Sommerfeld Theory Colloquium (ASC)

In a simple, constant environment does evolution continue forever? Does extensive diversification via small genetic and ecological differences? What are general evolutionary consequences of organismic complexity? Hints from long term laboratory evolution experiments and findings from genomic data of extensive within-species bacterial diversity motivate considering these questions. Several simple models of evolution with ecological feedback will be introduced, with the high dimensionality of phenotype space enabling analysis by statistical physics approaches.

Much of condensed matter physics is concerned with understanding how different kinds of order emerge from interactions between a large number of simple constituents. In ordered phases such as crystals, magnets, and superfluids, the order is understood through ”symme- try breaking”: in a crystal, for example, the continuous symmetries of space under rotations and translations are not reflected in the ground state. A major discovery of the 1980s was that electrons confined to two dimensions and in a strong magnetic field exhibit a completely different, ”topological” type of order that underlies the quantum Hall effect.

In the past few years, we have learned that topological order also occurs in some three-dimensional materials, dubbed ”topological in- sulators”, in zero magnetic field. Spin-orbit coupling, an intrinsic property of all solids, drives the formation of the topological state. This talk will explain what topological order means, how topologi- cal were predicted and discovered, and how they realize the ”axion electrodynamics” studied by particle physicists in the 1980s. Some possible applications of these new materials are discussed in closing.

In the standard picture of a quantum phase transition, a single quantum critical point separates the phases at zero temperature. Here

we show that the two-dimensional case is considerably more complex. Instead of the single point separating the antiferromagnet from

the normal metal, we have discovered a broad region between these two phases where the magnetic order is destroyed but certain areas of the Fermi surface are closed by a large gap. This gap reflects the formation of a novel quantum state characterized by a superposition of d-wave superconductivity and a quadrupole density wave

(QDW), which builds a checkerboard pattern with a period incommensurate with that of the original spin density wave. At moderate temperatures both orders co-exist over comparatively large distances but thermal fluctuations destroy the long-range order. Below

a critical temperature the

fluctuations are less essential and super-

conductivity becomes stable. Applying a magnetic field destroys the superconductivity but establishes QDW. In addition to these phases

we obtain also a charge density wave (CDW) arising as a result of interaction of electrons with superconducting fluctuations. This phase

is possible when the superconductivity is destroyed by either thermal fluctuations or a magnetic field. The results of our theory can serve as explanation of recent experiments on cuprates performed with the help of STM, NMR, hard and resonant soft X-ray scattering, sound

propagation, and other techniques.

This talk will overview the history of primordial black hole (PBH) research from the first papers around 50 years ago to the present time. I will first discuss their possible formation mechanisms, including critical collapse from inflationary fluctuations and various types of phase transition. I will then describe the numerous constraints on the number of PBHs from various quantum and astrophysical processes, this being the main focus of PBH research until recently. In the last decade there has been a shift of emphasis to the search for evidence for PBHs 13 what I term the bright side. So the final part of my talk will present this evidence, with particular emphasis on their possible role as dark matter candidates, sources of gravitational waves and seeds for supermassive black holes and early cosmic structures.

Einstein is well known for his rejection of quantum mechanics in the form it emerged from the work of Heisenberg, Born and Schrodinger in 1926. Much less appreciated are the many seminal contributions

he made to quantum theory prior to his �final scientifi�c verdict, that

the theory was at best incomplete. In this talk I present an overview

of Einsteins many conceptual breakthroughs and place them in historical context. I argue that Einstein, much more than Planck, introduced the concept of quantization of energy in atomic mechanics.

Einstein proposed the photon, the fi�rst force-carrying particle discovered for a fundamental interaction, and put forward the notion of wave-particle duality, based on sound statistical arguments 14 years before De Broglies work. He was the fi�rst to recognize the intrinsic

randomness in atomic processes, and introduced the notion of transition probabilities, embodied in the A and B coeffi�cients for atomic emission and absorption. He also preceded Born in suggesting the interpretation of wave fi�elds as probability densities for particles, photons, in the case of the electromagnetic �field. Finally, stimulated by

Bose, he introduced the notion of indistinguishable particles in the

quantum sense and derived the condensed phase of bosons, which is

one of the fundamental states of matter at low temperatures. His

work on quantum statistics in turn directly stimulated Schrodinger

towards his discovery of the wave equation of quantum mechanics. It

was only due to his rejection of the �final theory that he is not generally recognized as the most central �figure in this historic achievement

of human civilization.

Metals are found frequently in nature and their properties are usually

very well described within Landaus Fermi liquid theory. Various

strongly correlated materials exhibit strange metallic phases which do

not fit into the Fermi-liquid framework, however. The theoretical description

of such non-Fermi liquids remains one of the main unsolved

problems in condensed matter physics. In this talk I will give an

introduction to the problem and show how interesting strongly coupled

field theories arise in the low energy description of such states,

which are still very poorly understood. I will focus on the paradigmatic

problem of a metal coupled to fluctuations of a critical Ising

order parameter and discuss unexpected scaling properties at finite

temperature.

I will discuss the statistical physics of random growth processes which, on the one hand, model the non-perturbative gauge dynamics, emergence of space geometry in string theory on the other, yet could also model the evolution of language(s).

To pinpoint the microscopic mechanism for superconductivity has

proven to be one of the most outstanding challenges in the physics of

correlated quantum matter. Thus far, the most direct evidence for

an electronic pairing mechanism is the observation of a new symmetry

of the order-parameter, as done in the cuprate high-temperature

superconductors. Like distinctions based on the symmetry of a locally

defi�ned order-parameter, global, topological invariants allow for

a sharp discrimination between states of matter that cannot be transformed

into each other adiabatically. Here we propose an unconventional

pairing state for the electron

uid in two-dimensional oxide

interfaces and establish a direct link to the emergence of nontrivial

topological invariants. Topological superconductivity and Majorana edge states can then be used to detect the microscopic origin for

superconductivity. In addition, we show that also the density wave

states that compete with superconductivity sensitively depend on the

nature of the pairing interaction. Our conclusion is based on the special

role played by the spin-orbit coupling and the shape of the Fermi

surface in SrTiO3/LaAlO3-interfaces and closely related systems.

Learning algorithms using deep neural networks are currently having a major impact on basic sciences. The physics of complex quantum systems is no exception, with multiple applications that constitute a new field of research. Examples include the representation and optimization of wave functions of quantum systems with large numbers of degrees of freedom (neural quantum states), the determination of wave functions from measurements (quantum tomography), and applications to the electronic structure of materials, such as the determination of more precise density functionals or the learning of force fields to accelerate molecular dynamics simulations. I will survey some of these applications, with an emphasis on neural quantum states.

Since the discovery of the first binary black-hole merger in 2015, analytical and numerical solutions to the relativistic two-body problem have been essential for the detection and interpretation of more than 100 gravitational-wave signals from compact-object binaries. Future experiments will detect black holes at cosmic dawn, probe the nature of gravity and reveal the composition of neutron stars with exquisite precision. Theoretical advances (of up to two orders of magnitude in the precision with which we can predict relativistic dynamics) are needed to turn gravitational-wave astronomy into precision laboratories of astrophysics, cosmology, and gravity. In this talk, I will discuss recent advances in modeling the two-body dynamics and gravitational radiation, review the science that accurate waveform models have enabled with LIGO-Virgo gravitational-wave observations, and highlight the theoretical challenges that lie ahead to fully exploit the discovery potential of increasingly sensitive detectors on the ground, such as the Einstein Telescope and Cosmic Explorer, and in space, such as the Laser Interferometer Space Antenna (LISA).