Deep Quantum Geometry of Matrices

Han, Xizhi; Hartnoll, Sean A.

doi:10.1103/physrevx.10.011069

Cited by 47 publications

(65 citation statements)

References 71 publications

(119 reference statements)

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“…It therefore behooves us to find methods suitable for studying the zero temperature quantum states of multimatrix quantum mechanics directly. Progress was made recently in this direction by using a neural network variational wave function [17]. Here we describe a different approach.…”

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confidence: 99%

Bootstrapping Matrix Quantum Mechanics

2020

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Large N matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a "bootstrap" methodology. In this approach, operator expectation values are related by symmetries-such as time translation and SUðNÞ gauge invariance-and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional quantum anharmonic oscillator. We then reproduce the known solution of large N single matrix quantum mechanics. Finally, we present new results on the ground state of large N two matrix quantum mechanics.

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confidence: 99%

Bootstrapping Matrix Quantum Mechanics

2020

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“…Nanoparticles with sizes less than 10 nm are rapidly cleared by renal excretion due to the renal average filtration pore of 10 nm, while nanoparticles with sizes over 100 nm may be recognized by macrophages and cleared by the mononuclear phagocyte system. 38 Nanoparticle with sizes from 10 to 100 nm have demonstrated enhanced uptake in the abnormal vasculature of tumors. 39 The hydrodynamic Hyp-NP size of 37.3 nm is well within the size range known to passively accumulate in tumor tissue through the enhanced permeability and retention (EPR) effect and generate a longer circulation time for biological function, 38 which may putatively enable greater hypericin localization in necrotic tumor areas.…”

Section: Discussionmentioning

confidence: 99%

Biodegradable Hypericin-Containing Nanoparticles for Necrosis Targeting and Fluorescence Imaging

Han

Taratula

et al. 2020

Mol. Pharmaceutics

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Necrosis targeting and imaging has significant implications for evaluating tumor growth, therapeutic response, and delivery of therapeutics to peri-necrotic tumor zones. Hypericin is a hydrophobic molecule with high necrosis affinity and fluorescence imaging properties. To date, the safe and effective delivery of hypericin to areas of necrosis in vivo remains a challenge due to its incompatible biophysical properties. To address this issue, we have developed a biodegradable nanoparticle (Hyp-NP) for delivery of hypericin to tumors for necrosis targeting and fluorescence imaging. The nanoparticle was developed using methoxy poly(ethylene glycol)-b -poly(εcaprolactone) (PEG-PCL) and hypericin by a modified solvent evaporation technique. The size of Hyp-NP was 19.0±1.8 nm from cryo-TEM and 37.3±0.7 nm from dynamic light scattering analysis with a polydispersity index of 0.15±0.01. The encapsulation efficiency of hypericin was 95.05% w/w by UV-vis absorption. After storage for 30 days, 91.4% hypericin was retained in Hyp-NP with nearly no change in hydrodynamic size, representing nanoparticle stability. In an ovarian cancer cell line, Hyp-NP demonstrated cellular internalization with intracellular cytoplasmic localization and preserved fluorescence and necrosis affinity. In a mouse subcutaneous tumor model, tumor accumulation was noted at 8 h post-injection, with nearcomplete clearance at 96 h post-injection. Hyp-NP was shown to be tightly localized within necrotic tumor zones. Histologic analysis of harvested organs demonstrated no gross abnormalities, and in vitro, no hemolysis was observed. This proof-of-concept study demonstrates the potential clinical applications of Hyp-NP for necrosis targeting.

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“…Here, the choice b k = (J) k , corresponding to the replacement J i → Jn i seems natural. 14 This connection was also explored recently in[26].…”

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confidence: 91%

“…The recent work [26] that appeared while this paper was in preparation also considers the emergence of geometry and the connection between areas and entropies in matrix models (see also [27][28][29][30][31] for related considerations). For a discussion on entanglement and its potential dual in the c = 1 model, see [32,33].…”

Section: Introductionmentioning

confidence: 99%

Areas and entropies in BFSS/gravity duality

et al. 2020

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The BFSS matrix model provides an example of gauge-theory / gravity duality where the gauge theory is a model of ordinary quantum mechanics with no spatial subsystems. If there exists a general connection between areas and entropies in this model similar to the Ryu-Takayanagi formula, the entropies must be more general than the usual subsystem entanglement entropies. In this note, we first investigate the extremal surfaces in the geometries dual to the BFSS model at zero and finite temperature. We describe a method to associate regulated areas to these surfaces and calculate the areas explicitly for a family of surfaces preserving SO(8) symmetry, both at zero and finite temperature. We then discuss possible entropic quantities in the matrix model that could be dual to these regulated areas.

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Deep Quantum Geometry of Matrices

Cited by 47 publications

References 71 publications

Bootstrapping Matrix Quantum Mechanics

Bootstrapping Matrix Quantum Mechanics

Biodegradable Hypericin-Containing Nanoparticles for Necrosis Targeting and Fluorescence Imaging

Areas and entropies in BFSS/gravity duality

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