An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations

L. A. Markovich; R. Grimaudo; A. Messina; H. Nakazato

doi:10.1016/j.aop.2017.07.008

An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations

L. A. Markovich, R. Grimaudo^*, A. Messina, H. Nakazato

^*Corresponding author for this work

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.

Original language	English
Pages (from-to)	522-531
Number of pages	10
Journal	Annals of Physics
Volume	385
DOIs	https://doi.org/10.1016/j.aop.2017.07.008
Publication status	Published - 2017 Oct

Keywords

Riccati equation
Solvable model
Time-dependent Hamiltonian
Unitary evolution

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1016/j.aop.2017.07.008

Cite this

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title = "An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations",

abstract = "A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.",

keywords = "Riccati equation, Solvable model, Time-dependent Hamiltonian, Unitary evolution",

author = "Markovich, {L. A.} and R. Grimaudo and A. Messina and H. Nakazato",

note = "Funding Information: A. Messina and R. Grimaudo warmly thank Prof. A. Klimov and Prof. M. Kus for interesting and stimulating discussions about the argument. H. N. was supported by the Waseda University Grant for Special Research Projects (No. 2016B-173 ). The study in Sections 2 and 3 by Markovich L.A. was supported by the Russian Science Foundation grant ( 14-50-00150 ). R. G. was partially supported by research funds in memory of Francesca Palumbo ( DiFC 3100050001D08+ ). Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = oct,

doi = "10.1016/j.aop.2017.07.008",

language = "English",

volume = "385",

pages = "522--531",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

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T2 - Exact resolution of a new class of Riccati Equations

AU - Markovich, L. A.

AU - Grimaudo, R.

AU - Messina, A.

AU - Nakazato, H.

N1 - Funding Information: A. Messina and R. Grimaudo warmly thank Prof. A. Klimov and Prof. M. Kus for interesting and stimulating discussions about the argument. H. N. was supported by the Waseda University Grant for Special Research Projects (No. 2016B-173 ). The study in Sections 2 and 3 by Markovich L.A. was supported by the Russian Science Foundation grant ( 14-50-00150 ). R. G. was partially supported by research funds in memory of Francesca Palumbo ( DiFC 3100050001D08+ ). Publisher Copyright: © 2017 Elsevier Inc.

PY - 2017/10

Y1 - 2017/10

N2 - A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.

AB - A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.

KW - Riccati equation

KW - Solvable model

KW - Time-dependent Hamiltonian

KW - Unitary evolution

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SP - 522

EP - 531

JO - Annals of Physics

JF - Annals of Physics

ER -

An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations

Abstract

Keywords

ASJC Scopus subject areas

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