Andrew Lucas

Ising formulations of many NP problems

We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karps 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.

Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene

Electrons that flow like a fluid Electrons inside a conductor are often described as flowing in response to an electric field. This flow rarely resembles anything like the familiar flow of water through a pipe, but three groups describe counterexamples (see the Perspective by Zaanen). Moll et al. found that the viscosity of the electron fluid in thin wires of PdCoO2 had a major effect on the flow, much like what happens in regular fluids. Bandurin et al. found evidence in graphene of electron whirlpools similar to those formed by viscous fluid flowing through a small opening. Finally, Crossno et al. observed a huge increase of thermal transport in graphene, a signature of so-called Dirac fluids. Science, this issue p. 1061, 1055, 1058; see also p. 1026 Thermal transport is enhanced near the charge-neutrality point in graphene, owing to the dominant interelectron interactions. [Also see Perspective by Zaanen] Interactions between particles in quantum many-body systems can lead to collective behavior described by hydrodynamics. One such system is the electron-hole plasma in graphene near the charge-neutrality point, which can form a strongly coupled Dirac fluid. This charge-neutral plasma of quasi-relativistic fermions is expected to exhibit a substantial enhancement of the thermal conductivity, thanks to decoupling of charge and heat currents within hydrodynamics. Employing high-sensitivity Johnson noise thermometry, we report an order of magnitude increase in the thermal conductivity and the breakdown of the Wiedemann-Franz law in the thermally populated charge-neutral plasma in graphene. This result is a signature of the Dirac fluid and constitutes direct evidence of collective motion in a quantum electronic fluid.

Absence of Disorder-Driven Metal-Insulator Transitions in Simple Holographic Models.

We study electrical transport in a strongly coupled strange metal in two spatial dimensions at finite temperature and charge density, holographically dual to the Einstein-Maxwell theory in an asymptotically four-dimensional anti-de Sitter space spacetime, with arbitrary spatial inhomogeneity, up to mild assumptions including emergent isotropy. In condensed matter, these are candidate models for exotic strange metals without long-lived quasiparticles. We prove that the electrical conductivity is bounded from below by a universal minimal conductance: the quantum critical conductivity of a clean, charge-neutral plasma. Beyond nonperturbatively justifying mean-field approximations to disorder, our work demonstrates the practicality of new hydrodynamic insight into holographic transport.

In vivo evidence of differential impact of typical and atypical antipsychotics on intracortical myelin in adults with schizophrenia

CONTEXT Imaging and post-mortem studies provide converging evidence that patients with schizophrenia have a dysregulated developmental trajectory of frontal lobe myelination. The hypothesis that typical and atypical medications may differentially impact brain myelination in adults with schizophrenia was previously assessed with inversion recovery (IR) images. Increased white matter (WM) volume suggestive of increased myelination was detected in the patient group treated with an atypical antipsychotic compared to a typical one. OBJECTIVE In a follow-up reanalysis of MRI images from the original study, we used a novel method to assess whether the difference in WM volumes could be caused by a differential effect of medications on the intracortical myelination process. DESIGN, SETTING, AND PARTICIPANTS Two different male cohorts of healthy controls ranging in age from 18-35 years were compared to cohorts of subjects with schizophrenia who were treated with either oral risperidone (Ris) or fluphenazine decanoate (Fd). MAIN OUTCOME MEASURE A novel MRI method that combines the distinct tissue contrasts provided by IR and proton density (PD) images was used to estimate intracortical myelin (ICM) volume. RESULTS When compared with their pooled healthy control comparison group, the two groups of schizophrenic patients differed in the frontal lobe ICM measure with the Ris group having significantly higher volume. CONCLUSIONS The data suggest that in adults with schizophrenia antipsychotic treatment choice may be specifically and differentially impacting later-myelinating intracortical circuitry. In vivo MRI can be used to dissect subtle differences in brain tissue characteristics and thus help clarify the effect of pharmacologic treatments on developmental and pathologic processes.

Conformal field theories in a periodic potential: results from holography and field theory

We study ( 2 + 1 )-dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction x with zero average: μ ( x ) = V cos ( k x ) . The dynamics of such theories depends only on the dimensionless ratio V / k , and we expect that they flow in the infrared to new CFTs whose universality class changes as a function of V / k . We compute the frequency-dependent conductivity of strongly coupled CFTs using holography of the Einstein-Maxwell theory in four-dimensional anti–de Sitter space. We compare the results with the corresponding computation of weakly coupled CFTs, perturbed away from the CFT of free, massless Dirac fermions (which describes graphene at low energies). We find that the results of the two computations have significant qualitative similarities. However, differences do appear in the vicinities of an infinite discrete set of values of V / k : the universality class of the infrared CFT changes at these values in the weakly coupled theory, by the emergence of new zero modes of Dirac fermions which are remnants of local Fermi surfaces. The infrared theory changes continuously in holography, and the classical gravitational theory does not capture the physics of the discrete transition points between the infrared CFTs. We briefly note implications for a nonzero average chemical potential.

Memory matrix theory of magnetotransport in strange metals

We model strange metals as quantum liquids without quasiparticle excitations, but with slow momentum relaxation, and with slow diffusive dynamics of a conserved charge and energy. General expressions are obtained for electrical, thermal and thermoelectric transport in the presence of an applied magnetic field using the memory matrix formalism. In the appropriate limits, our expressions agree with previous hydrodynamic and holographic results. We discuss the relationship of such results to thermoelectric and Hall transport measurements in the strange metal phase of the hole-doped cuprates.

Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder

We compute the direct current resistivity of a scale-invariant,

Conductivity of a strange metal: from holography to memory functions

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Hydrodynamic transport in strongly coupled disordered quantum field theories

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Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains

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