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## Path Integral Quantum Mechanics: Theory, Simulation and Application

#### Location: CECAM-HQ-EPFL, Lausanne, Switzerland

#### Organisers

This school is focused in giving a theoretical background and presenting state of the art techniques involving Feynman path integral approaches to quantum dynamics and quantum statistical mechanics and their application to atomistic simulations. Path integral simulations allow for the inclusion of quantum effects, such as zero-point energy and tunneling, in the static and dynamical properties of nuclei that are highly important for correctly describing the behavior of light atoms, such as hydrogen.

The purpose of the school is to give a broad overview of the condensed-phase applications of the path integral formulation of quantum mechanics, covering the fundamental theoretical aspects, the implementation caveats, the potential for application and the practical aspects of performing a path integral-based atomistic simulation. In particular this school will cover:

* Equilibrium Properties from Path Integrals - Computing nuclear quantum effects on time-independent, thermodynamic averages. Topics covered will include:

- Imaginary-time Path Integrals
- Path Integral Molecular Dynamics and Path Integral Monte Carlo
- Path Integral Estimators
- Path Integrals for Indistinguishable particles.

* Ab Initio Path Integrals - Techniques to model simultaneously the quantum nature of electrons and nuclei. Topics covered will include:

- Accelerating Path Integral Calculations
- Path Integrals in Different Ensembles and other advanced topics
- Ab initio Path Integrals

* Dynamics from Path Integrals - Extracting time-dependent information both from the exact real time path integral formalism and from approximate techniques derived from it. Topics covered will include:

- Time Correlation Functions
- Exact Real Time Path Integral Approaches
- Semiclassical Dynamics
- Non-Adiabatic Path Integral Dynamics
- Quantum Rate Theories
- Matsubara Dynamics
- RPMD and CMD

The school wil also feature a poster session where all participants are encouraged to present their work as well as contributed talks.

Lecturers:

- Prof. Stuart Althorpe, University of Cambridge
- Prof. Nandini Ananth, Cornell University
- Dr. Ethan Brown, ETH
- Prof. Michele Ceriotti, EPFL
- Prof. Nancy Makri, University of Illinois Urbana-Champaign
- Prof. Tom Markland, Stanford University
- Dr. Ondrej Marsalek, Stanford University
- Prof. Angelos Michaelides, University College London
- Dr. Mariana Rossi, University of Oxford
- Prof. Mark Tuckerman, New York University
- Prof. Jiri Vanicek, EPFL

Prospective participants should apply from the CECAM website, following these instructions. A small number of grants to contribute towards local expenses will also be available.

**Please note that as of February 23rd we have already many more applications that we will be able to accept. Further applications will be put on a waiting list, and we will contact you should a place become available.**

## References

**Germany**

Mariana Rossi (Max Planck Institute for the Structure and Dynamics of Matter) - Organiser & speaker

**Switzerland**

Michele Ceriotti (Swiss Federal Institutes of Technology Lausanne (EPFL)) - Organiser & speaker

**United States**

Thomas Markland (Stanford University) - Organiser & speaker

Mark E. Tuckerman (New York University) - Organiser & speaker