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We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law ($1/r^\alpha$) interactions. For all power-law exponents $\alpha$ between $d$ and $2d+1$, where $d$ is the dimension of the system, the protocol yields a polynomial speedup for $\alpha>2d$ and a superpolynomial speedup for $\alpha\leq 2d$, compared to the state of the art. For all $\alpha>d$, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. In addition, the protocol provides a lower bound on the gate count in digital simulations of power-law interacting systems., Comment: Updated Table I, Additional discussion on a lower bound for the gate count in digital quantum simulation

We study the entanglement dynamics in a generic quantum automaton circuit subjected to projective measurements. We design an efficient algorithm which not only allows us to perform large scale simulation for the R\'enyi entropy but also provides a physical picture for the entanglement dynamics, which can be interpreted in terms of a classical bit-string model which belongs to the directed percolation universality class. We study the purification dynamics of a state formed by EPR pairs, and the growth of entanglement starting from a product state. In both cases, we verify numerically that the dynamics is in the universality class of classical directed percolation., Comment: 16 pages, 16 figures

We develop the theory of hydrodynamics of an isotropic Fermi liquid of electrons coupled to isotropic acoustic phonons, assuming that umklapp processes may be neglected. At low temperatures, the fluid is approximately Galilean invariant; at high temperatures, the fluid is nearly relativistic; at intermediate temperatures, there are seven additional temperature regimes with unconventional thermodynamic properties and hydrodynamic transport coefficients in a three-dimensional system. We predict qualitative signatures of electron-phonon fluids in incoherent transport coefficients, shear and Hall viscosity, and plasmon dispersion relations. Our theory may be relevant for numerous quantum materials where strong electron-phonon scattering has been proposed to underlie a hydrodynamic regime, including $\mathrm{WTe}_2$, $\mathrm{WP}_2$, and $\mathrm{PtSn}_4$., Comment: 24+10 pages, 4 figures. v2: published version

We describe an efficient protocol to perform quantum state transfer using Hamiltonian dynamics with long-range interactions. The time to transfer $n$ qubits a sufficiently large distance is proportional to $\sqrt{n}$. Even without error correction, the fidelity of this multi-qubit state transfer process remains finite for arbitrarily well-separated qubits in the presence of uncorrelated random errors in coupling constants., Comment: 14 pages, 6 figures

Subdiffusion is a generic feature of chaotic many-body dynamics with multipole conservation laws and subsystem symmetries. We numerically study this subdiffusive dynamics, using quantum automaton random unitary circuits, in a broad range of models including one dimensional models with dipole and quadrupole conservation, two dimensional models with dipole conservation, and two dimensional models with subsystem symmetry on the triangular lattice. Our results are in complete agreement with recent hydrodynamic predictions for such theories., Comment: 7 pages, 8 figures

We initiate a study of finite temperature transport in gapless and strongly coupled quantum theories with charge and dipole conservation using gauge-gravity duality. In a model with non-dynamical gravity, the bulk fields of our model include a suitable mixed-rank tensor which encodes the boundary multipole symmetry. We describe how such a theory can arise at low energies in a theory with a covariant bulk action. Studying response functions at zero density, we find that charge relaxes via a fourth-order subdiffusion equation, consistent with a recently-developed field-theoretic framework., Comment: 14+5 pages, 1+0 figure; v2: added references. v3: added discussions

We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles. As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations., Comment: 30 pages, 22 figures. v2: 32 pages, 25 figures, added sec. 6.4 with explanation of the apparent enhancement of diffusion

We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of $N$ interacting fermions with charge conservation, or $N$ interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger than any Lieb-Robinson bound. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model. We also study random automaton quantum circuits and Brownian Sachdev-Ye-Kitaev models, each of which exhibit a different density dependence for the Lyapunov exponent, and explain the discrepancy. We propose that our results are a cartoon for understanding Planckian-limited energy-conserving dynamics at finite temperature., Comment: 17+3 pages; 3+1 figures; v2, v3: minor changes

