Quantum chaos is a major subject of interest in condensed matter theory, and
has recently motivated new questions in the study of classical chaos. In
particular, recent studies have uncovered interesting physics in the
relationship between chaos and conserved quantities in models of quantum chaos.
In this paper, we investigate this relationship in two simple models of
classical chaos: the infinite-temperature Heisenberg spin chain, and the
directed polymer in a random medium. We relate these models by drawing
analogies between the energy landscape over which the directed polymer moves
and the magnetization of the spin chain. We find that the coupling of the chaos
to these conserved quantities results in, among other things, a marked
transition from the rough perturbation profiles predicted by analogy to the KPZ
equation to smooth, triangular profiles with reduced wandering exponents. These
results suggest that diffusive conserved quantities can, in some cases, be the
dominant forces shaping the development of chaos in classical systems.Comment: This was an undergraduate research paper by Henry Ando, which we are
posting now because it is relevant to some continuing wor