Sommerfeld Lecture Series (ASC)

Fifteenth Arnold Sommerfeld Lecture Series, 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?

Fifteenth Arnold Sommerfeld Lecture Series, “With four parameters I can fit an elephant; with five I can make it wag its tail.” Systems biology models of the cell have an enormous number of reactions between proteins, RNA, and DNA whose rates (parameters) are hard to measure. Models of climate change, ecosystems, and macroeconomics also have parameters that are hard or impossible to measure directly. If we fit these unknown parameters, fiddling with them until they agree with past experiments, how much can we trust their predictions? Multiparameter fits are sloppy; the parameters can vary over enormous ranges and still agree with past experiments. Nonetheless, they can often make useful predictions about future experiments, even allowing for these huge parameter uncertainties: a few stiff combinations of parameters govern the behavior. Third, these sloppy models all appear strikingly similar to one another – for example, the stiffnesses in every case we’ve studied are spread roughly uniformly over a range of over a million. We will use ideas and methods from differential geometry to explain what sloppiness is and why it happens so often. Finally, we shall show that models in physics are also sloppy – that sloppiness makes science possible.

Fifteenth Arnold Sommerfeld Lecture Series, 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.

“With four parameters I can fit an elephant; with five I can make it wag its tail.” Systems biology models of the cell have an enormous number of reactions between proteins, RNA, and DNA whose rates (parameters) are hard to measure. Models of climate change, ecosystems, and macroeconomics also have parameters that are hard or impossible to measure directly. If we fit these unknown parameters, fiddling with them until they agree with past experiments, how much can we trust their predictions? Multiparameter fits are sloppy; the parameters can vary over enormous ranges and still agree with past experiments. Nonetheless, they can often make useful predictions about future experiments, even allowing for these huge parameter uncertainties: a few stiff combinations of parameters govern the behavior. Third, these sloppy models all appear strikingly similar to one another – for example, the stiffnesses in every case we’ve studied are spread roughly uniformly over a range of over a million. We will use ideas and methods from differential geometry to explain what sloppiness is and why it happens so often. Finally, we shall show that models in physics are also sloppy – that sloppiness makes science possible.

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?

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.

Does the world embody beautiful ideas? Pythagoras and Plato intuited that it should, Newton and Maxwell showed, in impressive examples, how it could. Modern physics demonstrates, in depth and detail, that it does. I will narrate, through notable examples, how the concept of beauty in physical law has evolved – and how it continues to guide our quest for ultimate understanding.

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

Localization of the eigenfunctions of quantum particles in a random potential was discovered by P.W. Anderson more than 50 years ago in connection with spin relaxation and charge transport in disordered solids. Later experimentally was realized localization of other quantum particles and classical waves: light, microwaves, sound, cold atoms. At the same time it became clear that the domain of applicability of the concept of localization is much broader. In particular, it can be extended to various problems in condensed matter physics that involve not only disorder, but also interaction between quantum particles. We will consider manifestation of the Anderson localization in model systems: interacting Bose and Fermi gases and disordered spin models. This will allow us to discuss such phenomena as superconductor-metal-insulator (superfluid- normal fluid-glass) transitions. In particular, we will introduce a new class of finite-temperature phase transitions that can exist even in one-dimensional systems and manifest themselves in transport rather than equilibrium properties. We will also be able to get some insight on some problems in quantum computational complexity.

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.