Year: 2026
Type: preprint
Abstract: It is known that the Sachdev-Ye-Kitaev (SYK) model is exactly solvable at leading order in $1/q$; specifically, the instantaneously thermal time block after the quench is known in closed form. Thus far the remaining (inherently out of equilibrium) blocks have only been numerically accessible. Here we provide their analytical solutions for a quench between non-commuting $q/2$-body SYK Hamiltonians. We obtain the Green's functions in closed form for every time block. We extract a simple relation between the pre- and post-quench energies $ε_1 \propto ε_0$ leading to an exact temperature update rule. Via a Cauchy-Schwarz inequality, we show that heating is inevitable for the closed system; hence, the second law emerges geometrically. The solution is used in a companion paper to address what ``instantaneous thermalization'' means at finite $q$.
Source: arXiv (Cornell University)
Author: Louw, Jan C.
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213398053