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Kontsevich-Segal Criterion in the No-Boundary State Constrains Inflation.
Phys Rev Lett
November 2023
Institute for Theoretical Physics, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium.
We show that the Kontsevich-Segal (KS) criterion, applied to the complex saddles that specify the semiclassical no-boundary wave function, acts as a selection mechanism on inflationary scalar field potentials. Completing the observable phase of slow-roll inflation with a no-boundary origin, the KS criterion effectively bounds the tensor-to-scalar ratio of cosmic microwave background fluctuations to be less than 0.08, in line with current observations.
View Article and Find Full Text PDFRogue wave formation scenarios for the focusing nonlinear Schrödinger equation with parabolic-profile initial data on a compact support.
Phys Rev E
August 2023
Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom.
We study the (1+1) focusing nonlinear Schrödinger equation for an initial condition with compactly supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blowup in finite time, generalizing a result by Talanov et al. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semiclassical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time.
View Article and Find Full Text PDFAutomatic Detection of Epileptiform EEG Discharges based on the Semi-Classical Signal Analysis (SCSA) method.
Annu Int Conf IEEE Eng Med Biol Soc
November 2021
In this paper we utilize a signal processing tool, which can help physicians and clinical researchers to automate the process of EEG epileptiform spike detection. The semi-classical signal analysis method (SCSA) is a data-driven signal decomposition method developed for pulse-shaped signal characterization. We present an algorithm framework to process and extract features from the patient's EEG recording by deriving the mathematical motivation behind SCSA and quantifying existing spike diagnosis criterion with it.
View Article and Find Full Text PDFMachine learning for vibrational spectroscopy via divide-and-conquer semiclassical initial value representation molecular dynamics with application to N-methylacetamide.
J Chem Phys
November 2020
Dipartimento di Chimica, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy, https://sites.unimi.it/ceotto/.
A machine learning algorithm for partitioning the nuclear vibrational space into subspaces is introduced. The subdivision criterion is based on Liouville's theorem, i.e.
View Article and Find Full Text PDFThe Fluctuation-Dissipation Theorem as a Diagnosis and Cure for Zero-Point Energy Leakage in Quantum Thermal Bath Simulations.
J Chem Theory Comput
May 2019
Sorbonne Université, CNRS - UMR 7588 , Institut des NanoSciences de Paris, INSP , 4 Place Jussieu , F-75005 Paris , France.
Quantum thermal bath (QTB) simulations reproduce statistical nuclear quantum effects via a Langevin equation with a colored random force. Although this approach has proven efficient for a variety of chemical and condensed-matter problems, the QTB, as many other semiclassical methods, suffers from zero-point energy leakage (ZPEL). The absence of a reliable criterion to quantify the ZPEL without resorting to demanding comparisons with path integral-based calculations has so far hindered the use of the QTB for the simulation of real systems.
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