We study operator growth in a model of $N(N-1)/2$ interacting Majorana fermions, which live on the edges of a complete graph of $N$ vertices. Terms in the Hamiltonian are proportional to the product of $q$ fermions which live on the edges of cycles of length $q$. This model is a cartoon "matrix model": the interaction graph mimics that of a single-trace matrix model, which can be holographically dual to quantum gravity. We prove (non-perturbatively in $1/N$, and without averaging over any ensemble) that the scrambling time of this model is at least of order $\log N$, consistent with the fast scrambling conjecture. We comment on apparent similarities and differences between operator growth in our "matrix model" and in the melonic models., Comment: 17 pages, 1 figure

We prove bounds on operator growth and infinite temperature out-of-time-ordered correlators in many-body systems with $N$ spin-$\frac{1}{2}$ degrees of freedom which interact via two-body all-to-all interactions. Our results parametrically improve previous bounds, and sharply constrain when and how quantum simulators, including trapped ion crystals and cavity quantum electrodynamics, can study quantum gravity., Comment: 8 pages. v2: added result on tightness. v3: published version

Large-scale electrical and thermal currents in ordinary metals are well approximated by effective medium theory: global transport properties are governed by the solution to homogenized coupled diffusion equations. In some metals, including the Dirac fluid of nearly charge neutral graphene, microscopic transport is not governed by diffusion, but by a more complicated set of linearized hydrodynamic equations, which form a system of degenerate elliptic equations coupled with the Stokes equation for fluid velocity. In sufficiently inhomogeneous media, these hydrodynamic equations reduce to homogenized diffusion equations. We re-cast the hydrodynamic transport equations as the infimum of a functional over conserved currents, and present a functional framework to model and compute the homogenized diffusion tensor relating electrical and thermal currents to charge and temperature gradients. We generalize to this system two well-known results in homogenization theory: Tartar's proof of local convergence to the homogenized theory in periodic and highly oscillatory media, and sub-additivity of the above functional in random media with highly oscillatory, stationary and ergodic coefficients., Comment: 27 pages

We present random quantum circuit models for non-unitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends towards steady states with logarithmic violations of the entanglement area law and power law correlation functions. Moreover, starting with a short-range entangled many-body state, the dynamical evolution of entanglement and correlations quantitatively agrees with the predictions of two-dimensional conformal field theory with a space-like time direction. We argue that this behavior is generic in non-unitary free quantum dynamics with time-dependent randomness, and show that the emergent conformal dynamics of two-point functions arises out of a simple "nonlinear master equation".

We revisit the theory of strongly correlated quantum matter perturbed by Harris-marginal random-field disorder, using the simplest holographic model. We argue that for weak disorder, the ground state of the theory is not Lifshitz invariant with a non-trivial disorder-dependent dynamical exponent, as previously found. Instead, below a non-perturbatively small energy scale, we predict infrared physics becomes independent of the disorder strength., Comment: 12 pages; v2: published version

We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter. Fracton phases are characterized by elementary excitations (fractons) with restricted mobility. The hydrodynamic theories we introduce describe thermalization in systems with fracton-like mobility constraints, including fluids where charge and dipole moment are both locally conserved, and fluids where charge is conserved along every line or plane of a lattice. Each of these fluids is subdiffusive, and constitutes a new universality class of hydrodynamic behavior. There are infinitely many such classes, each with distinct subdiffusive exponents, all of which are captured by our formalism. Our framework naturally explains recent results on dynamics with constrained quantum circuits, as well as recent experiments with ultracold atoms in tilted optical lattices. We identify crisp experimental signatures of these novel hydrodynamics, and explain how they may be realized in near term ultracold atom experiments., Comment: 5 + 10 pages. v2: minor revisions; references added. v3: published version, with a few additional results

