Symmetric split-step Fourier solver for the scalar 2D Schrodinger equation. More...

#include <splitstepfouriersolver2d.h>

Public Member Functions
	SplitStepFourierSolver2D ()=default
	Constructs a solver with the default reduced-unit parameters.

	SplitStepFourierSolver2D (const SplitStepFourier2DParams &params)
	Constructs a solver with explicit parameters.

void	setParameters (const SplitStepFourier2DParams &params)
	Replaces physical/time-step parameters and invalidates prepared caches.

const SplitStepFourier2DParams &	parameters () const noexcept
	Returns the currently active solver parameters.

void	prepare (const ComplexField2D &field)
	Precomputes spectral kinetic phase factors for a specific grid.

bool	isPreparedFor (const ComplexField2D &field) const noexcept
	Returns whether the kinetic cache matches the supplied field geometry.

void	preparePotential (const PotentialField2D &potential)
	Precomputes the scalar-potential half-step phase cache.

bool	isPotentialPreparedFor (const PotentialField2D &potential) const noexcept
	Returns whether the potential half-step cache still matches `potential`.

void	step (ComplexField2D &field, const PotentialField2D &potential)
	Advances the scalar wave function by one second-order Strang step.

void	stepGaugeCovariant (ComplexField2D &field, const PotentialField2D &potential, const U1GaugeField2D &gauge)
	Advances one gauge-covariant Schrodinger step using U(1) links.

void	stepFree (ComplexField2D &field)
	Advances a free (`V=0`) scalar field by one cached kinetic step.

void	resetClock () noexcept
	Resets the shared solver time and step counter to zero.

void	advanceExternalClock () noexcept
	Advances only QPE's shared clock for an alternative authoritative propagator.

double	time () const noexcept
	Returns accumulated simulation time in solver units.

std::size_t	stepCount () const noexcept
	Returns the number of propagated/shared-clock steps since reset.

Private Member Functions
void	invalidatePreparation () noexcept
	Invalidates prepared numerical state.

void	invalidatePotentialPreparation () noexcept
	Invalidates the cached potential preparation.

void	applyPotentialHalfStep (ComplexField2D &field) const
	Applies potential half step.

void	applyKineticStep (ComplexField2D &field) const
	Applies kinetic step.

void	applyGaugeCayleyX (ComplexField2D &field, const U1GaugeField2D &gauge, double interval) const
	Applies gauge cayley x.

void	applyGaugeCayleyY (ComplexField2D &field, const U1GaugeField2D &gauge, double interval) const
	Applies gauge cayley y.

void	advanceClock () noexcept
	Advances clock.

Static Private Member Functions
static void	validateParameters (const SplitStepFourier2DParams &params)
	Validates parameters.

Private Attributes
SplitStepFourier2DParams	params_

std::size_t	width_ = 0

std::size_t	height_ = 0

float	dx_ = 0.0f

float	dy_ = 0.0f

std::vector< std::complex< float > >	kineticPhase_

const PotentialField2D *	potentialSource_ = nullptr

std::uint64_t	potentialRevision_ = 0

std::size_t	potentialWidth_ = 0

std::size_t	potentialHeight_ = 0

float	potentialDx_ = 0.0f

float	potentialDy_ = 0.0f

std::vector< std::complex< float > >	potentialHalfPhase_

double	time_ = 0.0

std::size_t	stepCount_ = 0

Detailed Description

Symmetric split-step Fourier solver for the scalar 2D Schrodinger equation.

For time-independent scalar potentials the propagator uses Strang splitting, applying potential half steps around a kinetic FFT step. Visual post-processing is never fed back into the propagated wave function.

Definition at line 58 of file splitstepfouriersolver2d.h.

Constructor & Destructor Documentation

◆ SplitStepFourierSolver2D() [1/2]

qpe::SplitStepFourierSolver2D::SplitStepFourierSolver2D ( )

default

Constructs a solver with the default reduced-unit parameters.

◆ SplitStepFourierSolver2D() [2/2]

qpe::SplitStepFourierSolver2D::SplitStepFourierSolver2D ( const SplitStepFourier2DParams & params )

explicit

Constructs a solver with explicit parameters.

Parameters

params Parameters copied into the solver.

Definition at line 54 of file splitstepfouriersolver2d.cpp.

References setParameters().

Member Function Documentation

◆ advanceClock()

void qpe::SplitStepFourierSolver2D::advanceClock ( )

privatenoexcept

Advances clock.

