Tootfinder

Two sequences of fully-nonlinear evolution equations and their symmetry properties
Marianna Euler, Norbert Euler
https://arxiv.org/abs/2509.05535 https://a…

Two sequences of fully-nonlinear evolution equations and their symmetry properties
We obtain the complete Lie point symmetry algebras of two sequences of odd-order evolution equations. This includes equations that are fully-nonlinear, i.e. nonlinear in the highest derivative. Two of the equations in the sequences have recently been identified as symmetry-integrable, namely a 3rd-order equation and a 5th-order equation [Open Communications in Nonlinear Mathematical Physics, Special Issue in honour of George W Bluman, ocnmp:15938, 1--15, 2025]. These two examples provided the m…

Gradient of the Adiabatic Gauge Potential in Classical Systems
Nathan Rose, Nachiket Karve, David K. Campbell
https://arxiv.org/abs/2508.03804 https://arxi…

Gradient of the Adiabatic Gauge Potential in Classical Systems
The adiabatic gauge potential (AGP) is the generator of unitary transformations which preserve the eigenbasis of a quantum Hamiltonian under parametric variation. While its usefulness in quantum mechanics has been thoroughly demonstrated in recent years, less attention has been given to its behavior in classical systems, where the AGP is a phase space function and its gradient defines special canonical transformations. In this paper we propose an efficient method to compute the gradient of the …

Toda lattice formed in nonequilibrium steady states of SWCNT
Heeyuen Koh, Shigeo Maruyama
https://arxiv.org/abs/2507.18412 https://arxiv.org/pdf/2507.18412…

Toda lattice formed in nonequilibrium steady states of SWCNT
Toda lattice or FPUT chain-like dynamics have been regarded as the prerequisite condition to explain the length dependency of high thermal conductivity of low-dimensional systems at the nanoscale. In this paper, a hypothetical condition is introduced that establishes a theoretical connection between the thermal conductivity of a nanoscale low-dimensional system in nonequilibrium steady states(NESS) and the canonical motion of the equation in the Toda lattice in equilibrium. The hypothesis relie…