What Am I Seeing?

This simulation visualizes a Complex Scalar Field evolving under the Ginzburg-Landau equation. Instead of arrows, you see a continuous field of color and light.

  • Color (Hue): Represents the Phase (angle) of the quantum wavefunction.
  • Brightness: Represents the Magnitude (density) of the field.
  • Black Dots: These are Topological Defects (Vortices).

Q: What are the black dots?

These are Vortices 🌀. In this model, the field wants to have a magnitude of 1 (bright), but if the phase twists by 360° around a specific point, the math forces the magnitude to drop to zero at the center to avoid a discontinuity.

Think of them as the "particles" of this universe. They are stable knots that cannot just fade away; a vortex must collide with an anti-vortex to annihilate 💥.

Q: Why do new dots appear at the edges when I click?

The universe is a Torus 🍩 (it wraps around). A Torus cannot hold a single topological charge (+1) without breaking. When you click to spawn one vortex, the math creates a Branch Cut—a "seam" where the phase doesn't match up at the edge of the world.

The physics engine instantly spawns a ghost Anti-Vortex (-1) at the seam to heal this tear and restore the total charge to zero. This violent correction is why you see the "messy" birth of particles!

Q: How do I annihilate them? 💥

Try double-clicking! The simulation alternates between spawning a +1 vortex and a -1 vortex on each click (like flipping a switch). If you click roughly in the same spot twice, the second vortex will cancel out the first one, and the field will heal back to a smooth state.

Q: What are the View Modes?

  • Combined: Shows physics reality (Phase + Magnitude).
  • Phase: Shows mathematical topology. You can clearly see the "Branch Cuts" (seams) here!
  • Density: Shows "Mass". It looks like black particles in a white fluid.

Q: Is this real Quantum Mechanics? ⚛️

Yes, but with a twist! You are simulating a Macroscopic Wavefunction. Unlike the Schrödinger equation which describes a single particle, this field describes a "Condensate" (like a Superconductor or Superfluid) where billions of particles lock into the exact same state and behave like a single, giant quantum object.

  • Quantization: The black dots demonstrate fundamental quantum topology. Because the phase must wrap exactly 360° to match up, rotation is quantized. You can have 1 twist, or 2 twists, but never 1.5 twists.
  • Dissipation: While standard quantum mechanics preserves energy forever, this simulation includes "dissipation." The system sheds energy to relax into its lowest energy state (the ground state), which is why you see the initial chaos settle into stable patterns.

Q: What is the Physics Equation? 📜

This uses the Time-Dependent Ginzburg-Landau (TDGL) equation: 

∂ψ/∂t = D∇²ψ + ψ(1 - |ψ|²)

It describes systems undergoing a phase transition, such as:

  • Superconductors: The onset of superconductivity and magnetic flux tubes.
  • Superfluids: The formation of quantum vortices in liquid helium.
  • Cosmology: The formation of cosmic strings in the early universe (Kibble-Zurek mechanism).

Q: What does the "Smooth" toggle do?

This controls how the simulation is drawn, illustrating a key difference between computational methods and physical theory:

  • Off (Pixelated): Shows the raw simulation grid. This is true to the Computer Science reality—we are calculating values on a discrete lattice (like a chessboard). It honestly reveals the limitations of the computer representation.
  • On (Smooth): Blends the pixels. This is true to the Physics reality—the Ginzburg-Landau theory describes a continuous fluid. The grid is just an artificial scaffold we use to calculate it, so smoothing attempts to reconstruct what the field "should" look like using bilinear interpolation.

Related Project:
Interactive U(1) XY Model Simulation →

Find the source code on GitHub.