Definition at line 424 of file splitstepfouriersolver2d.cpp.

References qpe::SplitStepFourier2DParams::dt, params_, stepCount_, and time_.

Referenced by advanceExternalClock(), step(), stepFree(), and stepGaugeCovariant().

◆ advanceExternalClock()

void qpe::SplitStepFourierSolver2D::advanceExternalClock ( )

noexcept

Advances only QPE's shared clock for an alternative authoritative propagator.

Definition at line 238 of file splitstepfouriersolver2d.cpp.

References advanceClock().

Referenced by MainWindow::advanceSimulation(), and MainWindow::singleStep().

◆ applyGaugeCayleyX()

void qpe::SplitStepFourierSolver2D::applyGaugeCayleyX	(	ComplexField2D &	field,
		const U1GaugeField2D &	gauge,
		double	interval ) const

private

Applies gauge cayley x.

Parameters

field	Field data to read or modify.
gauge	The gauge value used by the operation.
interval	The interval value used by the operation.

Definition at line 342 of file splitstepfouriersolver2d.cpp.

References qpe::ComplexField2D::dx(), qpe::SplitStepFourier2DParams::hbar, qpe::ComplexField2D::height(), qpe::U1GaugeField2D::linkX(), qpe::SplitStepFourier2DParams::mass, params_, and qpe::ComplexField2D::width().

Referenced by stepGaugeCovariant().

◆ applyGaugeCayleyY()

void qpe::SplitStepFourierSolver2D::applyGaugeCayleyY	(	ComplexField2D &	field,
		const U1GaugeField2D &	gauge,
		double	interval ) const

private

Applies gauge cayley y.

Parameters

field	Field data to read or modify.
gauge	The gauge value used by the operation.
interval	The interval value used by the operation.

Definition at line 383 of file splitstepfouriersolver2d.cpp.

References qpe::ComplexField2D::dy(), qpe::SplitStepFourier2DParams::hbar, qpe::ComplexField2D::height(), qpe::U1GaugeField2D::linkY(), qpe::SplitStepFourier2DParams::mass, params_, and qpe::ComplexField2D::width().

Referenced by stepGaugeCovariant().

◆ applyKineticStep()

void qpe::SplitStepFourierSolver2D::applyKineticStep ( ComplexField2D & field ) const

private

Applies kinetic step.

Parameters

field Field data to read or modify.

Definition at line 298 of file splitstepfouriersolver2d.cpp.

References qpe::ComplexField2D::data(), kineticPhase_, and qpe::ComplexField2D::size().

Referenced by step(), and stepFree().

◆ applyPotentialHalfStep()

void qpe::SplitStepFourierSolver2D::applyPotentialHalfStep ( ComplexField2D & field ) const

private

Applies potential half step.

Parameters

field Field data to read or modify.

Definition at line 290 of file splitstepfouriersolver2d.cpp.

References qpe::ComplexField2D::data(), potentialHalfPhase_, and qpe::ComplexField2D::size().

Referenced by step(), and stepGaugeCovariant().

◆ invalidatePotentialPreparation()

void qpe::SplitStepFourierSolver2D::invalidatePotentialPreparation ( )

privatenoexcept

Invalidates the cached potential preparation.

Definition at line 279 of file splitstepfouriersolver2d.cpp.

References potentialDx_, potentialDy_, potentialHalfPhase_, potentialHeight_, potentialRevision_, potentialSource_, and potentialWidth_.

Referenced by setParameters().

◆ invalidatePreparation()

void qpe::SplitStepFourierSolver2D::invalidatePreparation ( )

privatenoexcept

Invalidates prepared numerical state.

Definition at line 270 of file splitstepfouriersolver2d.cpp.

References dx_, dy_, height_, kineticPhase_, and width_.

Referenced by setParameters().

◆ isPotentialPreparedFor()

bool qpe::SplitStepFourierSolver2D::isPotentialPreparedFor ( const PotentialField2D & potential ) const

noexcept

Returns whether the potential half-step cache still matches potential.

Parameters

potential Potential to compare with the cache identity/revision.

Definition at line 158 of file splitstepfouriersolver2d.cpp.

Referenced by qpe::tests::runSplitStepFourierSolver2DTests(), step(), and stepGaugeCovariant().

◆ isPreparedFor()

bool qpe::SplitStepFourierSolver2D::isPreparedFor ( const ComplexField2D & field ) const

noexcept

Returns whether the kinetic cache matches the supplied field geometry.

Parameters

field Field to compare with the prepared geometry.

