Boundary Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-Dependent Bulk and Boundary Coupling Strengths
Abstract
The generalized Bethe ansatz framework formulated in [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)] provides a unified framework to find exact solutions to quantum many-body systems with time-dependent coupling strengths with periodic boundary conditions. In this work we extend this framework to the case of open boundary conditions where in addition to the time-dependent interactions in the bulk, the boundary conditions are explicitly time-dependent. We show that for integrable time-dependent bulk coupling strengths, the generalized Bethe ansatz framework provides the time-dependent boundary conditions compatible with integrability and reduces the time-dependent Schrodinger equation to a set of matrix difference equations called the boundary quantum Knizhnik-Zamolodchikov (BqKZ) equations. The solution to the BqKZ equations provides the explicit form of the exact wavefunction. We further show that the RG invariants of the corresponding static model identify with the dynamical invariants in the time-dependent model.
Related
- Initial and initial boundary value problems for the Navier-Stokes equations with temperature-dependent transport coefficients and large data
- On Bäcklund transformations preserving the Darboux integrability of hyperbolic equations
- What remains when integrability fails? Mathematical structure in the K(m,m) compacton equations
- Well-posedness of Rough Differential Equations at the Krylov-Röckner Integrability Threshold
- Six-wave scattering in Hamiltonian Dysthe equations: Euler matching and integrability obstructions
BibTeX
@misc{pasnoori2026boundary,
title = {{Boundary Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-Dependent Bulk and Boundary Coupling Strengths}},
author = {Parameshwar R. Pasnoori},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.31080},
eprint = {2608.31080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31080},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Boundary Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-Dependent Bulk and Boundary Coupling Strengths
AU - Parameshwar R. Pasnoori
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2608.31080
UR - https://arxiv.org/abs/2608.31080
AB - The generalized Bethe ansatz framework formulated in [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)] provides a unified framework to find exact solutions to quantum many-body systems with time-dependent coupling strengths with periodic boundary conditions. In this work we extend this framework to the case of open boundary conditions where in addition to the time-dependent interactions in the bulk, the boundary conditions are explicitly time-dependent. We show that for integrable time-dependent bulk coupling strengths, the generalized Bethe ansatz framework provides the time-dependent boundary conditions compatible with integrability and reduces the time-dependent Schrodinger equation to a set of matrix difference equations called the boundary quantum Knizhnik-Zamolodchikov (BqKZ) equations. The solution to the BqKZ equations provides the explicit form of the exact wavefunction. We further show that the RG invariants of the corresponding static model identify with the dynamical invariants in the time-dependent model.
ER -