scholarly journals Finding self-similar behavior in quantum many-body dynamics via persistent homology

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Daniel Spitz ◽  
Jürgen Berges ◽  
Markus Oberthaler ◽  
Anna Wienhard
Keyword(s):  
Persistent Homology ◽  
Geometric Analysis ◽  
Point Clouds ◽  
Statistical Simulation ◽  
Topological Data Analysis ◽  
Many Body ◽  
Scaling Exponents ◽  
Dynamical Scaling ◽  
Body Dynamics ◽  
Self Similar

Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a classical-statistical simulation of a two-dimensional Bose gas far from equilibrium. We discover a continuous spectrum of dynamical scaling exponents, which provides a refined classification of nonequilibrium self-similar phenomena. A possible explanation of the underlying processes is provided in terms of mixing strong wave turbulence and anomalous vortex kinetics components in point clouds. We find that the persistent homology scaling exponents are inherently linked to the geometry of the system, as the derivation of a packing relation reveals. The approach opens new ways of analyzing quantum many-body dynamics in terms of robust topological structures beyond standard field theoretic techniques.

Many body dynamics

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Statistical Mechanics ◽  
Body Problem ◽  
Many Body ◽  
Complex Objects ◽  
Constrained Dynamics ◽  
Gravitational Systems ◽  
Body Dynamics ◽  
System Temperature ◽  
Speed Up ◽  
Gravitating Systems

Specialized techniques for solving the classical many-body problem are explored in the context of simple gases, more complicated gases, and gravitating systems. The chapter starts with a brief review of some important concepts from statistical mechanics and then introduces the classic Verlet method for obtaining the dynamics of many simple particles. The practical problems of setting the system temperature and measuring observables are discussed. The issues associated with simulating systems of complex objects form the next topic. One approach is to implement constrained dynamics, which can be done elegantly with iterative methods. Gravitational systems are introduced next with stress on techniques that are applicable to systems of different scales and to problems with long range forces. A description of the recursive Barnes-Hut algorithm and particle-mesh methods that speed up force calculations close out the chapter.

scholarly journals Periodically refreshed baths to simulate open quantum many-body dynamics

2021 ◽  
Vol 104 (4) ◽  
Author(s):  
Archak Purkayastha ◽  
Giacomo Guarnieri ◽  
Steve Campbell ◽  
Javier Prior ◽  
John Goold
Keyword(s):  
Many Body ◽  
Open Quantum ◽  
Body Dynamics

scholarly journals Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Dominik Hahn ◽  
Juan-Diego Urbina ◽  
Klaus Richter ◽  
Rémy Dubertrand ◽  
S. L. Sondhi
Keyword(s):  
Many Body ◽  
Strongly Nonlinear ◽  
Nonlinear Lattices ◽  
Body Dynamics

scholarly journals Classification of apatite structures via topological data analysis: a framework for a ‘Materials Barcode’ representation of structure maps

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Scott Broderick ◽  
Ruhil Dongol ◽  
Tianmu Zhang ◽  
Krishna Rajan
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Crystal Chemistry ◽  
Persistent Homology ◽  
Hierarchical Classification ◽  
Topological Data Analysis ◽  
Learning Tool ◽  
Coordination Polyhedra ◽  
Machine Learning Tool ◽  
Topological Data

AbstractThis paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.

Stacking angle dependent multiple excitonic resonances in bilayer tungsten diselenide

Nanophotonics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 3881-3887
Author(s):  
Ankit Arora ◽  
Pramoda K. Nayak ◽  
Tejendra Dixit ◽  
Kolla Lakshmi Ganapathi ◽  
Ananth Krishnan ◽  
...  
Keyword(s):  
Chemical Vapour ◽  
Optoelectronic Devices ◽  
Interlayer Coupling ◽  
Higher Order ◽  
Doping Effect ◽  
Many Body ◽  
Si Substrate ◽  
Tungsten Diselenide ◽  
Body Dynamics ◽  
Insight Into

AbstractWe report on multiple excitonic resonances in bilayer tungsten diselenide (BL-WSe2) stacked at different angles and demonstrate the use of the stacking angle to control the occurrence of these excitations. BL-WSe2 with different stacking angles were fabricated by stacking chemical vapour deposited monolayers and analysed using photoluminescence measurements in the temperature range 300–100 K. At reduced temperatures, several excitonic features were observed and the occurrences of these exitonic resonances were found to be stacking angle dependent. Our results indicate that by controlling the stacking angle, it is possible to excite or quench higher order excitations to tune the excitonic flux in optoelectronic devices. We attribute the presence/absence of multiple higher order excitons to the strength of interlayer coupling and doping effect from SiO2/Si substrate. Understanding interlayer excitations will help in engineering excitonic devices and give an insight into the physics of many-body dynamics.

