Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ non-equilibrium quantum field theory and semi-classical phase-space simulations to show how this universality is replaced by a more general transport process in a long-range XY spin chain at infinite temperature with couplings decaying algebraically with distance as $r^{-α}$. While diffusion is recovered for $α>1.5$, longer-ranged couplings with $0.5<α\leq 1.5 $ give rise to effective classical Lévy flights; a random walk with step sizes drawn from a distribution with algebraic tails. We find that the space-time dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. As a consequence, for $0.5<α\leq1.5$ autocorrelations show hydrodynamic tails decaying in time as $t^{-1/(2α-1)}$ and linear-response theory breaks down. Our findings can be readily verified with current trapped ion experiments.
We develop a coarse-grained description of the point-vortex model, finding that a large number of planar vortices and antivortices behave as an inviscid non-Eulerian fluid at large scales. The emergent binary vortex fluid is subject to anomalous stresses absent from Euler's equation, caused by the singular nature of quantum vortices. The binary vortex fluid is compressible, and has an asymmetric Cauchy stress tensor allowing orbital angular momentum exchange with the vorticity and vortex density. An analytic solution for vortex shear flow driven by anomalous stresses is in excellent agreement …
We investigate emergent quantum dynamics of the tilted Ising chain in the regime of a weak transverse field. Within the leading order perturbation theory, the Hilbert space is fragmented into exponentially many decoupled sectors. We find that the sector made of isolated magnons is integrable with dynamics being governed by a constrained version of the XXZ spin Hamiltonian. As a consequence, when initiated in this sector, the Ising chain exhibits ballistic transport on unexpectedly long times scales. We quantitatively describe its rich phenomenology employing exact integrable techniques such as…
We provide a pure state formulation for hydrodynamic dynamics of isolated quantum many-body systems. A pure state describing quantum systems in local thermal equilibrium is constructed, which we call a local thermal pure quantum ($\ell$TPQ) state. We show that the thermodynamic functional and the expectation values of local operators (including a real-time correlation function) calculated from the $\ell$TPQ state converge to those from a local Gibbs ensemble in the large fluid-cell limit. As a numerical demonstration, we investigate a one-dimensional spin chain and observe the hydrodynamic rel…
We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a global conservation law that can be attributed to the presence of topological solitons. The correlation functions of local objects charged under this conservation law can then be used to study the universal properties of the dynamics at late times, applicable to both quantum and classical systems. Performing the time evolution via classically simulable autom…
The degenerate Bose-Fermi (BF) mixtures in one dimension present a novel realization of two decoupled Luttinger liquids with bosonic and fermionic degrees of freedom at low temperatures. However, the transport properties of such decoupled Luttinger liquids of charges have not yet been studied. Here we apply generalized hydrodynamics to study the transport properties of one-dimensional (1D) BF mixtures with delta-function interactions. The initial state is set up as the semi-infinite halves of two 1D BF mixtures with different temperatures, joined together at the time $t=0$ and the junction poi…
Generic far-away-from-equilibrium many-body dynamics involve entropy production, and hence are thermodynamically irreversible. Near quantum critical points, an emergent conformal symmetry can impose strong constraints on entropy production rates, and in some cases completely forbid entropy production, which usually occurs for systems that deviate from quantum critical points. In this article, we illustrate how the vanishing entropy production near a quantum critical point results in reversible far-away-from-equilibrium dynamics at finite temperatures that are otherwise irreversible. Away from …
Microscopic Origin of Emergent Elliptic Flow and Molecule Formation in Strongly Interacting Quasi-Two-Dimensional Few-Body Systems
The Chinese University of Hong Kong（香港中文大学）；Washington State University（华盛顿州立大学）；State Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（香港中文大学量子信息技术与材料国家重点实验室）；The Chinese University of Hong Kong Shenzhen Research Institute（香港中文大学（深圳）研究院）
We consider a massive complex scalar field with contact interactions with a source and show that, upon Bose-Einstein condensation, there is an emergent long-range interaction between sources. This interaction becomes long-range in the limit of vanishing self-interaction between Bose-Einstein constituents. More generally, the range is given by $\ell^{-1}\propto \sqrt{λn/m}$, with $λ$ being the 2-body self-interaction coupling constant, $n$ the particle number density in the condensate, and $m$ the mass of the condensed particles. Naively this may sound surprising since in $λ\rightarrow 0$ limit…
