RealTimeTransport::ResonantLevel Class Reference

#include <RealTimeTransport/Models/ResonantLevel.h>

This class implements a single spinless level. The Hamiltonian is given by

\[ H = \epsilon n, \]

where \( n=d^\dagger d \). It is coupled to the reservoirs via the tunneling Hamiltonian

\[ H_T = \sum_{r} \int d\omega \sqrt{\frac{\Gamma_{r}}{2\pi}} (d^\dagger a_{r}(\omega) + a^\dagger_{r}(\omega) d). \]

All operators are represented in the basis \( \ket{0}, \ket{1} \).

Public Member Functions
	ResonantLevel () noexcept=default
	Default constructor.
	ResonantLevel (ResonantLevel &&other) noexcept=default
	Default move constructor.
	ResonantLevel (const ResonantLevel &other)=default
	Default copy constructor.
ResonantLevel &	operator= (ResonantLevel &&other) noexcept=default
	Default move assignment operator.
ResonantLevel &	operator= (const ResonantLevel &other)=default
	Default copy assignment operator.
	ResonantLevel (SciCore::Real epsilon, const SciCore::RealVector &T, const SciCore::RealVector &mu, const SciCore::RealVector &Gamma)
	Constructs a new ResonantLevel object.
SciCore::Real	epsilon () const noexcept
	Returns the energy of the level.
int	dimHilbertSpace () const noexcept override
	The Hilbert space dimension is 2 (empty and full state).
int	numStates () const noexcept override
	Only one single particle state.
int	numChannels () const noexcept override
	Reservoirs are not spinful, thus returns 1.
int	numReservoirs () const override
	Returns the number of reservoirs the system is connected to.
OperatorType	H () const override
	Returns the Hamiltonian.
OperatorType	d (int l) const override
	Returns the annihilation operator. \(l\) is always 0.
SciCore::Complex	coupling (int r, int nu, int l) const override
	Returns the coupling coefficient in the tunneling Hamiltonian. Both \(\nu\) and \(l\) are always 0.
const SciCore::RealVector &	temperatures () const noexcept override
	Returns the temperatures of the reservoirs the system is connected to.
const SciCore::RealVector &	chemicalPotentials () const noexcept override
	Returns the chemical potentials of the reservoirs the system is connected to.
SupervectorType	vectorize (const OperatorType &op) const override
	Vectorizes an operator into its supervector form.
OperatorType	operatorize (const SupervectorType &supervector) const override
	Transforms a supervector back into operator form.
const std::vector< int > &	blockDimensions () const noexcept override
	The memory kernel and propagator are block diagonal. This function returns a reference to a vector containing the dimensions of these blocks.
std::unique_ptr< Model >	copy () const override
	Returns a deep copy of the model.
bool	isEqual (const Model &other) const override
	Returns true if other is the same as *this, otherwise false.
Public Member Functions inherited from RealTimeTransport::Model
bool	operator== (const Model &other) const
	Equality comparison operator.
bool	operator!= (const Model &other) const
	Inequality comparison operator.
virtual OperatorType	P () const
	Returns the parity operator.

Additional Inherited Members
Public Types inherited from RealTimeTransport::Model
using	OperatorType = SciCore::Matrix
	Type of ordinary operators.
using	SupervectorType = SciCore::Vector
	Type of vectorized operators.
using	SuperRowVectorType = SciCore::RowVector
	Type of adjoint of vectorized operators.
using	SuperoperatorType = SciCore::Matrix
	Type of superoperators.

Constructor & Destructor Documentation

ResonantLevel()

RealTimeTransport::ResonantLevel::ResonantLevel	(	SciCore::Real	epsilon,
		const SciCore::RealVector &	T,
		const SciCore::RealVector &	mu,
		const SciCore::RealVector &	Gamma )

Parameters

epsilon	Level energy
T	Temperature reservoirs
mu	Chemical potentials reservoirs
Gamma	Dot-reservoir coupling