Definition at line 115 of file splitstepfouriersolver2d.cpp.

Referenced by step(), and stepFree().

◆ parameters()

const SplitStepFourier2DParams & qpe::SplitStepFourierSolver2D::parameters ( ) const

noexcept

Returns the currently active solver parameters.

Definition at line 69 of file splitstepfouriersolver2d.cpp.

References params_.

◆ prepare()

void qpe::SplitStepFourierSolver2D::prepare ( const ComplexField2D & field )

Precomputes spectral kinetic phase factors for a specific grid.

Parameters

field Field whose dimensions and spacing define the FFT momentum grid.

Definition at line 74 of file splitstepfouriersolver2d.cpp.

References qpe::SplitStepFourier2DParams::dt, qpe::ComplexField2D::dx(), dx_, qpe::ComplexField2D::dy(), dy_, qpe::ComplexField2D::empty(), qpe::SplitStepFourier2DParams::hbar, qpe::ComplexField2D::height(), height_, kineticPhase_, qpe::SplitStepFourier2DParams::mass, params_, qpe::FFT2D::supportsSize(), validateParameters(), qpe::ComplexField2D::width(), and width_.

Referenced by MainWindow::resetSimulation(), qpe::tests::anonymous_namespace{quantumhalledge2d_tests.cpp}::runOne(), qpe::tests::runQuantumAharonovBohm2DTests(), qpe::tests::runQuantumAnderson2DTests(), qpe::tests::runQuantumBouncer2DTests(), qpe::tests::runQuantumLandau2DTests(), qpe::tests::runQuantumLoschmidt2DTests(), qpe::tests::runQuantumTalbot2DTests(), qpe::tests::runQuantumVortex2DTests(), step(), stepFree(), qpe::anonymous_namespace{quantumkickedrotor2d_tests.cpp}::testDynamicalLocalizationSignature(), and qpe::anonymous_namespace{quantumzeno2d_tests.cpp}::testWatchedEscapeSuppression().

◆ preparePotential()

void qpe::SplitStepFourierSolver2D::preparePotential ( const PotentialField2D & potential )

Precomputes the scalar-potential half-step phase cache.

Parameters

potential Potential sampled on the same grid as the propagated field.

The cache records PotentialField2D::revision() so edits automatically invalidate stale phase factors.

Definition at line 124 of file splitstepfouriersolver2d.cpp.

References qpe::PotentialField2D::data(), qpe::SplitStepFourier2DParams::dt, qpe::PotentialField2D::dx(), qpe::PotentialField2D::dy(), qpe::PotentialField2D::empty(), qpe::SplitStepFourier2DParams::hbar, qpe::PotentialField2D::height(), params_, potentialDx_, potentialDy_, potentialHalfPhase_, potentialHeight_, potentialRevision_, potentialSource_, potentialWidth_, qpe::PotentialField2D::revision(), qpe::PotentialField2D::size(), validateParameters(), and qpe::PotentialField2D::width().

Referenced by MainWindow::resetSimulation(), qpe::tests::anonymous_namespace{quantumhalledge2d_tests.cpp}::runOne(), qpe::tests::runQuantumAharonovBohm2DTests(), qpe::tests::runQuantumAnderson2DTests(), qpe::tests::runQuantumBouncer2DTests(), qpe::tests::runQuantumLandau2DTests(), qpe::tests::runQuantumLoschmidt2DTests(), qpe::tests::runQuantumVortex2DTests(), qpe::tests::runSplitStepFourierSolver2DTests(), step(), stepGaugeCovariant(), qpe::anonymous_namespace{quantumkickedrotor2d_tests.cpp}::testDynamicalLocalizationSignature(), and qpe::anonymous_namespace{quantumzeno2d_tests.cpp}::testWatchedEscapeSuppression().

◆ resetClock()

void qpe::SplitStepFourierSolver2D::resetClock ( )

noexcept

Resets the shared solver time and step counter to zero.

Definition at line 232 of file splitstepfouriersolver2d.cpp.

References stepCount_, and time_.

Referenced by MainWindow::resetSimulation(), qpe::tests::runSplitStepFourierSolver2DTests(), and setParameters().

◆ setParameters()

void qpe::SplitStepFourierSolver2D::setParameters ( const SplitStepFourier2DParams & params )

Replaces physical/time-step parameters and invalidates prepared caches.

Parameters

params New solver parameters; mass, hbar and dt must be positive.

Definition at line 60 of file splitstepfouriersolver2d.cpp.

