Landau levels and cyclotron dynamics — Model & Constraints

QPE preset #43

Values below come from the v7.9.4/Step 56 guided preset; live values may differ after user edits.

Numerical model actually used

Gauge-covariant Cayley/ADI branch

QPE evolves a scalar charged-particle wavefunction with U(1) Peierls links. The magnetic kinetic update uses a symmetric Cayley/ADI factorization so gauge phases enter the discrete covariant derivatives and probability current consistently.

Guided preset defaults

Domain	40.96 × 40.96
Grid	256 × 256
Boundary	Open with CAP absorber
CAP	width=0.15, strength=8
Initial packet	centre=(-5, 0), σ=1.5, p=(0, 1.125), m=1
Base geometry	None
Preparation	Landau/cyclotron state

For special modules (Ramsey, LZ, gauge, Dirac, kicks, measurement, etc.), complete authoritative parameters for the current run are exposed by Help → Current Experiment → Current Parameters.

Common assumptions

Dimensionless simulation units with ħ=1 unless explicitly stated otherwise.
Rendering, palettes, bloom and post-processing never modify ψ, V, observables or probabilities.
The grid is finite: structures below a few cells/pixels do not carry reliable physical meaning.

Experiment-specific assumptions and simplifications

Charged scalar particle in uniform B using gauge-covariant lattice links.
No spin Zeeman splitting, disorder, Fermi sea or interactions.
Finite domain and boundary conditions differ from the infinite Landau problem.

How not to over-interpret the result

A visually convincing result is not a substitute for a numerical check. Inspect the relevant norms, populations, fluxes or Analysis curves; if the packet reaches the CAP or a numerical wall, always separate the physical effect from finite-domain behaviour.

Real-world mapping

Representative platform	GaAs-like 2DEG in a uniform mesoscopic magnetic field
Mapping basis	effective-mass mapping (m*=0.067 m_e)
1 QPE length unit	50 nm
1 QPE time unit	1.45 ps
Note	With guided dimensionless b=0.45 and L0=50 nm, the magnetic-field unit gives B about 0.12 T. The GaAs-like effective mass sets a time unit near 1.45 ps.

This mapping is representative only. The model remains the one described above: changing units does not add missing degrees of freedom.

Model references

Numerical methods · Conventions and units · General bibliography