Spatio-temporal conjecture for diffusion

TL;DR

This paper proposes a conjecture linking the noise density of states in Langevin systems to energy density fluctuations in Hamiltonian systems, supported by evidence from a disordered Heisenberg model.

Contribution

It introduces a novel conjecture connecting stochastic noise characteristics with Hamiltonian energy fluctuations, supported by empirical evidence.

Findings

Evidence supports the conjecture in a disordered Heisenberg system.

Establishes a potential fundamental link between Langevin noise and Hamiltonian energy states.

Abstract

We present here a conjecture about the equivalence between the noise density of states of a system governed by a generalized Langevin equation and the fluctuation in the energy density of states in a Hamiltonian system. We present evidence of this for a disordered Heisenberg system.