Sommerfeld Lecture Series (ASC)

In November 2015, Albert Einstein finalized a new theory of gravitation, General Relativity (GR), which describes gravitation as a deformation of the structure of space-time. It took many years of conceptual deepening and observational discoveries to fully grasp several of the most novel predictions of GR (gravitational waves, black holes, cosmological expansion). GR is the current standard model for the gravitational interaction, and plays a crucial role in the description of many physical systems: solar system, neutron stars, binary pulsars, galaxies, black holes, cosmology. For many years, GR was considered as being completely separate from the (quantum) description of the other interactions. However, several theoretical frameworks (string theory, supergravity) point towards a key role of GR in the search for a unified description of physics. GR has passed with flying colors all current experimental tests, but some puzzles remain unanswered.

In many modern materials, electrons quantum‐entangle with each other across long distances, and produce new phases of matter, such as high temperature super‐conductors. We face the challenge of describing the entanglement of 10^{23} electrons, which is being met by many ideas, including some drawn from string theory.

Thermodynamics provides a robust conceptual framework and set of laws that govern the exchange of energy and matter. Although these laws were originally articulated for macroscopic objects, nanoscale systems also exhibit “thermodynamic-like” behavior – for instance, biomolecular motors convert chemical fuel into mechanical work. To what extent can the laws of thermodynamics be scaled down to apply to individual microscopic systems, and what new features emerge at the nanoscale? I will describe some of the recent progress and challenges associated with addressing these questions.

From copper-oxide superconductors to rare-earth compounds, materials with strong electronic correlations have focused enormous attention over the last two decades. Solid-state chemistry, new elaboration techniques and improved experimental probes are constantly providing us with examples of novel materials with surprising electronic properties, the latest example being the recent discovery of iron-based high-temperature superconductors. In this colloquium, I will emphasize that the classic paradigm of solid-state physics, in which electrons form a gas of wave-like quasiparticles, must be seriously revised for strongly correlated materials. Instead, a description accounting for both atomic-like excitations in real-space and quasiparticle excitations in momentum space is requested. I will review how Dynamical Mean-Field Theory -an approach that has led to significant advances in our understanding of strongly correlated materials- fulfills this goal. New frontiers are also opening up, which bring together condensed-matter physics and quantum optics. `Artificial materials' made of ultra-cold atoms trapped by laser beams can be engineered with a remarkable level of controllability, and allow for the study of strong- correlation physics in previously unexplored regimes.

The quantum adiabatic theorem governs the evolution of a wavefunction under a slowly time-varying Hamiltonian. I will consider the opposite limit of a Hamiltonian that is varied impulsively: a strong perturbation U(x,t) is applied over a time interval of infinitesimal duration e->0. When the strength of the perturbation scales like 1/eˆ2, there emerges an interesting dynamical behavior characterized by an abrupt displacement of the wave function in coordinate space. I will solve for the evolution of the wavefunction in this situation. Remarkably, the solution involves a purely classical construction, yet describes the quantum evolution exactly, rather than approximately. I will use these results to show how appropriately tailored impulses can be used to control the behavior of a quantum wavefunction.

In recent decades, physicists and astronomers have discovered two beautiful Standard Models, one for the quantum world of extremely short distances, and one for the universe as a whole. Both models have had spectacular success, but there are also strong arguments for new physics beyond these models. In this lecture, we will review these models, their successes and their shortfalls. We will describe how experiments in the near future could point to new physics suggesting a profound conceptual revolution, which could change our view of the world.

In a letter written in 1867, James Clerk Maxwell described a hypothetical creature: a “neat-fingered being” capable of separating fast molecules from slow ones. Maxwell mused that such a creature would seem to violate the second law of thermodynamics, which had recently been enunciated by Rudolf Clausius and is now a pillar of our understanding of the natural world. Over the past century and a half, that hypothetical creature – Maxwell’s demon – has wandered through the thoughts of eminent scientists, has appeared in research articles and popular cultural references, and in recent years has been observed in laboratory experiments. Along the way, the mischievous devil has sharpened our understanding of the second law of thermodynamics, exposing a deep relationship between physics and information. I will give an overview of the questions raised and the lessons learned from contemplating Maxwell’s demon, and I will summarize our current understanding of this topic. This story highlights the importance of imagination and whimsy in scientific discovery.

