2025年10月6日（月）13:30~（第11回）(11th: 13:30-, October 6, 2025)

理学部1号館206教室 (Room No. 206, Science 1st Bldg.) 

Speaker: Urei Miura (YITP, Kyoto University)

Title: Classical Integrable Lax Flows Meets Quantum Time Evolution – A Krylov Approach 

Abstract:

When we analyze quantum many-body systems such as spin systems, we inevitably use numerical linear algebraic methods, at least under the hood of computers. Especially, the Krylov subspace method including Lanczos or Arnoldi methods is used not only as the numerical methods but also for the defining and quantifying the operator growth in the quantum chaotic systems.

On the other hand, the classical Toda lattice and its variants in the classical integrable systems are formalized in the Lax form which keeps the spectra of matrix and its matrix form such as tridiagonal form or Hessenberg form.

In this talk, we discuss the relation between quantum pure imaginary time evolution and time evolution of classical Toda lattice and its variants, via the matrix reshaping by the Krylov subspace methods. By this relation, we see the identification of the autocorrelator as the τ-function and the reduction of the Toda lattice to the gradient flow of variational energy.

Additionally, we discuss the quantum geometrical perspective and the possibility of detecting the strong zero modes.