Time Crystals (Speaker: Prof. Krzysztof Sacha - Institute of Theoretical Physics Jagiellonian University)

The lectures provide a comprehensive overview of time crystals, which exhibit a repeating temporal structure. They introduce fundamental concepts related to time crystals and explore various branches of this emerging research area. The lectures begin with the original idea of time crystallization in quantum systems introduced by Wilczek and present the development of this field up to the present day. They describe both the spontaneous formation of time crystalline structures and the concepts of condensed matter physics in the time domain, from Anderson localization in time to many-body systems with exotic interactions. The lectures also outline the prospect of time-tronics development, which involves building useful devices where time crystalline structures play a crucial role.

The non-equilibrium real-time Green’s functions techniques and its applications // The method of the non-equilibrium statistical operator and its applications (Speaker: Prof. Armen Sedrakjan - University of Wroclaw)

 In the first lecture I will develop the real-time Green’s functions techniques. I will derive in this formalism the transport equations known as Kadanoff-Baym equations and will illustrate their applications via the evaluation of the collision integrals of several example systems, ranging from a dilute Bose gas to strongly interacting nuclear matter. Numerical examples will be given. The second lecture will develop an alternative non-equilibrium method known as the method of the non-equilibrium statistical operator. It will allow us to evaluate of transport properties of strongly correlated systems via Kubo-Green formulas for correlation functions. As an illustration, the method will be applied to quark-gluon plasma in the framework of the Nambu-Jona-Lasinio model of four-fermion interaction. Numerical examples of computation of the transport coefficient of quark-gluon plasma, such as the shear viscosity, will be given.

Hands on Introduction to Deep Reinforcement Learning for Qubit Manipulation (Speaker: Dr. Marin Bukov, MPI-PKS)

Reinforcement learning (RL) is one of the three modern pillars of modern machine learning, and constitutes the "learning from interactions" paradigm. Applications of RL include superhuman performance in playing video and board games, robotic steering and locomotion, control of physical systems, and many others. The two lectures will provide a brief hands-on introduction to deep reinforcement learning for quantum control. After a short overview of the topic to define the main concepts, we will consider the specifics of the RL framework for quantum control on NISQ and AMO devices. In particular, we will discuss how to incorporate quantum mechanical constraints such as the non-measurability of quantum states, the backaction on the system from strong measurements, and the binary nature of quantum data. As a specific example, we will learn how to manipulate the stochastic dynamics of a noisy qubit by coupling it to an ancilla.
We will use Jupyter notebooks and the JAX package [https://jax.readthedocs.io/en/latest/].

Surrogate modeling of laser plasma interaction using machine learning: Data (Speaker: Dr. Michael Bussman - Helmholtz-Zentrum Dresden-Rossendorf)

In this lecture we will introduce the role of data in modeling laser plasma interaction using machine learning. We will motivate the use of machine learning by explaining the challenges of modeling laser plasma interactions at high intensities, introducing the state of the art modeling techniques. We will discuss the various data sources and the challenges in making them useful for machine learning. We dive deeper into the role of nonlinear interactions in both experiments and simulations. We finally present a path forward using synthetic diagnostics and analysis routines for non-convex inverse problems to connect experimental measurements with simulation data. We conclude by presenting important ingredients in successfully using machine learning for modeling laser plasma interaction at high intensities.

Introduction to Deep Learning (Speaker: Dr. Attila Cangi - Helmholtz-Zentrum Dresden-Rossendorf)

In this lecture I will introduce the concept of neural networks. We will begin with a brief overview of the development of artificial neural networks. We will look at the basic perceptron model from a mathematical point of view and implement it to solve a simple classification problem. In the last part of the lecture, I will provide a gentle interactive introduction to deep learning using a simple toy problem about digital colors. We will learn how to build neural network pipelines and develop a qualitative understanding. The lecture will be both formal and interactive using Jupyter notebooks.