Aside from enabling revolutionary future technologies, quantum information science is providing powerful new tools for attacking deep problems in fundamental physical science. In particular, the recent convergence of quantum information and quantum gravity is sparking exciting progress on some old and very hard questions.

Spontaneous Symmetry Breaking is a very universal concept applicable for a wide range of subjects: crystal, superfluid, neutron stars, Higgs boson, magnets, and many others. Yet there is a variety in the spectrum of gapless excitations even when the symmetry breaking patterns are the same. We unified all known examples of internal symmetries in a single-line Lagrangian of the low-energy effective theory. In addition, we now have a better understanding of what happens with spacetime symmetries, and predict gaps for certain states exactly based on symmetries alone.

One hundred years ago, D’Arcy Thompson – a nineteenth century polymath, working at the turn of the twentieth century – wrote a beautiful monograph, “On Growth and Form”, in which he pondered the geometry of living forms and how it emerges in the process of Morphogenesis. Thompson was ahead of his time. Genetics and Developmental Biology have since come a long way in elucidating the general and particular aspects of Morphogenesis, uncovering the key genes and molecules that underlie the process in different animals and plants. Yet, Thompson’s agenda of understanding how developmental processes actually specify the geometry of tissues, limbs and organs is far from complete. A particular challenge is to bridge the gap between microscopic scales, where molecular mechanisms operate, and the macroscopic scales of animal “shape and form”. This challenge offers much for a Theoretical Physicist to think about. This talk will provide some examples, relating the study of order in the arrangement of fly wing hairs to ferromagnetism and uncovering an unexpected wealth of mechanical phenomena in the study of cellular flows in a fly embryo.

Where do we come from? Science is making progress on this age-old question of humankind. The Universe was once much smaller than the size of an atom. Small things mattered in the small Universe, where quantum physics dominated the scene. To understand the way the Universe is today, we have to solve remaining major puzzles. The Higgs boson that was discovered recently is holding our body together from evaporating in a nanosecond. But we still do not know what exactly it is. The mysterious dark matter is holding the galaxy together, and we would not have been born without it. But nobody has seen it directly. And what is the very beginning of the Universe?

Our understanding of simple solids, is firmly grounded on the Fermi liquid concept and powerful computational techniques built around the density functional theory. These ideas form the basis of our “standard model” of solid state physics and have provided us with an accurate description of many materials of great technological significance. Correlated electron systems are materials for which the the standard model of solid state physics fails dramatically. The best known example being the copper oxide high temperature superconductors. Correlated electron materials continue to be discovered accidentally and surprise us with their exceptional physical properties and their potential for new applications. The most recent example is provided by the iron arsenide based high temperature superconductors. From a theoretical perspective describing strongly correlated electron systems pose one of the most difficult non-perturbative challenges in physics. In this colloquium I will give an elementary introduction to the field of strongly correlated electron materials and Dynamical Mean Field Theory (DMFT) a non perturbative method which provides a zeroth order picture of the strong correlation phenomena in close analogy with the Weiss mean field theory in statistical mechanics. Applications materials containing f and d electrons will be presented to show how the anomalous properties of correlated materials emerge from their atomic constituents. I will conclude with an outlook of the challenges ahead and the perspectives for a rational material design.

I review what we know about dark matter right now and some hints about its nature. In particular, I discuss candidates away from the conventional WIMP (Weakly Interactive Massive Particle) paradigm.

