Thermalization and chaos in a 1+1d QFT

We study aspects of chaos and thermodynamics at strong coupling in a scalar model using LCT numerical methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak coupling, though the bulk of states satisfy RMT statistics, we find several scar states as well. We then use these chaotic states to compute the equation of state of the model, obtaining results consistent with Conformal Field Theory (CFT) expectations at temperatures above the scale of relevant interactions. We also test the Eigenstate Thermalization Hypothesis by computing the expectation value of local operators in eigenstates, and check that their behavior is consistent with thermal CFT values at high temperatures. Finally, we compute the Spectral Form Factor (SFF), which has the expected behavior associated with the equation of state at short times and chaos at long times. We also propose a new technique for extracting the connected part of the SFF without the need of disorder averaging by using different symmetry sectors.Comment: 16 pages, 17 figure

Radio-frequency ablation as primary management of well-tolerated sustained monomorphic ventricular tachycardia in patients with structural heart disease and left ventricular ejection fraction over 30%.

AIMS: Patients with well-tolerated sustained monomorphic ventricular tachycardia (SMVT) and left ventricular ejection fraction (LVEF) over 30% may benefit from a primary strategy of VT ablation without immediate need for a 'back-up' implantable cardioverter-defibrillator (ICD). METHODS AND RESULTS: One hundred and sixty-six patients with structural heart disease (SHD), LVEF over 30%, and well-tolerated SMVT (no syncope) underwent primary radiofrequency ablation without ICD implantation at eight European centres. There were 139 men (84%) with mean age 62 ± 15 years and mean LVEF of 50 ± 10%. Fifty-five percent had ischaemic heart disease, 19% non-ischaemic cardiomyopathy, and 12% arrhythmogenic right ventricular cardiomyopathy. Three hundred seventy-eight similar patients were implanted with an ICD during the same period and serve as a control group. All-cause mortality was 12% (20 patients) over a mean follow-up of 32 ± 27 months. Eight patients (40%) died from non-cardiovascular causes, 8 (40%) died from non-arrhythmic cardiovascular causes, and 4 (20%) died suddenly (SD) (2.4% of the population). All-cause mortality in the control group was 12%. Twenty-seven patients (16%) had a non-fatal recurrence at a median time of 5 months, while 20 patients (12%) required an ICD, of whom 4 died (20%). CONCLUSION: Patients with well-tolerated SMVT, SHD, and LVEF > 30% undergoing primary VT ablation without a back-up ICD had a very low rate of arrhythmic death and recurrences were generally non-fatal. These data would support a randomized clinical trial comparing this approach with others incorporating implantation of an ICD as a primary strategy

Essentially stable matchings

We propose a solution to the conflict between fairness and efficiency in one-sided matching markets. A matching is essentially stable if any priority-based claim initiates a chain of reassignments that results in the initial claimant losing the object. We show that an essentially stable and Pareto efficient matching always exists and that Kesten's (2010) EADA mechanism always selects one while other common Pareto efficient mechanisms do not. Additionally, we show that there exists a student-pessimal essentially stable matching and that the Rural Hospital Theorem extends to essential stability. Finally, we analyze the incentive properties of essentially stable mechanisms

Comparative statics for size-dependent discounts in matching markets

We prove a natural comparative static for many-to-many matching markets in which agents’ choice functions exhibit size-dependent discounts: reducing the extent to which some agent discounts additional partners leads to improved outcomes for the agents on the other side of the market, and worsened outcomes for the agents on the same side of the market. Our argument draws upon recently developed methods bringing tools from choice theory into matching