Quantum tunnelling — Model & Constraints

QPE preset #2

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

Numerical model actually used

Scalar Schrödinger split-step FFT

QPE evolves a complex scalar 2D wavefunction. The ordinary kinetic step is performed in Fourier space and the scalar potential in position space with Strang-type splitting; special events such as measurements, kicks or pulse recipes are layered on top without changing the rendering/physics separation.

Guided preset defaults

Domain	40.96 × 40.96
Grid	512 × 512
Boundary	Open with CAP absorber
CAP	width=0.15, strength=8
Initial packet	centre=(-8, 0), σ=1, p=(2.5, 0), m=1
Base geometry	Barrier
Geometry parameters	V₀=4.5, centre=(0, 0), size=(0.64, 30)
Preparation	Gaussian 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

Single-particle elastic tunnelling only.
The barrier is static and scalar; no phonons, dissipation or band-structure details.
Transmission depends on packet bandwidth and finite simulation time as well as the ideal plane-wave formula.

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 / semiconductor nanostructure
Mapping basis	effective-mass mapping (m*=0.067 m_e)
1 QPE length unit	10 nm
1 QPE time unit	57.9 fs
Note	Representative semiconductor mapping. One 10 nm simulation length unit with m*=0.067 m_e gives a time unit near 57.9 fs; material and confinement details can change the effective mass.

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