Claim OwnershipSommerfeld Lecture Series (ASC)
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Every semester the Arnold Sommerfeld Center for Theoretical Physics invites a distinguished theoretical physicist in order to present a short series of lectures with increasing level of specialization. Usually it includes a public talk for a general audience, a theory colloquium and a specialized seminar.
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In this talk, I will discuss the applications of cavity electrodynamics for controlling many-body electron systems. The focus will be on achieving strong coupling between cavities and collective excitations of interacting electrons at Terahertz and IR frequencies. As a specific example I will consider a cavity platform based on a two dimensional electronic material encapsulated by a planar cavity consisting of ultrathin polar van der Waals crystals. I will also discuss how metallic mirrors sandwiching a paraelectric material can modify the transition into the ferroelectric state. Finally, I will review a general question of theoretically describing ultrastrong coupling waveguide QED. I will present a novel approach to this problem based on a non-perturbative unitary transformation that entangles photons and matter excitations. In this new frame of reference, the factorization between light and matter becomes exact for infinite interaction strength and an accurate effective model can be derived for all interaction strengths.
It is commonly recognized that scientific discoveries result in new technologies. In this talk we will discuss the reverse: behind every conceptual breakthrough lies some technological advance. To illustrate this point, we will review how modern progress in optical technologies is revolutionizing our understanding of quantum matter. We will discuss experiments that showed that we can optically control materials, and even suggest light-induced superconductivity. We’ll delve into a new type of magnetism, discovered in layered materials using sensitive light reflection experiments rather than measurements of magnetization. We’ll cover how we can use optical lattices with tunable geometries to create several paradigmatic models of electron systems and shed light onto their puzzling properties. We will finally discuss why understanding technology is important for theoretical physicists.
Recent experiments suggest the phenomenon of light induced superconductivity above Tc in two different materials: fullerene superconductor K3C60 and high Tc cuprate YBCO. I will discuss the distinct phenomena taking place in these systems. In K3C60, the unusual character of electron-phonon interactions results in enhanced BCS pairing through optical driving and the slow relaxation of superconducting correlations after they have been created. In YBCO the light induced state is short lived and its properties can be explained from the perspective of a Floquet material. I will present a general theoretical framework for understanding Floquet materials, in which the pump-induced oscillations of a collective mode lead to the parametric generation of excitation pairs. This can result in features such as photo- induced edges in reflectivity, enhancement of reflectivity, and even light amplification.
The density of states of a unitary quantum field theory is known to have a universal behavior at high energy. In two dimensions, this behavior is described by the Cardy formula. When the theory has symmetry, it is interesting to find out how the Hilbert space is decomposed into irreducible representation of the symmetry. In this talk, I will derive universal formulas for the decomposition of states at high energy with respect to both internal global symmetry and spacetime symmetry. The formulae are applicable to any unitary quantum field theory in any spacetime dimensions. As a byproduct, we resolve one of the outstanding questions on the stability of non-abelian black holes. We will also derive the high energy asymptotic behavior of correlation functions. (Based on work with Nathan Benjamin, Daniel Harlow, Monica Kang, Jaeha Lee, Sridip Pal, David Simmons-Duffin, Zhengdi Sun, and Zipei Zhang.)
Although predictions of quantum gravity are typically at extremely high energy, several non-trivial constraints on its low energy effective theory have been found over the last decade or so. I will start by explaining why the unification of general relativity and quantum mechanics has been difficult. After introducing the holographic principle as our guide to the unification, I will discuss its use in finding constraints on symmetry in quantum gravity. I will also discuss other conjectural constraints on low energy effective theories, collectively called swampland conditions, and their consequences.
We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient computation. We study the correlation between quantum chaos diagnostics, the circuit expressibility and the optimization of the control parameters.
Fluid turbulence is a major unsolved problem of physics exhibiting an emergent complex structure from simple rules. We will briefly review the problem and discuss three avenues towards its solution: field theory, holography and machine learning.
The amazing and mysterious laws of the quantum world will be outlined: superposition, entanglement and no cloning. Their impact on science and technology will be discussed, including quantum teleportation, secure quantum communication, quantum money, powerful quantum algorithms and quantum machine learning.
Gravitational wave signals from coalescing binary black holes are detected, and analyzed, by using large banks of template waveforms. The construction of these templates makes an essential use of the analytical knowledge of the motion and radiation of gravitationally interacting binary systems. A new angle of attack on gravitational dynamics consists of considering (classical or quantum) scattering states. Modern amplitude techniques have recently given interesting novel results. These results are reaching a level where subtle conceptual issues arise (quantum-classical transition, radiative effects versus conservative dynamics, massless limit,...).
The observation of gravitational wave signals by the two interferometers of the Laser Interferometer Gravitational-Wave Observatory (LIGO), and by the Virgo interferometer, has brought the first direct evidence for the existence of black holes, and has also been the first observation of gravitational waves in the wave-zone. After reviewing the historical path that led to our understanding of gravitational waves and black holes, the colloquium will present the theoretical developments on the motion and gravitational radiation of binary black holes that have been crucial in interpreting the LIGO-Virgo
events as being emitted by the coalescence of two black holes.
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.
1Thermodynamics 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.
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 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.
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.
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?
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.
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?
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.
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.
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