Sandbox Physics · Research routes
Research routes
Each route is a course that starts from one research question, works through the models and methods behind it, and ends at a reproduced result and the questions that are still open.
Routes are independent courses. Where one route uses another, it is listed under “Read first”; you only need the chapters it relies on, not the whole route. The shared basics are in the textbook.
Open the textbook →Suggested reading orders
These orders link routes that build on each other. Start anywhere along an order if you already know the earlier topics.
Field theory
Branches of field theory
Chemistry
Chemistry through fluctuations
Living matter
Quantum experiments
All 42 routes
High-energy physics and field theory
Quantum field theory, renormalization and critical phenomena
Why does averaging over fast, short-wavelength motion change the low-energy parameters, yet still leave stable predictions at long distances?
Gauge theory and effective field theory
How can unresolved high-energy physics be packed into a few low-energy terms, and how do we know when that description fails?
Collider physics: event reconstruction, jets and inference
How do physicists infer a short-range interaction from detector records, and tell jet physics apart from detector effects and chance?
Lattice gauge theory: Gauss’s law, confinement and string breaking
In a model that obeys Gauss’s law at every site, how does the electric flux between two charges grow, and how do new particles screen it?
Scattering amplitudes: helicity, factorization and unitarity
Can symmetry, pole structure and consistency alone fix an interaction without listing every Feynman diagram?
Heavy-ion collisions and quark–gluon matter
Why can matter that is still far from local equilibrium already flow like a fluid, and how do experiments measure its viscosity?
Conformal field theory and the bootstrap
Without knowing the microscopic Hamiltonian, how far can consistency conditions alone pin down a critical system?
Nuclei, cosmology and spacetime
Nuclear structure, reactions and nuclear astrophysics
What part of the nucleus does each picture see: single particles in shells, collective deformation, or reaction data?
Cosmological perturbations, acoustic peaks and inference
How do correlations across the sky limit what the universe is made of, and why can different models predict nearly the same sky?
Holography and quantum gravity
Under stated assumptions, how does information in a boundary quantum state map to geometry in the bulk, and which pictures are only analogies?
Measuring in relativity: clocks, light signals and four-momentum
Why are seeing an event, assigning it a coordinate time and timing it on your own clock three different operations?
Quantum optics and many-body physics
Time–frequency quantum optics: photon sources, modes and pulse gates
Why can two photon-pair sources with the same joint spectral intensity give heralded photons of very different purity?
Cavity and waveguide QED: from one photon to several
Bound states and echoes are clear with one excitation. What is left of them when two photons arrive together?
Quantum optomechanics: cooling, measurement and back-action
Why does a stronger optical readout both measure a mechanical oscillator better and disturb its motion more?
Quantum many-body numerics: entanglement, MPS and DMRG
The state space grows exponentially with system size. How does entanglement structure keep some many-body states computable, and where does that stop?
Physical chemistry
Molecular electronic structure: correlation, DFT and bond breaking
Why can an electronic model that works well near the equilibrium bond length give the wrong physics once the bond is stretched?
Nonadiabatic dynamics: conical intersections and reaction branching
When electronic and nuclear motion cannot be separated, how do we tell which product a reaction will reach?
Free energy and rare events: enhanced sampling and kinetics
Why can trajectories that look well sampled still give a wrong free energy and a badly wrong reaction rate?
Nonlinear and two-dimensional spectroscopy
Peaks that overlap in a linear spectrum: how do several laser pulses separate their coupling, dephasing and chemical exchange?
Electrochemistry and ion transport
When current passes through an electrolyte and an electrode surface, how do charge storage, ion depletion and fluid flow change one another?
Dynamic interfaces: capillary waves, dewetting and Marangoni flow
Surface tension usually smooths an interface. Why does it make thin films, liquid threads and heated surfaces change shape faster?
Biophysics
Single-molecule biophysics: optical tweezers and molecular motors
How does one bead held in optical tweezers reveal a molecule’s elasticity, its random unfolding and its energy-burning steps?
Membranes and vesicles: bending, tethers and shapes
How does a soft membrane with no skeleton hold a stable shape, and how do its thermal ripples reveal its bending stiffness?
Morphogenesis: reaction–diffusion and mechanical feedback
How does a uniform tissue grow a spatial pattern by itself, and how can we tell the roles of diffusion, boundaries and mechanics apart?
Active matter: self-propelled particles and moving defects
Why do particles that keep burning energy cluster without any attraction, and why do their topological defects move on their own?
Microswimming at low Reynolds number
When inertia almost vanishes, why can a swimmer that strokes back and forth never move forward, however fast it strokes?
Statistical physics of evolution and ecology
Why can a variant with no local advantage still take over a whole expanding population?
Statistical physics of neural systems
When neural recordings look close to a critical point, how do we tell real dynamics from an artifact of the analysis?
Non-equilibrium physics and materials
Stochastic thermodynamics: work, heat and hidden entropy
If we observe only part of a system, can we still tell how much energy it dissipates and how far it is from equilibrium?
Complex fluids: elastic instabilities and elastic turbulence
How can a flow with almost no inertia still become violently unsteady in space and time?
Granular matter and jamming
At the same packing density, why do grains sometimes flow and sometimes suddenly bear a load?
Fracture mechanics: Griffith energy, phase-field cracks and branching
Why does a material crack along one path, and why can a faster load make the crack branch or wander?
Micromagnetics: domain walls, spin waves and skyrmions
When the magnetization direction is no longer set by hand, how do exchange, demagnetization, damping and driving decide the pattern?
Geometric elasticity: sheets, shells and multistability
Why does changing the lengths a thin sheet wants to have make it curl into a complex shape with no external force?
Crystal defects and microstructure: dislocations, grains and dendrites
How do energy, diffusion and interface motion together choose the grains and dendrites seen under a microscope?
Nanofriction: stick–slip, thermal activation and superlubricity
A friction coefficient looks simple. How do the atomic-scale periodic potential and the twist between lattices change the energy lost?
Waves, imaging and transport
Kinetic plasma physics: Landau damping and echoes
After the electric field dies away, is the information gone, or hidden in fine structure of the velocity distribution?
Fluctuational electrodynamics: near-field heat transfer and Casimir forces
When two surfaces are much closer than the thermal wavelength, why does the blackbody formula no longer describe the heat flow?
Acoustics and ultrasound: radiation force, echoes and cavitation
How can the same sound beam carry an image, push particles and drive bubbles?
Magnetic resonance imaging: Bloch dynamics and k-space
The coil records one total signal with no position label. How do field gradients turn it into an image that can be reconstructed?
Seismology: elastic waves, source location and inversion
From a few vibration records at the surface, how well can we know the structure underground?
Phonons and heat transport: ballistic flow and second sound
Does a temperature disturbance always spread like ink in water, or can it travel as a wave in some solids?