Statistical and Nonlinear Physics

13 topics

• Absorbing-state transitions and self-organized criticality

  5 problems

  Some processes, like an epidemic, can die out completely and then never restart; the boundary between dying out and spreading forever is an absorbing-state transition. Self-organized criticality is the idea that some systems tune themselves to such a boundary, producing avalanches of all sizes.

• Arrow of time and the low-entropy past

  3 problems

  The laws of motion work the same forwards and backwards in time, yet eggs break and never unbreak. Statistical physics explains this only if the universe started in a very special low-entropy state, and why it did is not explained.

• Extreme events and predictability in chaotic systems

  4 problems

  Chaotic systems such as the weather amplify small errors, so forecasts fail after a while, and they sometimes produce rare huge events such as rogue waves. Physicists want the ultimate forecast limits and the laws that govern the statistics of the rare extremes.

• Thermalization of nearly integrable lattices (FPUT)

  4 problems

  In 1955 Fermi, Pasta, Ulam and Tsingou simulated a chain of weakly nonlinear springs expecting energy to spread evenly among all vibration modes, and found it kept returning to where it started. How long such nearly solvable systems take to reach thermal equilibrium, and whether they always do, is still being settled.

• Critical behavior of the 3D Ising model

  3 problems

  The Ising model is the simplest model of a magnet, with spins that point only up or down. It was solved exactly in two dimensions in 1944, but in three dimensions its behavior at the critical temperature is known only from numerics.

• KPZ growth in two and more dimensions

  5 problems

  When a surface grows by random deposition with a speed that depends on its slope, as for a burning paper edge or a growing crystal film, its roughness follows universal laws called the KPZ class. In one dimension these laws are solved exactly; for two-dimensional surfaces and beyond they are mostly unknown.

• Statistical physics of learning and inference

  6 problems

  Methods from the physics of disordered systems explain how well large learning machines and statistical estimators can work, and when a hidden signal is present in data but no fast algorithm can find it. The same tools describe memory networks that store and recall patterns.

• Statistical physics of long-range interacting systems

  3 problems

  When every particle feels every other one, as with gravity or charges in a plasma, energy does not add up over parts in the usual way. Such systems can have negative heat capacity and can stay out of equilibrium for times that grow with the number of particles.

• Anomalous relaxation and Mpemba effects

  6 problems

  A system that starts farther from equilibrium can sometimes reach equilibrium sooner than one that starts closer, as in the claim that hot water can freeze before cold water. Physicists ask when this happens, why, and whether it has a common explanation in classical and quantum systems.

• Nonequilibrium steady states of driven systems

  5 problems

  A system kept out of equilibrium by a steady drive, such as a wire carrying current or a chain of atoms held between a hot and a cold wall, settles into a state with constant flows. No general rule gives the probabilities of its states, and transport in such states can behave in unexpected ways.

• Spin glasses in finite dimensions

  6 problems

  A spin glass is a magnet whose atomic magnets interact with random signs, so below a temperature they freeze into a disordered pattern. Physicists still disagree on what that frozen state is like in three dimensions.

• Stochastic thermodynamics bounds

  3 problems

  Small systems such as molecular motors are kicked around by thermal noise, so the energy and particle flows through them fluctuate. Exact inequalities link how much energy they dissipate to how precise and fast they can be, and the sharpest such bounds are still being found.

• Synchronization of coupled oscillators

  4 problems

  Fireflies flashing together, heart cells beating in step and power-grid generators turning at one frequency are all examples of many coupled oscillators synchronizing. The Kuramoto model captures the basic transition, but disorder, finite size and spatial structure leave open questions.