scholarly journals Quantum Many-Body Dynamics of Driven-Dissipative Rydberg Polaritons

2020 ◽  
Vol 125 (26) ◽  
Author(s):  
Tim Pistorius ◽  
Javad Kazemi ◽  
Hendrik Weimer
Keyword(s):  
Many Body ◽  
Body Dynamics

scholarly journals A topological characterization of DNA sequences based on chaos geometry and persistent homology

2021 ◽  
Author(s):  
Dong Quan Ngoc Nguyen ◽  
Phuong Dong Tan Le ◽  
Lin Xing ◽  
Lizhen Lin
Keyword(s):  
Dna Sequences ◽  
Algebraic Topology ◽  
Influenza A ◽  
Graphical Representation ◽  
Dimensional Space ◽  
Persistent Homology ◽  
Point Clouds ◽  
Influenza A Viruses ◽  
Topological Characterization ◽  
Topological Features

AbstractMethods for analyzing similarities among DNA sequences play a fundamental role in computational biology, and have a variety of applications in public health, and in the field of genetics. In this paper, a novel geometric and topological method for analyzing similarities among DNA sequences is developed, based on persistent homology from algebraic topology, in combination with chaos geometry in 4-dimensional space as a graphical representation of DNA sequences. Our topological framework for DNA similarity analysis is general, alignment-free, and can deal with DNA sequences of various lengths, while proving first-of-the-kind visualization features for visual inspection of DNA sequences directly, based on topological features of point clouds that represent DNA sequences. As an application, we test our methods on three datasets including genome sequences of different types of Hantavirus, Influenza A viruses, and Human Papillomavirus.

scholarly journals Topological Segmentation of Time-Varying Functional Connectivity Highlights the Role of Preferred Cortical Circuits

2020 ◽  
Author(s):  
Jacob Billings ◽  
Manish Saggar ◽  
Shella Keilholz ◽  
Giovanni Petri
Keyword(s):  
Functional Connectivity ◽  
Brain Function ◽  
Persistent Homology ◽  
Brain Regions ◽  
Topological Data Analysis ◽  
Time Varying ◽  
Imaging Data ◽  
Experimental Conditions ◽  
Common Time ◽  
Brain Imaging Data

Functional connectivity (FC) and its time-varying analogue (TVFC) leverage brain imaging data to interpret brain function as patterns of coordinating activity among brain regions. While many questions remain regarding the organizing principles through which brain function emerges from multi-regional interactions, advances in the mathematics of Topological Data Analysis (TDA) may provide new insights into the brain’s spontaneous self-organization. One tool from TDA, “persistent homology”, observes the occurrence and the persistence of n-dimensional holes presented in the metric space over a dataset. The occurrence of n-dimensional holes within the TVFC point cloud may denote conserved and preferred routes of information flow among brain regions. In the present study, we compare the use of persistence homology versus more traditional TVFC metrics at the task of segmenting brain states that differ across a common time-series of experimental conditions. We find that the structures identified by persistence homology more accurately segment the stimuli, more accurately segment volunteer performance during experimentally defined tasks, and generalize better across volunteers. Finally, we present empirical and theoretical observations that interpret brain function as a topological space defined by cyclic and interlinked motifs among distributed brain regions, especially, the attention networks.

scholarly journals Topological data analysis for true step detection in periodic piecewise constant signals

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180027 ◽  
Author(s):  
Firas A. Khasawneh ◽  
Elizabeth Munch
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Future Research ◽  
Accurate Identification ◽  
Piecewise Constant ◽  
Higher Dimensional ◽  
Powerful Approach ◽  
Hadamard Transforms ◽  
Topological Data

This paper introduces a simple yet powerful approach based on topological data analysis for detecting true steps in a periodic, piecewise constant (PWC) signal. The signal is a two-state square wave with randomly varying in-between-pulse spacing, subject to spurious steps at the rising or falling edges which we call digital ringing. We use persistent homology to derive mathematical guarantees for the resulting change detection which enables accurate identification and counting of the true pulses. The approach is tested using both synthetic and experimental data obtained using an engine lathe instrumented with a laser tachometer. The described algorithm enables accurate and automatic calculations of the spindle speed without any choice of parameters. The results are compared with the frequency and sequency methods of the Fourier and Walsh–Hadamard transforms, respectively. Both our approach and the Fourier analysis yield comparable results for pulses with regular spacing and digital ringing while the latter causes large errors using the Walsh–Hadamard method. Further, the described approach significantly outperforms the frequency/sequency analyses when the spacing between the peaks is varied. We discuss generalizing the approach to higher dimensional PWC signals, although using this extension remains an interesting question for future research.

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