Path Integral Methods in Molecular Dynamics

Course Description

Welcome to this advanced course on Path Integral Methods in Molecular Dynamics! This innovative and comprehensive program is designed to introduce you to the fascinating world of quantum mechanical effects in atomic nuclei behavior. By mastering the path integral formalism, you'll gain a deep understanding of how these effects influence systems from cryogenic temperatures to room temperature and beyond, with a particular focus on light elements.

This course is structured as a series of engaging lectures that progressively increase in difficulty and specialization. You'll benefit from a rich array of learning materials, including detailed lecture notes, challenging pen-and-paper exercises, informative recorded lectures, and hands-on practical exercises using Jupyter notebooks and an advanced molecular dynamics code.

What You'll Learn

• A thorough recap of molecular dynamics and related sampling techniques
• The fundamental theory behind path integral methods
• Advanced estimators for computing momentum-dependent observables
• Accelerated path integral techniques to reduce computational costs
• Approximate methods for quantum dynamics based on path integral formalism
• Ring-polymer molecular dynamics and its applications
• Colored-noise methods and their implementation
• Adiabatic and non-adiabatic ring-polymer rate theory

Prerequisites

While there are no specific prerequisites, it's recommended that students have a strong background in physics, mathematics, and computational methods. Familiarity with quantum mechanics, statistical mechanics, and basic programming skills would be highly beneficial.

Course Content

• Molecular dynamics and sampling techniques
• Basic theory of path integral methods
• Advanced estimators for momentum-dependent observables
• Accelerated path integral techniques (ring-polymer contractions, high-order path integral Hamiltonians)
• Colored-noise methods
• Approximate quantum dynamics using path integral formalism
• Ring-polymer molecular dynamics (RPMD)
• Adiabatic and non-adiabatic ring-polymer rate theory

Who This Course Is For

This course is ideal for advanced students, researchers, and professionals in the fields of physics, chemistry, materials science, and computational science who want to deepen their understanding of quantum mechanical effects in molecular dynamics. It's particularly suited for those interested in studying systems containing light elements or working with materials at various temperature ranges.

Real-World Applications

The skills acquired in this course have numerous practical applications in fields such as:

• Materials science: Designing and studying advanced materials with unique quantum properties
• Chemical physics: Understanding and predicting chemical reactions at the atomic level
• Drug discovery: Simulating molecular interactions for pharmaceutical research
• Energy research: Developing more efficient energy storage and conversion technologies
• Nanotechnology: Exploring quantum effects in nanoscale systems
• Atmospheric and environmental science: Modeling molecular processes in the atmosphere and environment

Syllabus

1. Molecular Dynamics and Sampling - Michele Ceriotti, EPFL
2. The basics of path integrals - Mariana Rossi, MPG Hamburg
3. Advanced path integral methods - Thomas Markland, Stanford
4. Ring Polymer molecular dynamics - David Manolopoulos, Oxford
5. Colored-noise methods - Michele Ceriotti, EPFL
6. Adiabatic ring-polymer rate theory - David Manolopoulos, Oxford
7. Non-adiabatic ring-polymer rate theory - David Manolopoulos, Oxford

This course offers a unique opportunity to learn from world-renowned experts in the field, providing you with cutting-edge knowledge and skills that will set you apart in your academic or professional career. Don't miss this chance to dive deep into the quantum world of molecular dynamics!