2. Renormalized perturbation theory

This page ontains classes and methods related to the implementation of the renormalized perturbation theory.

Classes
class	RealTimeTransport::RenormalizedPT::ConductanceKernel
	Defines the renormalized conductance kernel. More...
class	RealTimeTransport::RenormalizedPT::CurrentKernel
	Defines the renormalized current kernel. More...
class	RealTimeTransport::RenormalizedPT::MemoryKernel
	Defines the renormalized memory kernel. More...

Enumerations
enum class	RealTimeTransport::RenormalizedPT::Order { Order::_1 = 1 , Order::_2 = 2 }
	Defines the order of the approximation. More...

Functions
RenormalizedPT::ConductanceKernel	RealTimeTransport::computeConductanceKernel (const RenormalizedPT::MemoryKernel &K, const RenormalizedPT::CurrentKernel &KI, RenormalizedPT::Order order, int block=-1)
	Computes the conductance kernel for a given model in the same reservoir for which the current kernel was computed.
RenormalizedPT::ConductanceKernel	RealTimeTransport::computeConductanceKernel (const RenormalizedPT::MemoryKernel &K, const RenormalizedPT::CurrentKernel &KI, int r, RenormalizedPT::Order order, int block=-1)
	Computes the conductance kernel for a given model.
RenormalizedPT::CurrentKernel	RealTimeTransport::computeCurrentKernel (const std::unique_ptr< Model > &model, int r, RenormalizedPT::Order order, SciCore::Real tMax, SciCore::Real errorGoal, int block=-1)
	Computes the current kernel for a given model.
RenormalizedPT::CurrentKernel	RealTimeTransport::computeCurrentKernel (const std::unique_ptr< Model > &model, int r, RenormalizedPT::Order order, SciCore::Real tMax, SciCore::Real errorGoal, tf::Executor &executor, int block=-1)
	Computes the current kernel for a given model in parallel.
SciCore::ChebAdaptive< SciCore::Real >	RealTimeTransport::computeCurrent (const RenormalizedPT::CurrentKernel &KCurrent, const Propagator &propagator, const Model::OperatorType &rho0)
	Computes the transient current for a given initial state.
RenormalizedPT::MemoryKernel	RealTimeTransport::computeMemoryKernel (const std::unique_ptr< Model > &model, RenormalizedPT::Order order, SciCore::Real tMax, SciCore::Real errorGoal, int block=-1)
	Computes the memory kernel for a given model.
RenormalizedPT::MemoryKernel	RealTimeTransport::computeMemoryKernel (const std::unique_ptr< Model > &model, RenormalizedPT::Order order, SciCore::Real tMax, SciCore::Real errorGoal, tf::Executor &executor, int block=-1)
	Computes the memory mernel for a given model in parallel.
Propagator	RealTimeTransport::computePropagator (const RenormalizedPT::MemoryKernel &memoryKernel, int block=-1)
	Computes the propagator corresponding to a given memory kernel.

Enumeration Type Documentation

Order

enum class RealTimeTransport::RenormalizedPT::Order

strong

Enumerator
_1	Leading order.
_2	Next-to-leading order.

Function Documentation

computeConductanceKernel() [1/2]

RenormalizedPT::ConductanceKernel RealTimeTransport::computeConductanceKernel	(	const RenormalizedPT::MemoryKernel &	K,
		const RenormalizedPT::CurrentKernel &	KI,
		RenormalizedPT::Order	order,
		int	block = -1 )

Computes the conductance kernel for a given model in the same reservoir for which the current kernel was computed.

Parameters

K	The memory kernel for a given model.
KI	The current kernel for a given model.
order	The order of the renormalized perturbation series.
block	Computes the complete conductance kernel if block==-1, otherwise computes only a single block with index block.

computeConductanceKernel() [2/2]

RenormalizedPT::ConductanceKernel RealTimeTransport::computeConductanceKernel	(	const RenormalizedPT::MemoryKernel &	K,
		const RenormalizedPT::CurrentKernel &	KI,
		int	r,
		RenormalizedPT::Order	order,
		int	block = -1 )

Computes the conductance kernel which gives access to the (cross)conductance \(dI_{r_1}/d\mu_{r_2}\) for a given model. Here \(r_1\) is determined by the current kernel KI, and \(r_2\) by the parameter r.

