scholarly journals Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning

Science ◽  
2019 ◽  
Vol 365 (6457) ◽  
pp. eaaw1147 ◽  
Author(s):  
Frank Noé ◽  
Simon Olsson ◽  
Jonas Köhler ◽  
Hao Wu
Keyword(s):  
Molecular Dynamics ◽  
Deep Learning ◽  
Statistical Mechanics ◽  
Equilibrium Distribution ◽  
Condensed Matter ◽  
Computational Effort ◽  
Equilibrium States ◽  
Many Body ◽  
Reaction Coordinates ◽  
Many Body Systems

Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in “one shot,” vast computational effort is invested for simulating these systems in small steps, e.g., using molecular dynamics. Combining deep learning and statistical mechanics, we developed Boltzmann generators, which are shown to generate unbiased one-shot equilibrium samples of representative condensed-matter systems and proteins. Boltzmann generators use neural networks to learn a coordinate transformation of the complex configurational equilibrium distribution to a distribution that can be easily sampled. Accurate computation of free-energy differences and discovery of new configurations are demonstrated, providing a statistical mechanics tool that can avoid rare events during sampling without prior knowledge of reaction coordinates.

scholarly journals GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

2008 ◽  
Vol 22 (06) ◽  
pp. 561-581 ◽  
Author(s):  
SHI-LIANG ZHU
Keyword(s):  
Phase Transitions ◽  
Geometric Phase ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Many Body ◽  
Scientific Communities ◽  
Geometric Phases ◽  
Many Body Systems ◽  
The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

Geometric Phase in Condensed Matter III: Many-Body Systems

2003 ◽  
pp. 337-359
Author(s):  
Arno Bohm ◽  
Ali Mostafazadeh ◽  
Hiroyasu Koizumi ◽  
Qian Niu ◽  
Joseph Zwanziger
Keyword(s):  
Geometric Phase ◽  
Condensed Matter ◽  
Many Body ◽  
Many Body Systems

Thermal Gaussian molecular dynamics for quantum dynamics simulations of many-body systems: Application to liquid para-hydrogen

2011 ◽  
Vol 134 (17) ◽  
pp. 174109 ◽  
Author(s):  
Ionuţ Georgescu ◽  
Jason Deckman ◽  
Laura J. Fredrickson ◽  
Vladimir A. Mandelshtam
Keyword(s):  
Molecular Dynamics ◽  
Quantum Dynamics ◽  
Para Hydrogen ◽  
Many Body ◽  
Many Body Systems ◽  
Dynamics Simulations

Quantum Ensembles

2019 ◽  
pp. 285-296
Author(s):  
Robert H. Swendsen
Keyword(s):  
Statistical Mechanics ◽  
Probability Distributions ◽  
Quantum Statistical Mechanics ◽  
Stationary States ◽  
Mechanical State ◽  
Many Body ◽  
Model Probability ◽  
Exact Position ◽  
Quantum Statistical ◽  
Many Body Systems

The study of quantum statistical mechanics begins with a review of the basic principles of quantum mechanics. Schrödinger’s equation is introduced and Eigenstates (or stationary states) are defined. Model probability for quantum statistics is assumed to have a uniform distribution in phases. Wave functions for many-body systems are defined. The density matrix is introduced. The Planck entropy and the microcanonical ensemble are defined. The differences between classical and quantum statistical mechanics are all based on the differing concepts of a microscopic ‘state’. While the classical microscopic state (specified by a point in phase space) determines the exact position and momentum of every particle, the quantum mechanical state determines neither; quantum states can only provide probability distributions for observable quantities.

Hydrodynamics

2021 ◽  
pp. 49-66
Author(s):  
Robert W. Batterman
Keyword(s):  
Correlation Functions ◽  
Linear Response ◽  
Order Parameters ◽  
Equilibrium States ◽  
Conserved Quantities ◽  
Many Body ◽  
Hydrodynamic Description ◽  
Relative Autonomy ◽  
Many Body Systems ◽  
The Continuum

This chapter begins the argument that the best way to understand the relations of relative autonomy between theories at different scales is through a mesoscale hydrodynamic description of many-body systems. It focuses on the evolution of conserved quantities of those systems in near, but out of equilibrium states. A relatively simple example is presented of a system of spins where the magnetization is the conserved quantity of interest. The chapter introduces the concepts of order parameters, of local quantities, and explains why we should be focused on the gradients of densities that inhabit the mesoscale between the scale of the continuum and that of the atomic. It introduces the importance of correlation functions and linear response.

scholarly journals Maxwell electromagnetism as an emergent phenomenon in condensed matter

2016 ◽  
Vol 374 (2075) ◽  
pp. 20160093 ◽  
Author(s):  
J. Rehn ◽  
R. Moessner
Keyword(s):  
Magnetic Monopole ◽  
Condensed Matter ◽  
Many Body ◽  
Classical Electromagnetism ◽  
Magnetic Dipoles ◽  
Translational Invariance ◽  
Energy Behaviour ◽  
Many Body Systems ◽  
The One ◽  
Simple Systems

The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was only recognized much later. Here, we provide an account of how simple systems of localized spins manage to emulate Maxwell electromagnetism in their low-energy behaviour. They are much less constrained by symmetry considerations than the relativistically invariant electromagnetic vacuum, as their substrate provides a non-relativistic background with even translational invariance broken. They can exhibit rich behaviour not encountered in conventional electromagnetism. This includes the existence of magnetic monopole excitations arising from fractionalization of magnetic dipoles; as well as the capacity of disorder, by generating defects on the lattice scale, to produce novel physics, as exemplified by topological spin glassiness or random Coulomb magnetism. This article is part of the themed issue ‘Unifying physics and technology in light of Maxwell's equations’.

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