Loschmidt Echo / Quantum Time Reversal — Model & Constraints

QPE preset #39

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	256 × 256
Boundary	Periodic / closed numerical box
Initial packet	centre=(-6, -3.5), σ=0.7, p=(3.6, 2.4), m=1
Base geometry	None
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

Ideal reversal uses anti-unitary complex conjugation / momentum reversal in the model.
No microscopic bath is included.
A fidelity loss caused by intentional reversal error is not automatically environmental decoherence.

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 ballistic 2DEG in a mesoscopic cavity
Mapping basis	effective-mass mapping (m*=0.067 m_e)
1 QPE length unit	50 nm
1 QPE time unit	1.45 ps
Note	Representative ballistic-cavity mapping. The 40.96-unit domain is about 2.05 um across; microwave and acoustic billiards remain useful wave analogues but have different physical time conversions.

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