Parameters

K	The memory kernel for a given model.
KI	The current kernel for a given model.
r	Reservoir at which the derivative of the chemical potential is taken.
order	The order of the renormalized perturbation series.
block	Computes the complete conductance kernel if block==-1, otherwise computes only a single block with index block.

computeCurrentKernel() [1/2]

RenormalizedPT::CurrentKernel RealTimeTransport::computeCurrentKernel	(	const std::unique_ptr< Model > &	model,
		int	r,
		RenormalizedPT::Order	order,
		SciCore::Real	tMax,
		SciCore::Real	errorGoal,
		int	block = -1 )

Computes the current kernel for a given model.

Parameters

model	The model for which the current kernel is computed.
r	Index of the reservoir \( r=0,1,\dots \)
order	The order of the renormalized perturbation series.
tMax	Maximum time until the current kernel is resolved.
errorGoal	Error goal of the current kernel computation.
block	Computes the complete current kernel if block==-1, otherwise computes only a single block with index block.

computeCurrentKernel() [2/2]

RenormalizedPT::CurrentKernel RealTimeTransport::computeCurrentKernel	(	const std::unique_ptr< Model > &	model,
		int	r,
		RenormalizedPT::Order	order,
		SciCore::Real	tMax,
		SciCore::Real	errorGoal,
		tf::Executor &	executor,
		int	block = -1 )

Computes the current kernel for a given model in parallel.

Parameters

model	The model for which the current kernel is computed.
r	Index of the reservoir \( r=0,1,\dots \)
order	The order of the renormalized perturbation series.
tMax	Maximum time until the current kernel is resolved.
errorGoal	Error goal of the current kernel computation.
executor	An excecutor managing multiple threads.
block	Computes the complete current kernel if block==-1, otherwise computes only a single block with index block.

computeCurrent()

SciCore::ChebAdaptive< SciCore::Real > RealTimeTransport::computeCurrent	(	const RenormalizedPT::CurrentKernel &	KCurrent,
		const Propagator &	propagator,
		const Model::OperatorType &	rho0 )

Computes the transient current for a given initial state.

Parameters

KCurrent	The current kernel.
propagator	The propagator of the dynamics.
rho0	The initial state.

computeMemoryKernel() [1/2]

RenormalizedPT::MemoryKernel RealTimeTransport::computeMemoryKernel	(	const std::unique_ptr< Model > &	model,
		RenormalizedPT::Order	order,
		SciCore::Real	tMax,
		SciCore::Real	errorGoal,
		int	block = -1 )

Computes the memory kernel for a given model.

Parameters

model	The model for which the memory kernel is computed.
order	The order of the renormalized perturbation series.
tMax	Maximum time until the memory kernel is resolved.
errorGoal	Error goal of the memory kernel computation.
block	Computes the complete memory kernel if block==-1, otherwise computes only a single block with index block.

computeMemoryKernel() [2/2]

RenormalizedPT::MemoryKernel RealTimeTransport::computeMemoryKernel	(	const std::unique_ptr< Model > &	model,
		RenormalizedPT::Order	order,
		SciCore::Real	tMax,
		SciCore::Real	errorGoal,
		tf::Executor &	executor,
		int	block = -1 )

Computes the memory mernel for a given model in parallel.

Parameters

model	The model for which the memory kernel is computed.
order	The order of the renormalized perturbation series.
tMax	Maximum time until the memory kernel is resolved.
errorGoal	Error goal of the memory kernel computation.
executor	An excecutor managing multiple threads.
block	Computes the complete memory kernel if block==-1, otherwise computes only a single block with index block.

computePropagator()

Propagator RealTimeTransport::computePropagator	(	const RenormalizedPT::MemoryKernel &	memoryKernel,
		int	block = -1 )

Computes the propagator corresponding to a given memory kernel. This is done my numerically solving the time-nonlocal master equation.

Parameters

memoryKernel	The memory kernel.
block	Computes the complete propagator if block==-1, otherwise computes only a single block with index block.