Quantum Integrable Systems on a Classical Integrable Background

Standard

Quantum Integrable Systems on a Classical Integrable Background. / Liashyk, A.; Reshetikhin, N.; Sechin, I.

In: Communications in Mathematical Physics, Vol. 407, No. 1, 2026.

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

Harvard

Liashyk, A, Reshetikhin, N & Sechin, I 2026, 'Quantum Integrable Systems on a Classical Integrable Background', Communications in Mathematical Physics, vol. 407, no. 1. https://doi.org/10.1007/s00220-025-05523-y

APA

Liashyk, A., Reshetikhin, N., & Sechin, I. (2026). Quantum Integrable Systems on a Classical Integrable Background. Communications in Mathematical Physics, 407(1). https://doi.org/10.1007/s00220-025-05523-y

Vancouver

Liashyk A, Reshetikhin N, Sechin I. Quantum Integrable Systems on a Classical Integrable Background. Communications in Mathematical Physics. 2026;407(1). https://doi.org/10.1007/s00220-025-05523-y

Author

Liashyk, A. ; Reshetikhin, N. ; Sechin, I. / Quantum Integrable Systems on a Classical Integrable Background. In: Communications in Mathematical Physics. 2026 ; Vol. 407, No. 1.

BibTeX

@article{a5da06e195984af2ab2cad3b7363416d,

title = "Quantum Integrable Systems on a Classical Integrable Background",

abstract = "In this paper, we develop a framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the semiclassical limit of quantum integrable systems. We start with an outline of the concept of hybrid dynamical systems. Then, we give several examples of hybrid integrable systems. The first series of examples is a class of hybrid integrable systems that appear in the semiclassical limit of quantum spin chains. Then, we look at the semiclassical limit of the quantum spin Calogero–Moser–Sutherland (CMS) system. The result is a hybrid integrable system driven by usual classical Calogero–Moser–Sutherland dynamics. This system at the fixed point of the multi-time classical dynamics CMS system gives the commuting spin Hamiltonians of Haldane–Shastry model. {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.",

author = "A. Liashyk and N. Reshetikhin and I. Sechin",

note = "Export Date: 29 March 2026; Cited By: 0; Correspondence Address: N. Reshetikhin; BIMSA, Beijing, China; email: reshetik@math.berkeley.edu",

year = "2026",

doi = "10.1007/s00220-025-05523-y",

language = "Английский",

volume = "407",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Quantum Integrable Systems on a Classical Integrable Background

AU - Liashyk, A.

AU - Reshetikhin, N.

AU - Sechin, I.

N1 - Export Date: 29 March 2026; Cited By: 0; Correspondence Address: N. Reshetikhin; BIMSA, Beijing, China; email: reshetik@math.berkeley.edu

PY - 2026

Y1 - 2026

N2 - In this paper, we develop a framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the semiclassical limit of quantum integrable systems. We start with an outline of the concept of hybrid dynamical systems. Then, we give several examples of hybrid integrable systems. The first series of examples is a class of hybrid integrable systems that appear in the semiclassical limit of quantum spin chains. Then, we look at the semiclassical limit of the quantum spin Calogero–Moser–Sutherland (CMS) system. The result is a hybrid integrable system driven by usual classical Calogero–Moser–Sutherland dynamics. This system at the fixed point of the multi-time classical dynamics CMS system gives the commuting spin Hamiltonians of Haldane–Shastry model. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

AB - In this paper, we develop a framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the semiclassical limit of quantum integrable systems. We start with an outline of the concept of hybrid dynamical systems. Then, we give several examples of hybrid integrable systems. The first series of examples is a class of hybrid integrable systems that appear in the semiclassical limit of quantum spin chains. Then, we look at the semiclassical limit of the quantum spin Calogero–Moser–Sutherland (CMS) system. The result is a hybrid integrable system driven by usual classical Calogero–Moser–Sutherland dynamics. This system at the fixed point of the multi-time classical dynamics CMS system gives the commuting spin Hamiltonians of Haldane–Shastry model. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

UR - https://www.mendeley.com/catalogue/1b106d16-43cc-3259-bdd9-8abdc9aadcb0/

U2 - 10.1007/s00220-025-05523-y

DO - 10.1007/s00220-025-05523-y

M3 - статья

VL - 407

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -

ID: 151443329