Superconductivity is a state of matter where electrons can flow without resistance and where magnetic fields are expelled. It was discovered serendipitously more than a hundred years ago. Today, superconductors are essential components of medical imaging devices as well as high energy particles accelerators. Understanding this phenomena was one of the greatest intellectual challenges of the twentieth century. A dramatic advance was provided by the BCS (Bardeen Cooper Schrieffer) theory 45 years after. It posits that superconductivity is the result of macroscopic condensation of electron pairs, which are held together by the vibrations of the lattice. The condensate is a macroscopic quantum objects and its rigidity accounts for its striking macroscopic properties. The BCS theory was so successful that by the early 70’s superconductivity was considered a completely understood subject with the maximum achievable critical temperature having been reached experimentally around 30K. In the late 80’s this field of research took a dramatically turn with the discovery of new ceramic compounds which superconduct at temperatures as high as 160 K. These materials, cannot be described by straightforward extensions of the BCS theory. Scientists are still working on finding new explanations for these materials and we will describe the challenge they pose. The quest for room temperature superconductivity thus continues. A breakthrough in this field would have unimaginable consequences, changing the way we transmit electricity from its generation to its consumption to the way we design computers.

Mathematics has proven to be "unreasonably effective" in understanding nature. The fundamental laws of physics can be captured in beautiful formulae. Remarkably, ideas from quantum theory turn out to carry tremendous mathematical power as well, even though we have little daily experience dealing with elementary particles. The bizarre world of quantum physics not only represents a more fundamental description of nature than what preceded it, it also provides a rich context for modern mathematics. In recent years ideas from quantum field theory, elementary particles physics and string theory have completely transformed mathematics, leading to solutions of deep problems, suggesting new invariants in geometry and topology. Could the logical structure of quantum theory, once fully understood and absorbed, inspire a new realm of mathematics that might be called “quantum mathematics” and will this new language enable us to formulate the fundamental laws of physics?

The theory of phase transitions splits between abrupt transitions (nucleation and growth, critical droplets) and continuous transitions (scaling and universality). I’ll discuss wonderful biophysics examples for each: Michelle Wang’s twisting single molecules of DNA, and with Sarah Veatch’s discovery of universal Ising critical fluctuations in living cell membranes. (1) Plectonemes are the helically wound loops formed in garden hoses and electrical cords when they are overtwisted. Wang's group studies their equilibrium formation in overtwisted DNA, where they observe reversible transitions over the free energy barrier. This system, with well-known continuum elasticity and a controlled disorder, forms an unusual opportunity to test our ideas about the nucleation of phase transitions, and to generalize them to include randomness. (2) Sarah Veatch in Baird's group has recently made an amazing discovery – cell membranes, when stripped from the cytoskeleton, sit just above an Ising critical point. Cooled by 5%, they phase separate into two components: differing mixtures of lipids and proteins. We've tried to answer three questions: Why don't intact cells undergo this phase separation? Why would a cell want to sit near a critical point? What does statistical mechanics tell us about lipid rafts and the formation of protein aggregates?

Random matrix models are ubiquitous in physics and have been studied from many perspectives. One important application is producing exactly solvable toy models of quantum gravity and string theory. These models relate to deep mathematical structures of the moduli space of Riemann surfaces. Recent work has extended these models to open strings and surfaces with boundaries. This generalization is less straightforward that one imagines and involves the introduction of additional degrees of freedom. These models have become relevant in recent studies of the gravitational dual of the SYK model, two-dimensional black holes, and gravity with constant curvature. Based on work done in collaboration with Edward Witten.

A piece of paper or candy wrapper crackles when it is crumpled. A magnet crackles when you change its magnetization slowly. The earth crackles as the continents slowly drift apart, forming earthquakes. Crackling noise happens when a material, when put under a slowly increasing strain, slips through a series of short, sharp events with an enormous range of sizes. There are many thousands of tiny earthquakes each year, but only a few huge ones. The sizes and shapes of earthquakes show regular patterns that they share with magnets and many other systems. This suggests that there must be a shared scientific explanation. We shall hear about crackling noise and that it is a symptom of a surprising truth: the system behaves the same on small, medium, and large scales.

