RealTimeTransport::DoubleDot Class Reference

#include <RealTimeTransport/Models/DoubleDot.h>

This class implements a spinless double quantum dot. The Hamiltonian is given by

\[ H = \epsilon_1 n_1 + \epsilon_2 n_2 + \Omega d_1^\dagger d_2 + \Omega^* d_2^\dagger d_1 + U n_1 n_2. \]

The dots are coupled to the reservoirs via the tunneling Hamiltonian

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

All operators are represented in the basis \( \ket{00}, \ket{10}=d^\dagger_1 \ket{00}, \ket{01}=d^\dagger_2 \ket{00}, \ket{11} = d^\dagger_1 d^\dagger_2 \ket{00} \).

Public Member Functions
	DoubleDot () noexcept=default
	Default constructor.
	DoubleDot (DoubleDot &&other) noexcept=default
	Default move constructor.
	DoubleDot (const DoubleDot &other)=default
	Default copy constructor.
DoubleDot &	operator= (DoubleDot &&other) noexcept=default
	Default move assignment operator.
DoubleDot &	operator= (const DoubleDot &other)=default
	Default copy assignment operator.
	DoubleDot (SciCore::Real epsilon1, SciCore::Real epsilon2, SciCore::Real U, SciCore::Complex Omega, const SciCore::RealVector &T, const SciCore::RealVector &mu, const SciCore::RealVector &Gamma1, const SciCore::RealVector &Gamma2)
	Constructs a new double dot object.
SciCore::Real	epsilon1 () const noexcept
	Returns the energy of dot 1.
SciCore::Real	epsilon2 () const noexcept
	Returns the energy of dot 2.
SciCore::Real	U () const noexcept
	Returns the Coulomb interaction.
const SciCore::RealVector &	Gamma1 () const noexcept
	Returns the coupling \( \Gamma_{r1} \) between dot 1 and the reservoirs.
const SciCore::RealVector &	Gamma2 () const noexcept
	Returns the coupling \( \Gamma_{r2} \) between dot 2 and the reservoirs.
int	dimHilbertSpace () const noexcept override
	The Hilbert space dimension is 4.
int	numStates () const noexcept override
	There are two single particle states.
int	numChannels () const noexcept override
	Returns 1 (reservoirs are spinless).
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 of the dot \(l=0, 1\).
SciCore::Complex	coupling (int r, int nu, int l) const override
	Returns the coupling coefficient in the tunneling Hamiltonian. l represents the dot index. nu is not used in this model.
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

DoubleDot()

RealTimeTransport::DoubleDot::DoubleDot	(	SciCore::Real	epsilon1,
		SciCore::Real	epsilon2,
		SciCore::Real	U,
		SciCore::Complex	Omega,
		const SciCore::RealVector &	T,
		const SciCore::RealVector &	mu,
		const SciCore::RealVector &	Gamma1,
		const SciCore::RealVector &	Gamma2 )

Parameters

epsilon1	Energy of dot 1
epsilon2	Energy of dot 2
U	Coulomb interaction between the dots
Omega	Hybridization between the dots
T	Temperatures of the reservoirs
mu	Chemical potentials of the reservoirs
Gamma1	Coupling \( \Gamma_{r1} \) between dot 1 and the reservoirs
Gamma2	Coupling \( \Gamma_{r2} \) between dot 2 and the reservoirs