Klein tunneling — Model & Constraints

QPE preset #47

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

Numerical model actually used

Two-component Dirac split-step

QPE evolves a two-component spinor under a 2D Dirac Hamiltonian. Scalar-potential and kinetic/spinor steps are split in time; the displayed scalar proxy is reconstructed from the spinor and never replaces the spinor dynamics.

Guided preset defaults

Domain	40.96 × 40.96
Grid	256 × 256
Boundary	Open with CAP absorber
CAP	width=0.12, strength=5
Legacy scalar packet controls	centre=(-10, 0), σ=2.2; authoritative dynamics uses the preset Dirac spinor
Base geometry	None
Preparation	Dirac Klein packet

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

Two-component effective Dirac model with scalar barrier.
No QED pair creation or vacuum instability; “Klein zone” is branch propagation in a single-particle/effective pseudospin model.
Graphene-like mapping omits lattice, valleys, real spin, interactions and disorder.

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	gapped effective Dirac quasiparticle / graphene-like simulator
Mapping basis	effective-Dirac velocity mapping (v_D~10^6 m/s)
1 QPE length unit	10 nm
1 QPE time unit	10 fs
Note	Uses an effective Dirac velocity near 10^6 m/s, so one 10 nm length unit maps to about 10 fs. The nonzero QPE mass is an effective gap parameter, not the vacuum electron rest mass; this is not a material-specific graphene simulation.

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