Related papers: The Physical Basis of Integrable Spin Models
Studies of integrable quantum many-body systems have a long history with an impressive record of success. However, surprisingly enough, an unambiguous definition of quantum integrability remains a matter of an ongoing debate. We contribute…
In a previous paper, we introduce a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter. Here the main purpose is to give explicit solutions of several factorization…
Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or…
Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact…
This paper presents modeling and simulation of a spined quadruped robot. Extended literature survey is employed and spine joints researches of the quadruped robots are classified. Most of the researchers execute simplified quadruped robot…
Existing procedures for model validation have been deemed inadequate for many engineering systems. The reason of this inadequacy is due to the high degree of complexity of the mechanisms that govern these systems. It is proposed in this…
In [1] was considered the superintegrable system which describes the magnetic dipole with spin 1/2 (neutron) in the field of linear current. Here we present its generalization for any spin which preserves superintegrability. The dynamical…
Integrable spin systems are an important subclass of integrable (soliton) nonlinear equations. They play important role in physics and mathematics. At present, many integrable spin systems were found and studied. They are related with the…
Physics-based simulations typically operate with a combination of complex differentiable equations and many scientific and geometric inputs. Our work involves gathering data from those simulations and seeing how well tree-based machine…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…
Differentiable simulators continue to push the state of the art across a range of domains including computational physics, robotics, and machine learning. Their main value is the ability to compute gradients of physical processes, which…
In recent years inelastic spin-flip spectroscopy using a lowtemperature scanning tunneling microscope has been a very successful tool for studying not only individual spins but also complex coupled systems. When these systems interact with…
In this paper, the physical realizability property is investigated for a class of nonlinear quantum systems. This property determines whether a given set of nonlinear quantum stochastic differential equations corresponds to a physical…
Some questions concerning the calculation of the number of ``physical'' (metastable) states or complexity of the spherical $p$-spin spin glass model are reviewed and examined further. Particular attention is focused on the general…
Several studies have exploited the integrable structure of central spin models to deepen understanding of these fundamental systems. In recent years, an underlying supersymmetry for systems with XX interactions has been uncovered. Here we…
We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of…
In this talk I present some of the recent theoretical results that have been obtained on glassy systems like spin glasses or structural glasses. The physical principles at the basis of the theory are explained in a simple language (without…
A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous…
It has been proposed that human physical reasoning consists largely of running "physics engines in the head" in which the future trajectory of the physical system under consideration is computed precisely using accurate scientific theories.…