Presentation of IPhT : The Institute of Theoretical Physics (IPhT) is an Institute of the Direction of Fundamental Research (DRF) of the Commissariat for Atomic Energy and Alternative Energies (CEA).

Quantum bounds and fluctuation-dissipation relations

** The chaotic behaviour of classical non-linear systems is an ubiquitous effect which refers to the unpredictability of their complex dynamics, a phenomenon known as the butterfly effect. **

**In mathematical terms this concept is characterized by the so-called ****Lyapunov exponent**, a quantity which expresses the rate at which trajectories which start from close-by initial conditions (position and velocity), diverge with time. In quantum mechanics it is difficult to find good diagnostics of chaos and this question has been intensively debated since the beginnings of quantum mechanics. Recently, groundbreaking results from high energy physics [1] showed that quantum mechanics imposes a strict bound on the Lyapunov exponent.

This novel effect has motivated enormous interest over different fields, leaving, however, several outstanding open questions. In our work [2] we show that this bound can be regarded as a consequence of the **quantum fluctuation-dissipation theorem,** a fundamental result of statistical mechanics which connects the linear response to a perturbation with the equilibrium thermal fluctuations. These findings establish a direct connection between quantum chaos and other thermodynamic properties. They could give rise to new applications to different problems.

In mathematical terms this concept is characterized by the so-called Lyapunov exponent, a quantity which expresses the rate at which trajectories which start from close-by initial conditions (position and velocity), diverge with time. In quantum mechanics it is difficult to find good diagnostics of chaos and this question has been intensively debated since the beginnings of quantum mechanics. Recently, groundbreaking results from high energy physics [1] showed that quantum mechanics imposes a strict bound on the Lyapunov exponent. This novel effect has motivated enormous interest over different fields, leaving, however, several outstanding open questions. In our work [2] we show that this bound can be regarded as a consequence of the quantum fluctuation-dissipation theorem, a fundamental result of statistical mechanics which connects the linear response to a perturbation with the equilibrium thermal fluctuations. These findings establish a direct connection between quantum chaos and other thermodynamic properties. They could give rise to new applications to different problems.

[1] J. Maldacena, S. H. Shenker and D. Stanford, Journal of High Energy Physics 2016(8) (2016).

[2] S. Pappalardi, L. Foini and J. Kurchan, SciPost Phys. 12, 130 (2022).

E. De-laborderie, 2022-05-12 11:47:00

Colloquium Rencontres de l'IPhT in Autrans (Vercors) from 23 to 25 May.

The next colloquium **Rencontres de l'IPhT** conference will be held **in Autrans (Vercors) from 23 to 25 May.** It will consist of conferences and lectures concerning both the major fields of research in theoretical physics and supporting activities.

**The main themes of physics will be:**

- Mathematical physics: group A

- Cosmology, particles and nuclei: group B

- Statistical physics - condensed matter: group C

**Main goals:**

- To share knowledge on scientific topics and strengthening cohesion within the Institute.

- To bring together all of the Institute's collaborators in order to discuss common subjects and activities and to strengthen interactions between members of the different teams, including support.

- To unite the teams around a common project.

See you soon in Autrans!

E. De-laborderie, 2022-05-12 10:02:00

An extension of Tutte's formula 60 years later

Given a set of deformable **polygons** with prescribed numbers of sides, in how many inequivalent ways can one glue them edge to edge so as **to build a sphere**? This mathematical question, which pertains to **map combinatorics in random geometry**, was partially answered by the mathematician William Tutte in a famous 1962 article "A census of slicings" where he solves the problem in the particular case where all the polygons, except at most two of them, have an even number of sides.

In a recent article, **Jérémie Bouttier and Emmanuel Guitter (IPhT)**, in collaboration with the mathematician Grégory Miermont (ENS de Lyon), succeeded, 60 years later, in extending Tutte's formula to the most general case, namely for polygons whose numbers of sides have arbitrary parities. Even though more complex, their general explicit formula is still very elegant and conceals numerous symmetries. It is with no doubt the starting point for new combinatorial discoveries.

The image shows the 8 ways to assemble two 1-sided and two 3-sided polygons to build a sphere.

E. De-laborderie, 2022-04-20 11:13:00

2022-04-05 11:28:00

2022-03-16 17:38:00

Public talk of Stephane Lavignac on Tuesday March 15th

2022-03-11 09:17:00

A new book written by Marc Barthélémy about spatial networks

2022-02-22 11:05:00

Cédric Villani at IPhT on March 1st

2022-02-22 10:26:00

Summer School in Cargèse around exotic superconductivity

2022-02-07 15:39:00

Langevin Prize of the French Society of Physics for Mariana Graña

2022-02-04 10:46:00

2022-02-01 09:59:00

2022-02-01 09:21:00

Junior Permanent Position in Theoretical Quantum Physics at IPhT

2022-01-17 13:07:00

Junior Permanent Position in Theoretical Physics at IPhT

2022-01-01 09:00:00

Un lien entre la masse du boson de Higgs et la constante cosmologique

2021-11-25 14:11:00

Conférence exceptionnelle de Cédric Villani le lundi 22 novembre à 19h30 (Institut Pascal)

2021-11-18 14:33:00

2021-11-09 15:21:00

Giorgio Parisi Nobel Prize in Physics 2021

2021-10-12 11:18:00

Problems in Quantum Field Theory : a book by François Gelis.

2021-10-11 16:12:00

Mathematical Harmony and the Quantum World

2021-10-07 15:24:00

The art of mathematical physics

2021-09-01 16:31:00

Correlation functions and wave functions in solvable models

2021-08-31 16:44:00

Black-hole microstructure conference (June 7th - 11th, 2021)

2021-06-03 16:55:00

2021-05-01 11:45:00

Multipole Ratios : A New Window into Black Holes

2020-11-27 15:16:00

Orazio Scarlatella lauréat du prix de thèse Physique des Ondes et de la Matière (PhOM) 2020

2020-11-26 11:07:00

Modeling the city: an equation ends centuries-old controversies

2020-11-19 11:10:00

Quantum entanglement: A single photon takes two optical paths by "entangling" them!

2020-10-15 15:06:00

An strongly secured encryption

2020-09-17 17:01:00

David Kosower lauréat de l'ERC Advanced Grant "Ampl2Einstein"

2020-04-03 15:57:00

Un nouvel ouvrage co-écrit par Pierfrancesco Urbani, physicien à l’IPhT

2020-01-31 14:15:00

Un nouvel ouvrage co-écrit par Henri Orland, physicien à l'IPhT

2020-01-28 16:16:00

2019-11-18 09:39:00

Philippe Brax (IPhT), representing UP Saclay in EuCAPT

2019-11-04 14:18:00

Quantum Field Theory : A book by François Gélis.

2019-07-25 00:00:00

Mon, May. 30th, 11:00-12:00

Séminaire de physique mathématique - Rob Klabbers

Fri, Jun. 03rd, 10:00

Cours de physique théorique de Saclay - Michele Vallisneri