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute -- given a many-body state, $\mathcal{O}_x(t) \mathcal{O}_y |\psi\rangle \approx \mathcal{O}_y\mathcal{O}_x(t) |\psi\rangle$ with arbitrarily small errors -- so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance $r$ interact with potential energy $V(r) \propto 1/r^{\alpha}$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same $\alpha$, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, this linear light cone exists for every many-body state when $\alpha>3$ (Lieb-Robinson light cone); for a typical state chosen uniformly at random from the Hilbert space when $\alpha>\frac{5}{2}$ (Frobenius light cone); for every state of a non-interacting system when $\alpha>2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones -- and their tightness -- also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds., Comment: 36 pages; 6 figures; v2: revised and expanded introduction, a few extra results; v3: minor revisions. v4: corrections in Section 7

We explore quantum dynamics in Floquet many-body systems with local conservation laws in one spatial dimension, focusing on sectors of the Hilbert space which are highly polarized. We numerically compare the predicted charge diffusion constants and quantum butterfly velocity of operator growth between models of chaotic Floquet dynamics (with discrete spacetime translation invariance) and random unitary circuits which vary both in space and time. We find that for small but finite polarization per length (in the thermodynamic limit), the random unitary circuit correctly predicts the scaling of the butterfly velocity but incorrectly predicts the scaling of the diffusion constant. We argue that this is a consequence of quantum coherence on short time scales. Our work clarifies the settings in which random unitary circuits provide correct physical predictions for non-random chaotic systems, and sheds light into the origin of the slow down of the butterfly effect in highly polarized systems or at low temperature., Comment: 9 + 4 pages; 7 figures; v2: published version

We prove non-perturbative bounds on the time evolution of the probability distribution of operator size in the $q$-local Sachdev-Ye-Kitaev model with $N$ fermions, for any even integer $q>2$ and any positive even integer $N>2q$. If the couplings in the Hamiltonian are independent and identically distributed Rademacher random variables, the infinite temperature many-body Lyapunov exponent is almost surely finite as $N\rightarrow\infty$. In the limit $q \rightarrow \infty$, $N\rightarrow \infty$, $q^{6+\delta}/N \rightarrow 0$, the shape of the size distribution of a growing fermion, obtained by leading order perturbation calculations in $1/N$ and $1/q$, is similar to a distribution that locally saturates our constraints. Our proof is not based on Feynman diagram resummation; instead, we note that the operator size distribution obeys a continuous time quantum walk with bounded transition rates, to which we apply concentration bounds from classical probability theory., Comment: 23 pages. v2: published version

Compressible electron flow through a narrow cavity is theoretically unstable, and the oscillations occurring during the instability have been proposed as a method of generating Terahertz radiation. We numerically demonstrate that the endpoint of this instability is a nonlinear hydrodynamic oscillator, consisting of an alternating shock wave and rarefaction-like relaxation flowing back and forth in the device. This qualitative physics is robust to cavity inhomogeneity and changes in the equation of state of the fluid. We discuss the frequency and amplitude dependence of the emitted radiation on physical parameters (viscosity, momentum relaxation rate, and bias current) beyond linear response theory, providing clear predictions for future experiments.

In sufficiently clean metals, it is possible for electrons to collectively flow as a viscous fluid at finite temperature. These viscous effects have been predicted to give a notable magnetoresistance, but whether the magnetoresistance is positive or negative has been debated. We argue that regardless of the strength of inhomogeneity, bulk magnetoresistance is always positive in the hydrodynamic regime. We also compute transport in weakly inhomogeneous metals across the ballistic-to-hydrodynamic crossover, where we also find positive magnetoresistance. The non-monotonic temperature dependence of resistivity in this regime (a bulk Gurzhi effect) rapidly disappears upon turning on any finite magnetic field, suggesting that magnetotransport is a simple test for viscous effects in bulk transport, including at the onset of the hydrodynamic regime., Comment: 14 pages, 5 figures; v2: published version

