On thermalization in the SYK and supersymmetric SYK models

The eigenstate thermalization hypothesis is a compelling conjecture which strives to explain the apparent thermal behavior of generic observables in closed quantum systems. Although we are far from a complete analytic understanding, quantum chaos is often seen as a strong indication that the ansatz holds true. In this paper, we address the thermalization of energy eigenstates in the Sachdev-Ye-Kitaev model, a maximally chaotic model of strongly-interacting Majorana fermions. We numerically investigate eigenstate thermalization for specific few-body operators in the original SYK model as well as its $\mathcal{N}=1$ supersymmetric extension and find evidence that these models satisfy ETH. We discuss the implications of ETH for a gravitational dual and the quantum information-theoretic properties of SYK it suggests.Comment: Published versio

David

Hunter Jones is majoring in English with a concentration in creative writing. In his free time, he enjoys practicing photography and videography

Chaos, Complexity, and Random Matrices

Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an $\mathcal{O}(1)$ scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce $k$-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate $k$-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.Comment: 61 pages, 14 figures; v2: references added, typos fixe

Sanctions for E-Discovery Violations: By the Numbers

This Article reviews our comprehensive survey of written opinions from cases in federal courts prior to January 1, 2010, involving motions for sanctions relating to the discovery of electronically stored information (ESI) We analyzed each case for various factors, including date, court, type of case, sanctioning authority, sanctioned party, sanctioned misconduct, sanction type, sanctions to counsel, if any, and the protections provided from sanctions by Federal Rule of Civil Procedure 37(e) The survey identified 401 sanction cases and 230 sanction awards and showed that sanction motions and awards have increased over time, particularly in the last five years Sanctions against counsel are rare but are also increasing Sanction motions have been filed in all types of cases and in courts across the country Failure to produce ESI is the most common basis for sanctions Courts have used a variety of different rules, statutes, and powers to sanction parties for e-disco very violations, including Rule 37 and the inherent power of the court, and courts impose many different sanction types on e-discovery violators, including the severe sanctions of dismissal, default Judgment, adverse jury instructions, and sizeable monetary awards Rule 37(e) has not provided broad protection from such sanction

Sanctions for E-Discovery Violations: By the Numbers

This Article reviews our comprehensive survey of written opinions from cases in federal courts prior to January 1, 2010, involving motions for sanctions relating to the discovery of electronically stored information (ESI) We analyzed each case for various factors, including date, court, type of case, sanctioning authority, sanctioned party, sanctioned misconduct, sanction type, sanctions to counsel, if any, and the protections provided from sanctions by Federal Rule of Civil Procedure 37(e) The survey identified 401 sanction cases and 230 sanction awards and showed that sanction motions and awards have increased over time, particularly in the last five years Sanctions against counsel are rare but are also increasing Sanction motions have been filed in all types of cases and in courts across the country Failure to produce ESI is the most common basis for sanctions Courts have used a variety of different rules, statutes, and powers to sanction parties for e-disco very violations, including Rule 37 and the inherent power of the court, and courts impose many different sanction types on e-discovery violators, including the severe sanctions of dismissal, default Judgment, adverse jury instructions, and sizeable monetary awards Rule 37(e) has not provided broad protection from such sanction

Potential Consequences of Intra-Regional Trade in Short-Term Food Security Crises in Southeastern Africa

A report prepared by Michigan State University for the World Bank under contract No. 7144132, Strengthening Food Security in Sub-Saharan Africa through Trade Liberalization and Regional IntegrationAfrica, trade, emergency, Food Security and Poverty, International Relations/Trade, Q13,

Facing up to the challenge of behavioural observation in infant hearing assessment

The ability to assess detection and discrimination of speech by infants has proved elusive. Dr Iain Jackson and colleagues discuss how new technologies and fresh approaches might offer valuable insight into young infants’ behavioural responses to sound

Characterization of Stream Quality of Five Ouachita River Tributaries Utilizing Macrobenthic Species and Fish Populations

The Ouachita River originates in west-central Arkansas and exits the state in south-central Arkansas near El Dorado. There are many tributaries that make up the Ouachita River through its Arkansas journey. Five of these tributaries are located in Clark County and were selected for this research. Basic in situ water quality parameters were measured and the riparian zone was characterized at each sample site. The five streams selected were Decieper/Little Deceiper Creek, Mill Creek, DeRoche Creek, Saline Bayou, and Tupelo Creek. Macrobenthic and fish surveys were conducted at two sites (upper and lower) on each creek except Saline Bayou and Tupelo Creek which included only one site each. Streams will be characterized using the tolerant and intolerant species. Potential impacts of these streams include runoff from agriculture, municipal runoff from the city of Arkadelphia, and miscellaneous anthropomorphic sources from town. The presence of intolerant species indicates less impact while finding only tolerant species indicates potential disturbance that warrants further investigation