applied to the radiation oscillators describing light, and thus used to define quasi-classical states of light. These states are called “coherent”, because the expectation value of any normally ordered product of creation and annihilation operators factorizes for them. A theoretical discussion of possible sources for coherent states is followed by experimental evidence for their existence. The mathematical properties of coherent states, e.g., nonorthogonality and overcompleteness, are explained in order to use them to represent states and operators. These representations provide a suitable replacement for the classical phase space description of light, which is forbidden by the uncertainty principle. The quantum phase space approach leads to the definition of the Wigner distribution, the Q-function, the P-function, and Gaussian mixed states.

Oxford University Press eBooks•Jun 5, 2008•0 citations

Forms of quantum mechanics

Sibel Başkal, Young S Kim, Marilyn E. Noz

Quantum mechanics takes various forms. For atomic and nuclear physics, the Schrödinger picture is convenient. For quantum field theory and for correspondence with classical mechanics through Poisson brackets, the Heisenberg picture is useful. The interaction picture is useful in calculations. The Wigner phase-space is convenient for studying the uncertainty relations and their symmetries. The density matrix and probability distribution are necessary for extracting measurable dynamic quantities and are essential for ensemble averages. Mathematical instruments, such as the Lie algebra of the rotation group, the creation and annihilation operators of the Fock space and the Lie algebra governing Dirac’s two oscillators are shown to be derivable from Heisenberg’s commutation relations.

Institute of Physics eBooks•Jun 1, 2019•0 citations

Generalized Coherent States Representation

R. Sh. Kalmetev, Yu. N. Orlov, Vsevolod Zhanovich Sakbaev

Abstract The properties of the system of eigenvectors of the annihilation operator are investigated for the case of non-classical commutation relations between the operators of creation and annihilation. The existence of a measure on the set of eigenvalues of the annihilation operator is proved, with respect to which coherent states form a generalized crowded system. Formulas of covariant symbols of vectors and operators in the representation of generalized coherent states are obtained. It is shown that, similarly to the classical boson case, generalized coherent states are states with minimal uncertainty.

Lobachevskii Journal of Mathematics•Nov 1, 2021•5 citations

Four-parameter Mittag-Leffler functions and their associated coherent states

Dušan Popov

We defined and used a pair of Hermitian annihilation and creation operators which generate the generalized coherent states, defined in the Barut-Girardello manner, whose normalization function is just the four-parameter generalized Mittag-Leffler function. We examined the characteristic properties for these pure, as well as mixed (thermal) coherent states. All calculations are made using the rules of the technique of diagonal ordering of operators. Finally, the integral counterpart of the Mittag-Leffler coherent states are examined which is connected with nu-function. The paper is an example of the application of a mathematical entity (Mittag-Leffler function) in quantum mechanics (coherent states formalism).

arXiv:2410.19462•Oct 25, 2024•1 citation

An axiomatics and a combinatorial model of creation/annihilation operators

Marcelo Fiore

Abstract A categorical axiomatic theory of creation/annihilation operators on symmetric Fock space is introduced, and the combinatorial model that motivated it is presented. Commutation relations and coherent states are considered in both frameworks.

arXiv:1506.06402•Mathematical Structures in Computer Science•Jan 1, 2025•6 citations
Abstract A study is performed of the theory of coherent states’ applicability to solving statistical problems in the reactor physics. A mathematical description of the theory is provided in the formalism of both overlap integrals and operators of the creation and annihilation of phonons. The Poisson distribution is compared to coherent states, and the applicability of the formalism of the theory of coherent states to the physics of reactors is analyzed.
Abstract A new formalism that combines the simplicity of the mathematical apparatus of the Poisson distribution and a correct description of the decay of the last nucleus of a system in a binomial distribution is proposed, based on Poisson and binomial distributions. The mathematical apparatus of the model for the creation and death of particles in a sub-Poisson distribution is presented, along with the results from comparing descriptions of the radioactive decay of nuclei using Poisson, binomial, and sub-Poisson distributions for a medium based on uranium-235.
The elementary quantum theory of quasi-classical states for mechanical harmonic oscillators is applied to the radiation oscillators describing light, and thus used to define quasi-classical states of light. These states are called “coherent”, because the expectation value of any normally ordered product of creation and annihilation operators factorizes for them. A theoretical discussion of possible sources for coherent states is followed by experimental evidence for their existence. The mathematical properties of coherent states, e.g., nonorthogonality and overcompleteness, are explained in order to use them to represent states and operators. These representations provide a suitable replacement for the classical phase space description of light, which is forbidden by the uncertainty principle. The quantum phase space approach leads to the definition of the Wigner distribution, the Q-function, the P-function, and Gaussian mixed states.
Quantum mechanics takes various forms. For atomic and nuclear physics, the Schrödinger picture is convenient. For quantum field theory and for correspondence with classical mechanics through Poisson brackets, the Heisenberg picture is useful. The interaction picture is useful in calculations. The Wigner phase-space is convenient for studying the uncertainty relations and their symmetries. The density matrix and probability distribution are necessary for extracting measurable dynamic quantities and are essential for ensemble averages. Mathematical instruments, such as the Lie algebra of the rotation group, the creation and annihilation operators of the Fock space and the Lie algebra governing Dirac’s two oscillators are shown to be derivable from Heisenberg’s commutation relations.
Abstract The properties of the system of eigenvectors of the annihilation operator are investigated for the case of non-classical commutation relations between the operators of creation and annihilation. The existence of a measure on the set of eigenvalues of the annihilation operator is proved, with respect to which coherent states form a generalized crowded system. Formulas of covariant symbols of vectors and operators in the representation of generalized coherent states are obtained. It is shown that, similarly to the classical boson case, generalized coherent states are states with minimal uncertainty.
We defined and used a pair of Hermitian annihilation and creation operators which generate the generalized coherent states, defined in the Barut-Girardello manner, whose normalization function is just the four-parameter generalized Mittag-Leffler function. We examined the characteristic properties for these pure, as well as mixed (thermal) coherent states. All calculations are made using the rules of the technique of diagonal ordering of operators. Finally, the integral counterpart of the Mittag-Leffler coherent states are examined which is connected with nu-function. The paper is an example of the application of a mathematical entity (Mittag-Leffler function) in quantum mechanics (coherent states formalism).