Modified Enskog equation for hard rods

We point out that Percus's collision integral for hard rods [J. K. Percus, Physics of Fluids 12, 1560-1563 (1969)] does not preserve the thermal equilibrium state in an external trapping potential. We derive a modified Enskog equation for hard rods and show that it preserves this thermal state exactly. In contrast to recent proposed kinetic equations for dynamics in integrability-breaking traps, both our kinetic equation and its thermal states are explicitly nonlocal in space. Our equation differs from earlier proposals at third order in spatial derivatives and we attribute this discrepancy to the molecular chaos assumption underlying our approach.Comment: v2: minor revisions and clarifications, 8+3 page

The classical limit of Quantum Max-Cut

It is well-known in physics that the limit of large quantum spin $S$ should be understood as a semiclassical limit. This raises the question of whether such emergent classicality facilitates the approximation of computationally hard quantum optimization problems, such as the local Hamiltonian problem. We demonstrate this explicitly for spin-$S$ generalizations of Quantum Max-Cut ($\mathrm{QMaxCut}_S$), equivalent to the problem of finding the ground state energy of an arbitrary spin-$S$ quantum Heisenberg antiferromagnet ($\mathrm{AFH}_S$). We prove that approximating the value of $\mathrm{AFH}_S$ to inverse polynomial accuracy is QMA-complete for all $S$, extending previous results for $S=1/2$. We also present two distinct families of classical approximation algorithms for $\mathrm{QMaxCut}_S$ based on rounding the output of a semidefinite program to a product of Bloch coherent states. The approximation ratios for both our proposed algorithms strictly increase with $S$ and converge to the Bri\"et-Oliveira-Vallentin approximation ratio $\alpha_{\mathrm{BOV}} \approx 0.956$ from below as $S \to \infty$.Comment: 19+4 page

Solvable Hydrodynamics of Quantum Integrable Systems

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudo-momenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudo-momentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.Comment: 6+5 pages, published versio

Superdiffusive transport of energy in generic Luttinger liquids

Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic Luttinger-liquid metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response. We show that the expansion of energy when such a non-integrable Luttinger liquid is locally heated above its ground state shows superdiffusive behavior (i.e., spreading of energy that is intermediate between diffusion and ballistic propagation), by combining an analytical anomalous diffusion model with numerical matrix product state calculations.Comment: 5 pages, 3 figure

Quantum tasks assisted by quantum noise

We introduce a notion of expected utility for quantum tasks and discuss some general conditions under which this is increased by the presence of quantum noise in the underlying resource states. We apply the resulting formalism to the specific problem of playing the parity game with ground states of the random transverse-field Ising model. This demonstrates a separation in the ground-state phase diagram between regions where rational players will be ``risk-seeking'' or ``risk-averse'', depending on whether they win the game more or less often in the presence of disorder. The boundary between these regions depends non-universally on the correlation length of the disorder. Strikingly, we find that adding zero-mean, uncorrelated disorder to the transverse fields can generate a weak quantum advantage that would not exist in the absence of noise.Comment: 18 pages, 6 figure

Nonlinear breathers with crystalline symmetries

Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models are dynamically unstable. Nevertheless, symmetric and exponentially localized Wannier states are a central tool in the classification of band structures with crystalline symmetries. Moreover, the quantized transport observed in nonlinear Thouless pumps relies on the fact that -- at least in a specific model -- discrete breathers recover Wannier states in the limit of vanishing nonlinearity. Motivated by these observations, we investigate the correspondence between nonlinear breathers and linear Wannier states for a family of discrete nonlinear Schr\"odinger equations with crystalline symmetries. We develop a formalism to analytically predict the breathers' spectrum, center of mass and symmetry representations, and apply this to nonlinear generalizations of the Su-Schrieffer-Heeger chain and the breathing kagome lattice.Comment: 16+4 pages, 8+1 figure