Tootfinder

Hamilton decompositions of regular tripartite tournaments
Francesco Di Braccio, Joanna Lada, Viresh Patel, Yani Pehova, Jozef Skokan
https://arxiv.org/abs/2507.12460

Hamilton decompositions of regular tripartite tournaments
Kühn and Osthus conjectured in 2013 that regular tripartite tournaments are decomposable into Hamilton cycles. Somewhat surprisingly, Granet gave a simple counterexample to this conjecture almost 10 years later. In this paper, we show that the conjecture of Kühn and Osthus nevertheless holds in an approximate sense, by proving that every regular tripartite tournament admits an approximate decomposition into Hamilton cycles. We also study Hamilton cycle packings of directed graphs in the same …

LevelSetPy: A GPU-Accelerated Package for Hyperbolic Hamilton-Jacobi Partial Differential Equations
Lekan Molu
https://arxiv.org/abs/2507.11542 https://

LevelSetPy: A GPU-Accelerated Package for Hyperbolic Hamilton-Jacobi Partial Differential Equations
This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In scope, we provide implementations of numerical algorithms for the resolution of Hamilton-Jacobi-Isaacs equations: the spatial derivatives of the associated value function via upwinding, the Hamiltonian via Lax-Friedrichs schemes, and the integration of the Hamil…

Approximating the operator norm of local Hamiltonians via few quantum states
Lars Becker, Joseph Slote, Alexander Volberg, Haonan Zhang
https://arxiv.org/abs/2509.11979 https://…

Approximating the operator norm of local Hamiltonians via few quantum states
Consider a Hermitian operator $A$ acting on a complex Hilbert space of dimension $2^n$. We show that when $A$ has small degree in the Pauli expansion, or in other words, $A$ is a local $n$-qubit Hamiltonian, its operator norm can be approximated independently of $n$ by maximizing $|\braket{ψ|A|ψ}|$ over a small collection $\mathbf{X}_n$ of product states $\ketψ\in (\mathbf{C}^{2})^{\otimes n}$. More precisely, we show that whenever $A$ is $d$-local, \textit{i.e.,} $°(A)\…

Hamilton's identity and rigidity of complete gradient solitons
Antonio W. Cunha, Antonio N. Silva Jr, William Wylie
https://arxiv.org/abs/2507.12381 ht…

Hamilton's identity and rigidity of complete gradient solitons
In this work, we study gradient solitons to general geometric flows. Our approach is to understand what assumptions need to be made about a flow in order to extend results about Ricci solitons. In this direction, we identify an identity, first exploited in the pioneering work of Richard Hamilton in the case of Ricci solitons, which we call Hamilton's identity. We show that a version of this identity for an arbitrary geometric flow allows one to recover results about rigidity, the growth of the …

Canonical and Canonoid transformations for Hamiltonian systems on locally conformal symplectic manifolds
Rafael Azuaje, Xuefeng Zhao
https://arxiv.org/abs/2509.11953 https://

Canonical and Canonoid transformations for Hamiltonian systems on locally conformal symplectic manifolds
This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic manifolds. Both, time-independent and time-dependent dynamics are considered. Noether-like theorems relating one-parameter groups of transformations with canonical and noncanonical symmetries, are formulated, proved as well as illustrated with elementary examples.

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Relations between parameters of the Hamiltonian and Neel-type states in the anisotropic Heisenberg model
Pavel Babaian, Gennady Koval
https://arxiv.org/abs/2507.12225

Relations between parameters of the Hamiltonian and Neel-type states in the anisotropic Heisenberg model
This article investigates Neel-type states in the anisotropic Heisenberg model with an external field. For arbitrary spin $s$ and arbitrary dimension of the space $d$ we find the expressions relating the angles which define the directions of spin polarisation to the parameters of the Hamiltonian.

Beyond Ground States: Physics-Inspired Optimization of Excited States of Classical Hamiltonians
Erik Altelarrea-Ferr\'e, J\'ulia Barber\`a-Rodr\'iguez, David Jansen, Antonio Ac\'in
https://arxiv.org/abs/2507.12394

Beyond Ground States: Physics-Inspired Optimization of Excited States of Classical Hamiltonians
We introduce excited local quantum annealing (ExcLQA), a classical, physics-inspired algorithm that extends local quantum annealing (LQA) to identify excited states of classical Ising Hamiltonians. LQA simulates quantum annealing while constraining the quantum state to remain in a product state and uses a gradient-based approach to find approximate solutions to large-scale quadratic unconstrained binary optimization problems. ExcLQA extends this framework by adding a penalty term in the cost fu…

Certifying and learning quantum Ising Hamiltonians
Andreas Bluhm, Matthias C. Caro, Francisco Escudero Guti\'errez, Aadil Oufkir, Cambyse Rouz\'e
https://arxiv.org/abs/2509.10239

Certifying and learning quantum Ising Hamiltonians
In this work, we study the problems of certifying and learning quantum Ising Hamiltonians. Our main contributions are as follows: Certification of Ising Hamiltonians. We show that certifying an Ising Hamiltonian in normalized Frobenius norm via access to its time-evolution operator requires only $\widetilde O(1/\varepsilon)$ time evolution. This matches the Heisenberg-scaling lower bound of $Ω(1/\varepsilon)$ up to logarithmic factors. To our knowledge, this is the first nearly-optimal algor…