Solving Differential Equations with Machine Learning (Speaker: Dr. Attila Cangi - Helmholtz-Zentrum Dresden-Rossendorf)

In this lecture I will show how neural networks can be used to solve differential equations. We will consider the basic example of the quantum harmonic oscillator. After reviewing some basic concepts, we will implement two machine learning methods to solve the time-dependent Schrödinger equation for the harmonic oscillator. First, we will consider a data-driven approach where a fully connected neural network is used to learn the solutions of the differential equation based on input labels. In the second approach, we will consider physics-informed neural networks. In contrast to the data-driven approach, the solution of the differential equation is not learned by mapping input features to outputs, but by minimizing a loss term related to the form of the differential equation. The lecture will be both formal and interactive using Jupyter notebooks.

Surrogate modeling of laser plasma interaction using machine learning: Methods (Speaker: Dr. Michael Bussman - Helmholtz-Zentrum Dresden-Rossendorf)

In this second part we focus on the technologies used for modeling laser plasma interaction. Among these are

• Bayesian modeling techniques for linear optimization problems for few shot experiments
• Generative models such as variational autoencoders to efficiently reduce the complexity of laser matter interactions
• Generative models such as normalizing flows to model highly nonlinear behavior
• Invertible neural networks to connect observables with initial conditions

Which we will put in context with some important applications in laser matter interaction. We conclude with an outlook on the role of foundation models, ML-OPS, data repositories, metadata and ontologies

BCS–BEC crossover in ultracold gases and nuclear systems (Speaker: Prof. Gabriel Wlazłowski - Warsaw University of Technology)

The lecture introduces the BCS (Bardeen–Cooper–Schrieffer)–BEC (Bose-Einstein condensation) crossover phenomenon, which will be used as a platform for comprehensive studies of superfluidity in bosonic and fermionic systems. A survey of experimental progress in the realization of BCS-BEC crossover with ultracold atomic gases will be provided. Next, the main theoretical frameworks for describing bosonic and fermionic superfluids will be discussed. The emphasis will be put on mean-field methods: the Bogoliubov–de Gennes theory for Fermi gases and the Gross–Pitaevskii equation for Bose systems. In the last part of the lecture, the relation of the BCS-BEC crossover to nuclear systems will be highlighted. In particular, similarities and differences to superfluid neutron matter will be explained under conditions as expected in neutron stars.
 

Density Functional Theory for systems with pairing correlations (Speaker: Prof. Gabriel Wlazłowski - Warsaw University of Technology)

The lecture will introduce Density Functional Theory (DFT) extended to superfluid systems. The DFT approach overcomes the limitations of mean-field methods and can be applied to strongly interacting systems, like unitary Fermi gas or nuclear matter. The fundamental theorems constituting the method will be explained, together with the methodology of constructing energy density functional for superfluid systems and the concept's practical implementation. Next, an extension of the method to a time-dependent variant will be presented. Finally, examples of applications of the method to various systems will be provided, which include dynamics of superfluid Fermi gases or neutron matter, quantum vortices, nuclear reactions, and quantum turbulence. 

Macroscopic description of many-body systems (Speaker: Prof. Piotr Surowka - Wroclaw University of Science and Technology)

Neural networks have demonstrated exceptional performance in classification tasks involving structured, high-dimensional datasets. However, their macroscopic description remains poorly understood. It is widely believed that hydrodynamics offers a macroscopic description of many-body physics. Constructing the hydrodynamic, macroscopic description of neural networks is, therefore, a crucial step towards our understanding of these systems.

In these lectures, we will present state-of-the-art knowledge about constructing hydrodynamic theories based on symmetries of the underlying many-body state. We will discuss a general approach, based on classical Poisson brackets, that facilitates the automatic and straightforward derivation of hydrodynamic equations for any many-body system with spontaneously broken symmetries. In the final part of the lecture, we will illustrate the connection between these domains by providing an example of the hydrodynamic description of a simple binary neural network.