In a locally interacting many-body system, two isolated qubits, separated by a large distance $r$, become correlated and entangled with each other at a time $t \ge r/v$. This finite speed $v$ of quantum information scrambling limits quantum information processing, thermalization and even equilibrium correlations. Yet most experimental systems contain long range power law interactions -- qubits separated by $r$ have potential energy $V(r)\propto r^{-\alpha}$. Examples include the long range Coulomb interactions in plasma ($\alpha=1$) and dipolar interactions between spins ($\alpha=3$). In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large $\alpha$. This result parametrically improves previous bounds, compares favorably with recent numerical simulations, and can be realized in quantum simulators with dipolar interactions. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems, and improve bounds on environmental decoherence in experimental quantum information processors., Comment: 4+10 pages; 1+1 figures; v2: corrected an error; v3: published version

Let $A$ and $B$ be local operators in Hamiltonian quantum systems with $N $ degrees of freedom and finite-dimensional Hilbert space. We prove that the commutator norm $\lVert [A(t),B]\rVert$ is upper bounded by a topological combinatorial problem: counting irreducible weighted paths between two points on the Hamiltonian's factor graph. Our bounds sharpen existing Lieb-Robinson bounds by removing extraneous growth. In quantum systems drawn from zero-mean random ensembles with few-body interactions, we prove stronger bounds on the ensemble-averaged out-of-time-ordered correlator $\mathbb{E}\left[ \lVert [A(t),B]\rVert_F^2\right]$. In such quantum systems on Erd\"os-R\'enyi factor graphs, we prove that the scrambling time $t_{\mathrm{s}}$, at which $\lvert [A(t),B]\rVert_F=\mathrm{\Theta}(1)$, is almost surely $t_{\mathrm{s}}=\mathrm{\Omega}(\sqrt{\log N})$; we further prove $t_{\mathrm{s}}=\mathrm{\Omega}(\log N) $ to high order in perturbation theory in $1/N$. We constrain infinite temperature quantum chaos in the $q$-local Sachdev-Ye-Kitaev model at any order in $1/N$; at leading order, our upper bound on the Lyapunov exponent is within a factor of 2 of the known result at any $q>2$. We also speculate on the implications of our theorems for conjectured holographic descriptions of quantum gravity., Comment: 49 pages, 14 figures. v2: published version with errors fixed

Recent experiments have observed hints of hydrodynamic electron flow in a number of materials, not all of which have an isotropic Fermi surface. We revisit these experiments in $\mathrm{PdCoO}_2$, a quasi-two-dimensional material whose Fermi surface is a rounded hexagon, and observe that the data appears quantitatively consistent with a non-hydrodynamic interpretation. Nevertheless, motivated by such experiments, we develop a simple model for the low temperature kinetics and hydrodynamics of a two-dimensional Fermi liquid with a polygonal Fermi surface. A geometric effect leads to a finite number of additional long-lived quasihydrodynamic "imbalance" modes and corresponding qualitative changes in transport at the ballistic-to-hydrodynamic crossover. In the hydrodynamic limit, we find incoherent diffusion and a new dissipative component of the viscosity tensor arising from the explicit breaking of rotational invariance by the Fermi surface. Finally, we compute the conductance of narrow channels across the ballistic-to-hydrodynamic crossover and demonstrate a modification of the Gurzhi effect that allows for non-monotonic temperature and width dependence in the channel conductance., Comment: 27 + 11 pages (main text + appendices/references); 8+1 figures; 1+2 tables. v2: published version

