Sommerfeld Theory Colloquium (ASC)

Tensor Networks and Quantum Computers

Tensor Network States, like matrix product or projected entangled pair states play an important role in both, quantum information theory and many-body physics. They offer a compact and efficient representation, enabling accelerated numerical computations and providing intuitive insights into many-body phenomena. In this talk, I will discuss how certain states can be efficiently prepared and manipulated using quantum devices, highlighting the use of local operations and classical communication. Tensor networks can also be used to efficiently describe quantum channels. I will also mention how those channels can be efficiently implemented as quantum circuits.

Chemomechanical self-organization across scales in living systems

A hallmark of living systems is their ability to generate and maintain order under constant fluctuations. In cells, such order often emerges from chemomechanical pattern formation, where proteins both sense and remodel the geometry of the cell. Here, I will discuss how theoretical modeling and simulations can capture this feedback across different spatial scales, using three example systems: on the macroscopic scale of individual cells, we used optogenetic control over a chemomechanical protein system to control the shape of starfish oocytes and induce self-organized surface contractions in these cells. On the mesoscopic scale of synthetic vesicles, I will discuss how protein patterns can drive the motility of synthetic liposomes, providing a minimal mechanism to transform chemical energy into motion without molecular motors. Finally, on the intracellular nanometer scale, I will present a mechanism for pattern formation without active energy consumption that relies on curvature sensitivity of membrane-binding proteins. Looking forward, I will discuss data-driven avenues for systematically analyzing biological self-organization, with particular focus on bringing experiments and simulations closer together.

Emergent cosmology from quantum gravity: the universe as a quantum condensate

The construction of a quantum theory of gravity remains an open problem despite decades of efforts. In time, the very perspective on this problem evolved. From quantising General Relativity, the goal is now mostly understood to be unraveling a more fundamental microstructure of spacetime, based on non-geometric building blocks, and to show how spacetime and matter emerge as effective, approximate notions. Given some candidate building blocks, the task becomes analogous to that of extracting the macroscopic, collective behaviour of the atoms of a condensed matter system, but even more challenging since we cannot use the usual spacetime intuition and no direct observational input is available to guide theory construction. Lacking a fundamental theory of quantum gravity, existing cosmological models which have proven extremely successful in accounting for the observed features of the very early universe (via CMB data) remain without a solid foundation, having to make a number of assumptions about a physical regime (close to the big bang), where the quantum nature of gravity and spacetime is expected to be relevant. This is all the LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN SEITE 2 VON 2 more unfortunate, since the very early universe is also where any proposed quantum theory of gravity has the highest chance of finding its observational test-bed. The gap needs to be bridged. In this talk I will first of all review the basic aspects of the problem of quantum gravity, and of some current approaches. I will then focus on one specific formalism for quantum gravity, so-called group field theories (strictly related to a number of other modern approaches). I will introduce its main features, trying to clarify the nature of the suggested building blocks of spacetime and their mathematical description. Next, I will outline a general strategy to extract an effective cosmological dynamics from quantum gravity, within this formalism. In this setting, the universe emerges as a quantum condensate of the fundamental “atoms of spacetime”, and cosmology is its corresponding hydrodynamics. Finally, I will summarize the recent results obtained along this research direction.

Gauge Theories and Non-Commutative Geometry

We shall review the attempts to extend the quantum mechanical property of non-commutativity from phase space to ordinary space. These attempts took a more precise form in the case of gauge theories for which some concrete results have been obtained. In flat space they amount to a reformulation of the theory which looks interesting but they have not given so far any novel physical results. However, the introduction of gravity gives a richer structure and may offer some new insights.

High order correlation and what we can learn about the solution for many body problems from experiment

The knowledge of all correlation functions of a system is equivalent to solving the corresponding quantum many-body problem. If one can identify the relevant degrees of freedom, the knowledge of a finite set of correlation functions is in many cases sufficient to determine a sufficiently accurate solution of the corresponding field theory. Complete factorization is equivalent to identifying the relevant degrees of freedom where the Hamiltonian becomes diagonal. I will give examples how one can apply this powerful theoretical concept in experiment. A detailed study of non-translation invariant correlation functions reveals that the pre-thermalized state a system of two 1-dimensional quantum gas relaxes to after a splitting quench [1], is described by a generalized Gibbs ensemble [2]. This is verified through phase correlations up to 10th order. Interference in a pair of tunnel-coupled one-dimensional atomic super-fluids, which realize the quantum Sine-Gordon / massive Thirring models, allows us to study if, and under which conditions the higher correlation functions factorize [3]. This allowed us to characterize the essential features of the model solely from our experimental measurements: detecting the relevant quasi-particles, their interactions and the different topologically distinct vacuum-states the quasi-particles live in. The experiment thus provides a comprehensive insight into the components needed to solve a non-trivial quantum field theory. Our examples establish a general method to analyse quantum systems through experiments. It thus represents a crucial ingredient towards the implementation and verification of quantum simulators. Work performed in collaboration with E.Demler (Harvard), Th. Gasenzer und J. Berges (Heidelberg). Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF): SFB FoQuS: F40-P10 and the EU: ERC-AdG QuantumRelax [1] M. Gring et al., Science, 337, 1318 (2012); [2] T. Langen et al., Science 348 207-211 (2015). [3] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126