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## Seeking synergy between dynamics and statistics for non-equilibrium quantum processes

#### ENS Paris

#### Organisers

**Abstract Submission - Deadline: April 30th, 2017 (see below)**

The need to develop accurate theoretical descriptions of non-equilibrium processes in quantum mechanical systems is a goal that unifies a diverse set of fields ranging from physics, chemistry, and mathematics, to biology and materials science. One of the major difficulties in reaching this goal is framed by the desire to provide a representation of the system of interest that is as realistic as possible, in a manner that is computationally tractable. The coupling of electronic and nuclear motion involving excited states, the quantum nature of the nuclear degrees of freedom, and the application of time-dependent driving forces, are just few examples of the effects that must be addressed in order to simulate these processes. Each of these effects poses unique challenges to theoretical progress. Hence, due to the computational complexity of treating such effects appropriately in molecular systems and in the condensed phase, a number of exact and approximate quantum dynamics techniques are being developed and refined in order to provide algorithms that respond to the demand for a balance between computational efficiency and physical accuracy. Currently available techniques are typically based upon two different, but equivalent, formulations of many-body quantum mechanics, the wave function approach or the density matrix picture.

Wave-function-based methods generate the dynamical evolution of a system by solving the time-dependent Schroedinger equation. Prominent examples of such methods are wave packet propagation techniques, such as the multiconfigurational time-dependent Hartree (MCTDH) approach [1], and trajectory-based approaches such as Gaussian-based MCTDH (G-MCTDH) [2], the variational multiconfigurational Gaussian (v-MCG) [3] schemes, multiple spawning approaches [4], and methods based on the exact factorization approach such as the coupled-trajectory mixed quantum-classical (CT-MQC) scheme [5].

Density-matrix-based approaches are typically developed starting with the Liouville-von Neumann equation. Numerically exact approaches such as real-time path integral methods [6–10], and approximate methods such as the family of (partially) linearized density matrix (LDM) propagation scheme [10–12], the hierarchy of techniques derivable from the quantum-classical Liouville equation (QCLE) [13], and mapping-variable ring polymer molecular dynamics (MV-RPMD) [14], are examples of density matrix based techniques that have been applied to a variety of systems.

The non-equilibrium evolution of a subset of degrees of freedom in the overall system can be rigorously formulated using the quantum master equation formalism [15–18, 20]. The solution to such quantum master equations can be evaluated using information generated from either wave function based methods or density matrix techniques. However, a disconnect between the descriptions that the two formalisms offer is created when approximations are introduced [19, 21–23] that prevent one from achieving a fully quantum mechanical treatment of the problem. It is thus of great importance to address this interstitial region between these approaches, where the dynamical picture and the statistical picture of the process coalesce. The goal of the proposed workshop is to stimulate discussion that bridges these two descriptions.

The community of molecular quantum dynamics method developers has expressed, on several occasions, the need and the will to cooperate in order to assess the state of the art of existing approaches and to understand the connections among different techniques in the field. Consequently, in June 2015 the CECAM workshop “Molecular Quantum Dynamics Methods: Benchmarks and state of the art” was organized with the aim of providing a general overview of the most established methods. During this workshop, a few selected topics were identified and pro- posed as central subjects for a following CECAM meeting in June 2016, “Different Routes to Quantum Molecular Dynamics”. The focus of both workshops was mainly to understand the fundamentals and the approximations involved in the discussed methods. In this way, experts and non-experts in such approaches acquire the capability to critically discuss and propose ideas for future developments. The workshop of 2016 reached exactly its purpose, and from animated discussions among the participants of the workshop it was apparent that the gap between dynamics and statistics has emerged as an area that needs to be addressed in the future.

The proposed workshop aims to:

(i) bring together the two principal molecular quantum dynamics communities (wave-function methods and density matrix approaches) to identify and explore common goals and obstacles.

(ii) help in fostering new ideas to connect these approaches, and bridge the apparent gap between approximate dynamical and statistical descriptions.

(iii) identify possible routes to extend dynamics approaches to the domain of statistics.

It is clear that the quantum molecular dynamics community is broad, as is the range of physical methodologies and algorithmic implementations that are employed within it. However, all these techniques stem from the same root. This workshop, as the past workshops, is an attempt toward a stewardship of the connections between the branches of this (quantum molecular dynamics) tree. We propose an alternative format: experts (invited speakers) will be asked to uncover the fundamental details of the methods in pedagogical lectures for the audience. These lectures will be followed by extensive discussions; the contributed speakers, posters’ presenters and participants will be asked to put forth some of their doubts and problems in the relation between dynamics and statistics. A small number of contributed talks will be scheduled, covering topics related to the invited lectures. A poster session will also be organized, with active participation from some of the invited speakers in evaluating the posters (for the purposes of awarding poster prizes). The workshop must be intended as a moment to constructively and with a common effort achieve a better understanding of approximate quantum dynamics methods. To this end, 2 discussion sessions will be organized: the participants will be divided into working groups (based on their statement of interest) and parallel round-table discussions will be led by experts of the fields covering questions put forth by the participants both prior to, and during, the meeting. At the end of each round-table session, a synergy session will be scheduled: leading experts from each discussion group will outline the topics that were discussed and a moderator will attempt to propose a coherent framework about synergies between different approaches, with the aim of constructing a bridge between dynamical and statistical descriptions.

**CONTRIBUTED TALKS AND POSTERS**

Participants are invited to submit abstracts for contributed talks and posters. Since we have a limited number of slots for contributed talks, please state in your application email if you would like to be considered for an oral presentation by **April 30th, 2017**. After that date, you will be notified by the organizers if your abstract has been selected for an oral presentation or for a poster presentation. Abstract for poster may be submitted at any time.

## References

**France**

Federica Agostini (Université Paris-Sud) - Organiser

David Lauvergnat (Université Paris Saclay / CNRS) - Organiser

**Germany**

Aaron Kelly (Max Planck Institute for the Structure and Dynamics of Matter) - Organiser

**United States**

David Coker (Boston University) - Organiser