We study 2-local Hamiltonian quantum systems, consisting of qubits interacting on the star graph of N vertices. We numerically demonstrate that these models are generically non-integrable at infinite temperature, and find evidence for a finite temperature phase transition to a glassy phase in generic models. Operators can become complicated in constant time: we explicitly find that there is no bound on out-of-time-ordered correlators, even at finite temperature. Operator growth is not correctly modeled by stochastic quantum dynamics, including Brownian Hamiltonian dynamics or random unitary circuits. The star graph (and similar constructions) may serve as a useful testing ground for conjectures about universality, quantum chaos and Planckian dissipation in k-local systems, including in experimental quantum simulators., Comment: 30 pages, 14 figures; v2: minor changes

Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling constants. Secondly, the interaction graph of the QUBO must have an effective minor embedding into a two-dimensional nonplanar lattice graph. We describe new strategies for constructing QUBOs for NP-complete/hard combinatorial problems that address both of these challenges. Our results include asymptotically improved embeddings for number partitioning, filling knapsacks, graph coloring, and finding Hamiltonian cycles. These embeddings can be also be found with reduced computational effort. Our new embedding for number partitioning may be more effective on next-generation hardware., Comment: 26+7 pages; 9+1 figures

We study dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry. The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion equation for the probability of all spatial configurations of energy. This is equivalent to nonlinear stochastic hydrodynamics, describing the diffusion of energy in physical spacetime. We find the absence of non-hydrodynamic slow degrees of freedom, a nonlinear fluctuation-dissipation theorem, and the emergence of a (weakly interacting) kinetic theory for hydrodynamic modes near thermal equilibrium. The observable part of the microscopic entropy obeys the local second law of thermodynamics, and quantitatively agrees with the phenomenological predictions of hydrodynamics. Our approach naturally generalizes to ergodic systems with additional symmetries, may lead to numerical algorithms to calculate diffusion constants for lattice models, and implies sufficiency conditions for a rigorous derivation of hydrodynamics in quantum systems., Comment: 28 pages, 2 figures. v2: published version

Hydrodynamics is a theory of long-range excitations controlled by equations of motion that encode the conservation of a set of currents (energy, momentum, charge, etc.) associated with explicitly realized global symmetries. If a system possesses additional weakly broken symmetries, the low-energy hydrodynamic degrees of freedom also couple to a few other "approximately conserved" quantities with parametrically long relaxation times. It is often useful to consider such approximately conserved operators and corresponding new massive modes within the low-energy effective theory, which we refer to as quasihydrodynamics. Examples of quasihydrodynamics are numerous, with the most transparent among them hydrodynamics with weakly broken translational symmetry. Here, we show how a number of other theories, normally not thought of in this context, can also be understood within a broader framework of quasihydrodynamics: in particular, the M\"uller-Israel-Stewart theory and magnetohydrodynamics coupled to dynamical electric fields. While historical formulations of quasihydrodynamic theories were typically highly phenomenological, here, we develop a holographic formalism to systematically derive such theories from a (microscopic) dual gravitational description. Beyond laying out a general holographic algorithm, we show how the M\"uller-Israel-Stewart theory can be understood from a dual higher-derivative gravity theory and magnetohydrodynamics from a dual theory with two-form bulk fields. In the latter example, this allows us to unambiguously demonstrate the existence of dynamical photons in the holographic description of magnetohydrodynamics., Comment: 65 pages, 5 figures. v2: minor changes, more references; v3: published version

It has long been believed that dissipative time scales $\tau$ obey a "Planckian" bound $\tau \gtrsim \frac{\hbar}{k_{\mathrm{B}}T}$ in strongly coupled quantum systems. Despite much circumstantial evidence, however, there is no known $\tau$ for which this bound is universal. Here we define operator size at finite temperature, and conjecture such a $\tau$: the time scale over which small operators become large. All known many-body theories are consistent with this conjecture. This proposed bound explains why previously conjectured Planckian bounds do not always apply to weakly coupled theories, and how Planckian time scales can be relevant to both transport and chaos., Comment: 8+14 pages; 1+0 figures; v2: major revisions, published version

