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Path Integral Methods in Atomistic Modelling

Michele Ceriotti, Mariana Rossi, Thomas Markland, David Manolopoulos, and Venkat Kapil

The path integral formalism allows to introduce quantum mechanical effects on the equilibrium and (approximately) time-dependent behavior of atomic nuclei, which is relevant from cryogenic temperatures to room temperature and above, particularly for systems that contain light elements.

The course is conceived as a series of lectures on topics of increasing difficulty and specialization. For each topic, the complete course will provide a set of lecture notes, complete with pen-and-paper exercises, recorded lectures, and practical exercises based on jupyter notebooks and an advanced molecular dynamics code. The various chapters and content will appear in the coming months, as they become ready.

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What's inside

Learning objectives

A re-cap of molecular dynamics and related sampling techniques
An introduction to the basic theory of path integral methods
Advanced estimators to compute momentum-dependent observables

Accelerated path integrals to reduce the computational cost, including ring-polymer contractions, high-order path integral hamiltonians and colored-noise methods
Approximate techniques for quantum dynamics based on the path integral formalism: ring-polymer md

A re-cap of molecular dynamics and related sampling techniques
An introduction to the basic theory of path integral methods
Advanced estimators to compute momentum-dependent observables
Accelerated path integrals to reduce the computational cost, including ring-polymer contractions, high-order path integral hamiltonians and colored-noise methods
Approximate techniques for quantum dynamics based on the path integral formalism: ring-polymer md

Syllabus

Molecular Dynamics and Sampling - Michele Ceriotti, EPFL

The basics of path integrals - Mariana Rossi, MPG Hamburg

Advanced path integral methods - Thomas Markland, Stanford

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Taught by Michele Ceriotti, Mariana Rossi, Thomas Markland, David Manolopoulos, and Venkat Kapil, who have significant experience and expertise in the domain of path integral molecular dynamics

Examines the application of path integral methods to study the equilibrium and time-dependent behavior of atomic nuclei

Develops skills in using path integral formalism to compute momentum-dependent observables and accelerate path integrals

Covers a range of methods in path integral theory, including ring-polymer molecular dynamics, colored-noise methods, and adiabatic and non-adiabatic ring-polymer rate theory

Provides a mix of lectures, exercises, and hands-on modules to facilitate learning

Suitable for researchers, academics, and advanced students interested in the study of nuclear dynamics using path integral methods

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Reviews summary

Advanced atomistic modelling with path integrals

According to learners, this course offers an outstanding deep dive into path integral methods for atomistic modelling, praised for its cutting-edge content delivered by leading experts in the field. Students highlight the incredibly clear lectures and valuable practical exercises, particularly the Jupyter notebooks, as instrumental for application. While many find it an indispensable resource that fills a critical gap in online learning, prospective students should note it demands a strong prerequisite knowledge of quantum and statistical mechanics, with some finding the pace quite demanding and not suitable for beginners.

Taught by leading authorities, offering diverse insights.

"Prof. Ceriotti and the others have done an amazing job."

"I found the content cutting-edge and presented by leading experts in the field."

"I particularly liked the diverse set of instructors, each an expert in their sub-field. The quality of the lecturers is superb."

Hands-on application through Jupyter notebooks and MD code.

"The Jupyter notebooks provided were a game-changer, allowing me to apply the concepts immediately."

"The practical exercises using an advanced MD code were crucial for understanding."

"I found the practical components very helpful, especially the well-designed Jupyter notebooks."

Covers niche, advanced topics with unparalleled depth.

"This course is simply outstanding for anyone serious about atomistic simulations. The lectures are incredibly clear, even for such complex topics."

"The content is cutting-edge and presented by leading experts in the field. I particularly appreciated the modules on Ring Polymer MD and colored-noise methods."

"I found this an indispensable resource for anyone working in quantum simulations. The explanations of advanced path integral methods are unparalleled."

Fast-paced and dense, requiring significant effort.

"The theoretical parts are well explained, though sometimes a bit dense, and I struggled with the pace and depth."

"I found this course extremely difficult to follow; the quantum aspects were presented very rapidly."

"It's a challenging course, but I found the rewards immense for the effort."

Assumes strong prior knowledge in QM and MD.

"I would highly recommend this if you have a solid background in QM and MD."

"I found some of the earlier modules assumed a higher level of familiarity with molecular dynamics than I possessed..."

"This course is definitely not for beginners. I needed to be comfortable with quantum mechanics and statistical mechanics to get the most out of it."

"I found this course extremely difficult to follow as the instructors assume a very high level of prior knowledge."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Path Integral Methods in Atomistic Modelling with these activities:

Review quantum mechanics

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Review core concepts of quantum mechanics to strengthen foundational understanding for this course.

Browse courses on Quantum Mechanics

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Re-visit textbooks or lecture notes on quantum mechanics.
Solve practice problems to reinforce your understanding.

Review molecular dynamics and related sampling techniques

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This review will help students refresh their understanding of molecular dynamics and related sampling techniques, ensuring they are well-equipped to delve into the path integral formalism.

Browse courses on Molecular Dynamics

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Revisit the concepts of molecular dynamics, including force fields and integration methods.
Review free energy methods such as umbrella sampling, steered MD, and metadynamics.
Practice implementing molecular dynamics simulations using a software package.

Discuss path integral applications

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Gain diverse perspectives and enhance understanding through discussions with peers.

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Initiate a study group or join an existing one.
Select specific path integral topics for discussion.
Prepare by reviewing materials and formulating questions.

Five other activities

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Path integral exercises

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Deepen comprehension of path integral methods by completing exercises and drills.

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Work through the pen-and-paper exercises provided in the course notes.
Attempt the practice problems based on jupyter notebooks.

Explore advanced path integral methods

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These tutorials will guide students through advanced path integral methods, enhancing their understanding of the theoretical foundations of the course.

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Follow video tutorials on topics such as ring-polymer contractions and high-order path integral Hamiltonians.
Work through interactive simulations that demonstrate the application of these methods.

Explain path integral concepts

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Solidify understanding by explaining path integrals to someone else.

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Choose a specific path integral concept.
Prepare a clear and concise explanation.
Present your explanation to a friend or colleague.

Advanced path integral techniques

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Expand knowledge by exploring advanced path integral techniques through dedicated tutorials.

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Identify reputable tutorials on advanced path integral techniques.
Follow the tutorials, taking notes and completing any exercises.

Implement path integral code

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Apply knowledge by implementing path integral methods in code.

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Choose a specific path integral algorithm to implement.
Write code based on the chosen algorithm.
Test and debug the implementation.

Career center

Learners who complete Path Integral Methods in Atomistic Modelling will develop knowledge and skills that may be useful to these careers:

Reading list

We've selected 45 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Path Integral Methods in Atomistic Modelling.

Dynamics of Proteins and Nucleic Acids

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Provides a comprehensive overview of molecular dynamics simulations, including the theory, methods, and applications. It is written by leading experts in the field and is suitable for both beginners and experienced researchers.

Path Integral Methods in Atomistic Modelling

What's inside

Learning objectives

Syllabus

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Reviews summary

Advanced atomistic modelling with path integrals

Activities

Career center

Reading list

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