Quantum Kicked Rotor / Dynamical Localization — Model & Constraints

QPE preset #35

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	20.48 × 20.48
Grid	256 × 256
Boundary	Periodic / closed numerical box
Initial packet	centre=(0, 0), σ=1.5, p=(0, 0), m=0.1
Base geometry	Harmonic
Preparation	kicked-rotor 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

Idealized short kicks applied to a coherent rotor-like state.
No spontaneous emission, finite laser linewidth or atom–atom interactions.
Momentum-space localization is distinguished from real-space Anderson localization.

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	ultracold Na atoms in a pulsed 589 nm standing wave
Mapping basis	Na-23 kicked-rotor mapping with m_sim=0.10
1 QPE length unit	14.4 nm
1 QPE time unit	0.749 µs
Note	One full 20.48-unit periodic X domain maps to one 589 nm/2 standing-wave period. Because the guided rotor uses m_sim=0.10, T0=m_phys L0^2/(m_sim hbar), giving about 0.749 us rather than the m_sim=1 kinetic time.

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