References invalidatePotentialPreparation(), invalidatePreparation(), params_, resetClock(), and validateParameters().

Referenced by MainWindow::MainWindow(), SplitStepFourierSolver2D(), MainWindow::resetSimulation(), qpe::tests::anonymous_namespace{quantumhalledge2d_tests.cpp}::runOne(), qpe::tests::runQuantumAharonovBohm2DTests(), and qpe::tests::runQuantumLandau2DTests().

◆ step()

void qpe::SplitStepFourierSolver2D::step	(	ComplexField2D &	field,
		const PotentialField2D &	potential )

Advances the scalar wave function by one second-order Strang step.

Parameters

field	Wave function modified in place.
potential	Real scalar potential used for both symmetric half steps.

\[ U(\Delta t) \approx e^{-iV\Delta t/(2\hbar)} e^{-iT\Delta t/\hbar} e^{-iV\Delta t/(2\hbar)}. \]

Definition at line 170 of file splitstepfouriersolver2d.cpp.

References advanceClock(), applyKineticStep(), applyPotentialHalfStep(), qpe::FFT2D::forward(), qpe::FFT2D::inverse(), isPotentialPreparedFor(), isPreparedFor(), qpe::PotentialField2D::matchesGrid(), prepare(), and preparePotential().

Referenced by MainWindow::advanceSimulation(), qpe::tests::runQuantumAnderson2DTests(), qpe::tests::runQuantumBackflow2DTests(), qpe::tests::runQuantumBouncer2DTests(), qpe::tests::runQuantumLoschmidt2DTests(), qpe::tests::runQuantumVortex2DTests(), qpe::tests::runSplitStepFourierSolver2DTests(), MainWindow::singleStep(), qpe::anonymous_namespace{quantumkickedrotor2d_tests.cpp}::testDynamicalLocalizationSignature(), and qpe::anonymous_namespace{quantumzeno2d_tests.cpp}::testWatchedEscapeSuppression().

◆ stepCount()

std::size_t qpe::SplitStepFourierSolver2D::stepCount ( ) const

noexcept

Returns the number of propagated/shared-clock steps since reset.

Definition at line 248 of file splitstepfouriersolver2d.cpp.

References stepCount_.

Referenced by MainWindow::advanceSimulation(), MainWindow::currentParametersHelpHtml(), qpe::tests::runSplitStepFourierSolver2DTests(), MainWindow::setRunning(), MainWindow::singleStep(), MainWindow::updateMomentumSpaceCache(), MainWindow::updateStatusText(), and MainWindow::updateTransportUi().

◆ stepFree()

void qpe::SplitStepFourierSolver2D::stepFree ( ComplexField2D & field )

Advances a free (V=0) scalar field by one cached kinetic step.

Parameters

field Wave function modified in place.

Definition at line 219 of file splitstepfouriersolver2d.cpp.

References advanceClock(), applyKineticStep(), qpe::FFT2D::forward(), qpe::FFT2D::inverse(), isPreparedFor(), and prepare().

Referenced by qpe::tests::runQuantumTalbot2DTests(), qpe::tests::runSplitStepFourierSolver2DTests(), and qpe::tests::runWavePacketObservables2DTests().

◆ stepGaugeCovariant()

void qpe::SplitStepFourierSolver2D::stepGaugeCovariant	(	ComplexField2D &	field,
		const PotentialField2D &	potential,
		const U1GaugeField2D &	gauge )

Advances one gauge-covariant Schrodinger step using U(1) links.

Parameters

field	Wave function modified in place.
potential	Scalar potential sampled on the field grid.
gauge	U(1) link field encoding the vector-potential connection.

A symmetric X/2 - Y - X/2 Cayley/ADI kinetic factorization preserves the lattice gauge transformation law and is norm preserving before any CAP.

Definition at line 195 of file splitstepfouriersolver2d.cpp.

References advanceClock(), applyGaugeCayleyX(), applyGaugeCayleyY(), applyPotentialHalfStep(), qpe::SplitStepFourier2DParams::dt, isPotentialPreparedFor(), qpe::PotentialField2D::matchesGrid(), qpe::U1GaugeField2D::matchesGrid(), params_, and preparePotential().

Referenced by MainWindow::advanceSimulation(), qpe::tests::anonymous_namespace{quantumhalledge2d_tests.cpp}::runOne(), qpe::tests::runQuantumAharonovBohm2DTests(), qpe::tests::runQuantumLandau2DTests(), and MainWindow::singleStep().