Given a quantum many-body system with few-body interactions, how rapidly can quantum information be hidden during time evolution? The fast scrambling conjecture is that the time to thoroughly mix information among N degrees of freedom grows at least logarithmically in N. We derive this inequality for generic quantum systems at infinite temperature, bounding the scrambling time by a finite decay time of local quantum correlations at late times. Using Lieb-Robinson bounds, generalized Sachdev-Ye-Kitaev models, and random unitary circuits, we propose that a logarithmic scrambling time can be achieved in most quantum systems with sparse connectivity. These models also elucidate how quantum chaos is not universally related to scrambling: we construct random few-body circuits with infinite Lyapunov exponent but logarithmic scrambling time. We discuss analogies between quantum models on graphs and quantum black holes, and suggest methods to experimentally study scrambling with as many as 100 sparsely-connected quantum degrees of freedom., Comment: 11+24 pages; 1+3 figures. v2: minor revisions, added references. v3: many revisions to improve presentation

We present the theory of thermoelectric transport in metals with long-lived quasiparticles, carefully addressing the interplay of electron-electron scattering as well as electron-impurity scattering, but neglecting electron-phonon scattering. In Fermi liquids with a large Fermi surface and weak electron-impurity scattering, we provide universal and simple formulas for the behavior of the thermoelectric conductivities across the ballistic-to-hydrodynamic crossover. In this regime, the electrical conductivity is relatively unchanged by hydrodynamic effects. In contrast, the thermal conductivity can be parametrically smaller than predicted by the Wiedemann-Franz law. A less severe violation of the Mott law arises. We quantitatively compare the violations of the Wiedemann-Franz law arising from (i) momentum-conserving electron-electron scattering in the collision integral, (ii) hydrodynamic modifications of the electron-impurity scattering rate, and (iii) thermal broadening of the Fermi surface, and show that (i) is the largest. We present simple formulas for electrical and thermal magnetoconductivity across the ballistic-to-hydrodynamic limit, along with a more complicated formula for the thermoelectric magnetoconductivity. In a finite magnetic field, the Lorenz number may be smaller or larger than predicted by the Wiedemann-Franz law, and the crossover between these behaviors is a clear prediction for experiments. The arbitrarily strong violation of the Wiedemann-Franz law found in our work arises entirely from electron-electron interaction effects within the Fermi liquid paradigm, and does not imply any non-Fermi liquid behavior. We predict clear experimental signatures of bulk hydrodynamics in high-mobility 2D GaAs semiconductor structures, where failure of the Wiedemann-Franz law should persist down to very low temperatures in high-quality, low-density samples., Comment: 21+8 pages

We numerically solve semiclassical kinetic equations and compute the growth rate of the Dyakonov-Shur instability of a two-dimensional Fermi liquid in a finite length cavity. When electron-electron scattering is fast, we observe the well-understood hydrodynamic instability, and its disappearance due to viscous dissipation. When electron-electron scattering is negligible, we find that the instability re-emerges for certain boundary conditions, but not for others. We discuss the implications of these findings for experiments., Comment: 7+10 pages, 4+0 figures; v2: published version

Using an analytically tractable kinetic model of a two dimensional Fermi liquid of electrons, we characterize the crossovers between zero sound, first sound and plasmons. For experimentally realized Fermi liquids in a hydrodynamic limit, both zero and first sound waves are essentially replaced by plasmons. The plasmon dispersion relation is robust against hydrodynamic effects, up to acquiring the viscous-limited decay rate of a first sound wave in the hydrodynamic limit. We discuss implications for experiments in clean two dimensional electron gases., Comment: 14 pages. v2: published version