Turbulence is the last great unsolved problem of classical physics. But there is no consensus on what it would mean to actually solve this problem. In this colloquium, I propose that turbulence is most fruitfully regarded as a problem in non-equilibrium statistical mechanics, and will show that this perspective explains turbulent drag behavior measured over 80 years, and makes predictions that have been experimentally tested in 2D turbulent soap films. I will also explain how this perspective is useful in understanding the laminarturbulence transition, establishing it as a non-equilibrium phase transition whose critical behavior has been predicted and tested experimentally. This work connects transitional turbulence with statistical mechanics and renormalization group theory, high energy hadron scattering, the statistics of extreme events, and even population biology.

This talk is devoted to quantum propagation of dipole excitations in two dimensions in the presence of disorder. This problem differs from the conventional Anderson localization due to existence of long range hops. We found that the critical wave functions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T-invariant the states are critical for all values of the parameters. Otherwise, there can be a “normal metal - perfect metal" transition between this “ordinary" diffusion and the Levy-flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified non-linear supermatrix

Life on Earth is wonderfully diverse, with a multitude of life forms, structures and evolutionary mechanisms. However, there are two aspects of life that are universal --- shared by all known organisms. These are the genetic code, which governs how DNA is converted into the proteins making up your body, and the unexpected left-handedness of the amino acids in your body. One would expect that your amino acids were a mixture of left and right-handed molecules, but none are right handed! In this talk, I describe how these universal aspects of biology can be understood as arising from evolution, but generalised to an era where genes, species and individuality had not yet emerged. I will also discuss to what extent one can find general principles of biology that can apply to all life in the universe, and what this would mean for the nascent field of astrobiology.

During more than 100 years of its history Quantum Mechanics passed all of the experimental checks and transformed itself from a counterintuitive concept to the undisputable foundation of the modern physics. Along with this it did not lose its ability to surprise and still allows for new astonishing discoveries such as Bose-Einstein condensation of ultracold gases. Manifestations of the quantum mechanics on the macroscopic scales are especially impressive. In recent years the interest in condensed matter physics evolved from studying bulk properties of naturally occurring materials to constructing complex materials and systems not found in nature, and controlling rather than observing quantum mechanics. Within this tendency the concept of quantum condensation remains the central one. Controllable quantum behavior can be achieved in systems of weakly coupled locally coherent elements. An array of Josephson junctions between superconducting islands is a representative but not the exclusive example. Other examples of such systems are ultracold gases in optical lattices, excitons and photons in semiconductor cavities, etc. Global phase coherence exists in these systems can be destroyed by reducing the coupling. In Josephson arrays this destruction is manifested by the phase transition from superconducting to insulating state. This talk is about the relation between the classical and the quantum worlds. Some of the quantum effects, e.g. interference, can be realized in classical systems, others like Einstein- Podolsky-Rosen paradox are “truly quantum”. It turns out that the quantum condensation has a classical analog: synchronization (mode-locking) in nonlinear dynamics. Discovered by Huygens almost 350 years ago the synchronization is the most fundamental nonlinear phenomenon. However the synchronization happens when the system is driven by outside forces, while one can think about BEC in thermodynamic equilibrium. On the other hand quantum systems can be also driven. One of the familiar examples is coherent state of photons generated by a laser: this generation happens only in the presence of a pumping and does not exist in the equilibrium. The interest to the quantum systems out of equilibrium is rapidly growing due to the desire to control and manipulate quantum states. I will discuss the similarities between macroscopic quantum and classical behaviors. It looks like new interesting physics emerges on the crossroads of the quantum mechanics, condensed matter physics, and nonlinear dynamics.

Advances in light sources and time resolved spectroscopy have made it possible to excite specific atomic vibrations in solids and to observe the resulting changes in electronic properties. I argue that in narrow-band systems the dominant symmetry-allowed coupling between electron density and dipole active modes implies an electron density-dependent squeezing of the phonon state which provides an attractive contribution to the electron-electron interaction, independent of the sign of the bare electron-phonon coupling and with a magnitude proportional to the degree of laser-induced phonon excitation. Reasonable excitation amplitudes lead to non-negligible attractive interactions that may cause significant transient changes in electronic properties including superconductivity. The mechanism is generically applicable to a wide range of systems, offering a promising route to manipulating and controlling electronic phase behavior in novel materials.

