Scientific Series

In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus break unitarity. Here we show that these expectations can be made precise in loop quantum cosmology. Concretely, even when loop quantum cosmology is unitary at the fundamental level, when microscopic degrees of freedom, irrelevant to low-energy cosmological observers, are suitably ignored, pure states in the effective description evolve into mixed states due to decoherence with the Planckian microscopic structure. When extrapolated to black hole formation and evaporation, this concrete example provides a key physical insight for a natural resolution of Hawking's information paradox.

Cosmological perturbation theory has a long tradition for describing the early phases of the Universe. As the observations of the CMB radiation suggest, it is reasonable, at least as a first approximation, to implement cosmological inhomogeneities as small perturbations around homogeneous and isotropic FRW solutions. In these approaches, backreactions between the inhomogeneities and the background are usually neglected. There is an ongoing debate about how and to which extend these backreactions affect the large scale structure of the Universe. Even at a purely classical level, there is no conclusive answer to this question yet.

In my talk, I am going to present a new systematic formalism for implementing backreactions in cosmological perturbation theory, in which both, the perturbations and the homogeneous degrees of freedom are considered as quantum degrees of freedom. As a more realistic theory of quantum fields on quantum cosmological space times, it can help to close the gap between a full theory of quantum gravity and symmetry-reduced models of quantum cosmology, and to confront these theories with observations. Our results show that quantum backreactions imply non-trivial corrections that are potentially phenomenologically significant.

Bergman's Diamond Lemma for ring theory gives an algorithm to produce a (non-canonical) basis for a ring presented by generators and relations. After demonstrating this algorithm in concrete, geometrically-minded examples, I'll turn to preprojective algebras and their multiplicative counterparts. Using the Diamond Lemma, I'll reprove a few classical results for preprojective algebras. Then I'll propose a conjectural basis for multiplicative preprojective algebras. Finally I'll explain why the set is a basis in the case of multiplicative preprojective algebras for quivers containing a cycle, the subject of joint work with Travis Schedler.

Results from the first digital quantum simulation of an SU(2) gauge theory are presented. This was done by analytically constructing gauge-invariant states and implementing a Trotterized time evolution operator for that basis on superconducting hardware. By using error mitigation techniques, electric energy measurements could be reliably extracted following one Trotter-Suzuki time step. This work is a small but important step toward determining what field-theoretic calculations will be possible using near-term devices.

In quantum spin systems, the existence of a spectral gap above the ground state has strong implications for the low-energy physics. We survey recent results establishing spectral gaps in various frustration-free spin systems by verifying finite-size criteria. The talk is based on collaborations with Abdul-Rahman, Lucia, Mozgunov, Nachtergaele, Sandvik, Yang, Young, and Wang.

I will explain how dark energy in cosmology could arise from the

noisy diffusion of energy from the low energy degrees of freedom of matter (described in terms of QFT)

to the fundamental Planckian granularity (expected from quantum gravity). This

perspective leads to a natural model resolving the fine tuning problem associated to the small

value of the cosmological constant. However, recent observations suggest that the dark energy

component in our universe might not be constant and should  instead have grown from the recombination time to the present.

I will present new ideas suggesting a possible explanation within the same framework.

Analytic renormalisation "à la Speer" using a multivariable approach typically leads to meromorphic germs in several variables whose poles are linear.  In particular,  Feynman integrals, multizeta functions and their generalisations, namely  discrete sums on cones and discrete sums associated with trees give rise to meromorphic germs at zero with linear poles. We shall present  a multivariable renormalisation scheme which amounts to a minimal subtraction scheme in several variables. It preserves locality in so far as the  evaluation at poles is expected to factor  on functions with independent sets of variables. Inspired by Speer, we shall discuss a class of generalised evaluators that do the job. Using a theory of  Laurent expansions  on meromorphic germs with linear poles at zero, we shall relate these generalised evaluators to the geometry of cones.

This talk is based on joint work with Pierre Clavier, Li Guo and Bin Zhang.

Many of the most mysterious phenomena in condensed matter physics involve systems near quantum phase transitions where the interplay of quenched disorder and strong interactions likely plays an essential role. Examples include the appearance of "anomalous" 2d metallic phases and the sharing of critical exponents between seemingly different quantum Hall plateau transitions. However, few organizing principles have been developed for understanding quantum critical systems with interactions and disorder, and analytically tractable models have proven rare. In this talk, I will describe some of the first examples of quantum critical theories in 2d characterized by finite disorder and interaction strengths, focusing on particular examples of quenched disorder in systems of (i) Dirac fermions coupled to an emergent gauge field (QED3) and (ii) scalar bosons at their Wilson-Fisher fixed point. Both of these examples exhibit universal features not found together in systems with interactions or disorder alone, such as vanishing density of states, finite DC conductivities, and novel critical exponents.

It is a curious numerology that the dynamical scale associated with the instanton of the electroweak SU(2) gauge group is approximately the energy scale of dark energy. We revisit this electroweak quintessence axion scenario, taking into account observational as well as swampland constraints.

Solving classical and quantum physics many-body systems are amongst the hardest problems in the natural sciences, but also of fundamental importance for applications such as material and drug design. In this talk, I will give a an overview of fundamental physics problems at multiple time- and lengthscales and describe deep learning methods to address them: 1) solving the quantum-chemical electronic Schrödinger equation with deep variational Monte Carlo, 2) learning to coarse-grain many-body systems, and 3) sampling equilibrium states of classical many-body systems with generative learning.

Cloud computing allows users to rent computers from vendors including Amazon, Microsoft, and Google, paying for only the resources they use.  In this tutorial, I will give an intro to some of the services offered by the Google Cloud Platform, including bare and containerized Virtual Machines.

It has long been argued that combining the uncertainty principle with gravity will lead to an effective minimum length at the Planck scale. A particular challenge is to model the presence of a smallest length scale in a manner which respects continuous spacetime symmetries. One path for deriving low-energy descriptions of an invariant minimum length in quantum field theory is based on generalized uncertainty principles. Here I will consider the question how this approach enables one to retain Euclidean or even Lorentzian symmetries. The Euclidean case yields a ultraviolet cutoff in the form of a bandlimit, and this then allows one to apply the powerful Shannon sampling theorem of classical information theory which establishes the equivalence between continuous and discrete representations of information. As a consequence, one obtains discrete representations of fields which are more subtle than a simple discretization of space, and are in fact equivalent to a continuum representation. Quantum fields in this model exhibit a finite density of information and a corresponding regularization of the entanglement of the vacuum, as I will demonstrate in detail. We then examine the Lorentzian symmetry generalization. This case leads to a Lorentz-invariant analogue of bandlimitation, and we discuss the nature of the corresponding sampling theory.