We present the theory of quasiparticle transport in perturbatively small inhomogeneous magnetic fields across the ballistic-to-hydrodynamic crossover. In the hydrodynamic limit, the resistivity $\rho$ generically grows proportionally to the rate of momentum-conserving electron-electron collisions at large enough temperatures $T$. In particular, the resulting flow of electrons provides a simple scenario where viscous effects suppress conductance below the ballistic value. This new mechanism for $\rho\propto T^2$ resistivity in a Fermi liquid may describe low $T$ transport in single-band $\mathrm{SrTiO}_3$., Comment: v2: published version. 7+8 pages, 1+0 figures

Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective motion of electrons in solid-state systems, including graphene. We present a review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene, written for physicists from diverse communities. We begin by discussing the "phase diagram" of graphene, and the inevitable presence of impurities and phonons in experimental systems. We derive hydrodynamics, both from a phenomenological perspective and using kinetic theory. We then describe how hydrodynamic electron flow is visible in electronic transport measurements. Although we focus on graphene in this review, the broader framework naturally generalizes to other materials. We assume only basic knowledge of condensed matter physics, and no prior knowledge of hydrodynamics., Comment: Review article. 79 pages, 21 figures. v2: published version

Is the hydrodynamics of an interacting many-body system fundamentally limited by basic principles of quantum mechanics? Starting with the conjecture that viscosity is at least as large as entropy density (as measured in fundamental units), there has been a long search for a precise answer to this question. In this work, we identify a simple relationship between hydrodynamics and many-body quantum chaos in a broad class of experimentally realizable systems. Consistency with the quantum butterfly effect leads to upper bounds on the speed of sound and diffusion constants of hydrodynamics. These bounds link two very different theories of quantum many-body dynamics, clarify the relationship between classical hydrodynamics and quantum information loss, and provide a simple way to constrain theories of thermalization and quantum chaos in experiments., Comment: 7 + 19 pages, 1+0 figures. v2: revised presentation of key results, added small calculations on SYK chains

At zero temperature, the charge current operator appears to be conserved, within linear response, in certain holographic probe brane models of strange metals. At small but finite temperature, we analytically show that the weak non-conservation of this current leads to both a collective "zero sound" mode and a Drude peak in the electrical conductivity. This simultaneously resolves two outstanding puzzles about probe brane theories. The nonlinear dynamics of the current operator itself appears qualitatively different., Comment: 11 pages

We study the spread of R\'enyi entropy between two halves of a Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermofield double (TFD) state. The SYK chain model is a model of chaotic many-body systems, which describes a one-dimensional lattice of Majorana fermions, with spatially local random quartic interaction. We find that for integer R\'enyi index $n>1$, the R\'enyi entanglement entropy saturates at a parametrically smaller value than expected. This implies that the TFD state of the SYK chain does not rapidly thermalize, despite being maximally chaotic: instead, it rapidly approaches a prethermal state. We compare our results to the signatures of thermalization observed in other quenches in the SYK model, and to intuition from nearly-$\mathrm{AdS}_2$ gravity., Comment: 1+46 pages, 11 figures

The interplay between electronic interactions and disorder is neglected in the conventional Boltzmann theory of transport, yet can play an essential role in determining the resistivity of unconventional metals. When quasiparticles are long-lived, one can account for these intertwined effects by solving spatially inhomogeneous Boltzmann equations. Assuming smooth disorder and neglecting umklapp scattering, we solve these inhomogeneous kinetic equations and compute the electrical resistivity across the ballistic-to-hydrodynamic transition. An important consequence of electron-electron interactions is the modification of the momentum relaxation time; this effect is ignored in the conventional theory. We characterize precisely when interactions enhance the momentum scattering rate, and when they decrease it. Our approach unifies existing semiclassical theories of transport and reveals novel transport mechanisms. In particular, we explain how the resistivity can be proportional to the rate of momentum-conserving collisions. We compare this result with existing transport mysteries, including the disorder-independent $T^2$ resistivity of many Fermi liquids, and the linear-in-$T$ "Planckian-limited" resistivity of many strange metals., Comment: 1+37+15 pages; 9 figures. v2: minor changes. v3: published version