String theory was originally constructed as a unification of the quantum field theory of elementary particles with Einstein's theory of gravitation. Unexpectedly, it has led to the discovery of new "dualities" which have given us a new perspective on quantum field theories not coupled to gravity. Some of the latter theories are relevant to the strongly-interacting quantum many body problems of condensed matter physics. I will survey some of the challenging open problems associated with condensed matter experiments, and discuss the insights gained from string theory.

This talk will present an overview of recent progress towards a solution of one of the grand-challenges of modern science: understanding the properties of interacting electrons in molecules and solids. After an introduction to the physics I will argue our theoretical understanding of a basic model system, the two dimensional Hubbard model, has reached the level that we can say with confidence that its superconducting properties capture key aspect of the high-Tc superconductivity in copper-oxide materials. I will then summarize the current status of our extension of the methods to fully physically realistic systems, emphasizing the areas of theoretical uncertainty and the prospects for resolution.

Cosmic strings are linear defects that could be formed at a phase transition in the early universe. Strings are predicted in a wide class of particle physics models. In particular, fundamental strings of superstring theory can have astronomical dimensions and play the role of cosmic strings. I will discuss recent progress in understanding the evolution of cosmic strings and possible ways of detecting them.

Superconductivity, the ability of certain materials to conduct electricity with no resistance whatsoever, has fascinated scientists since its discovery by Kammerlingh-Onnes in 1911. While much has been understood, the question of predicting which materials will become superconducting, and at what temperatures, remains one of the grand challenges of modern materials theory. This talk will outline the evolution of our understanding as the subject has progressed from its primitive beginnings through the ''bronze age'' marked by the 1986 discovery of high temperature superconductivity in copper-oxide compounds to the present-day ''iron age'' of the Fe-As based superconducting materials. The current status of the theory of the origin of superconductivity will be described.

According to the Landau description of Fermi liquids, low- energy excitations in metals are constructed out of quasiparticles – long-lived excitations which have the same quantum numbers as those of an electron in vacuum. In metals with strong correlations however, quasiparticles become fragile: they are destroyed above a characteristic energy or temperature scale, the quasiparticle coherence scale. This energy scale can be remarkably low, even in materials which are not close to a Mott metal-insulator transition, for example as a result of the Hund's rule coupling. I will provide evidence that this is relevant for many materials, especially oxides of the 4d transition metals. In other materials, such as cuprates, quasiparticles are destroyed selectively in specific regions of momentum-space. The understanding of charge and thermal transport in such ``bad metals'' is a key issue, with both fundamental and practical implications.

A combination of ideas originating from Condensed Matter physics, Supersymmetric Field Theory, and AdS/CFT has led to a detailed web of conjectured dualities. These relate the long distance behavior of different short distance theories. These dualities clarify a large number of confusing and controversial issues in Condensed Matter physics and in the study of 2+1 dimensional quantum field theory.

Which property of a material is more familiar to us than its color? And yet, the strange laws of quantum mechanics, which rule atoms, electrons and photons, are key to the understanding of this most beautiful feature! The invention and engineering of novel materials has shaped human civilization, from the Bronze age to the Silicon age. This lecture is an invitation to explore materials down to the scale of their intimate constituents – atoms and electrons. We'll address questions such as: do we master quantum mechanics well enough today to explain how materials behave from the only knowledge of the atoms which build them? Have we reached the stage where the principles of quantum mechanics allow for the design of a novel material with specific functionalities?

Global symmetries and gauge symmetries have played a crucial role in physics. The idea of duality demonstrates that gauge symmetries can be emergent and might not be fundamental. During the past decades it became clear that the circle of ideas about emergent gauge symmetries and duality is central in different branches of physics including Condensed Matter Physics, Quantum Field Theory, and Quantum Gravity. We will review these developments, which highlight the unity of physics.