A partition-free approach to transient and steady-state charge currents

We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand-canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady-state value, which is given by a Landauer-type formula.We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand-canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady-state value, which is given by a Landauer-type formula.

arXiv:1005.3914Journal of Physics A Mathematical and TheoreticalNov 9, 201012 citations

On the steady state correlation functions of open interacting systems

Horia D. Cornean, Valeriu Moldoveanu, Claude‐Alain Pillet

We address the existence of steady state Green-Keldysh correlation functions of interacting fermions in mesoscopic systems for both the partitioning and partition-free scenarios. Under some spectral assumptions on the non-interacting model and for sufficiently small interaction strength, we show that the system evolves to a NESS which does not depend on the profile of the time-dependent coupling strength/bias. For the partitioned setting we also show that the steady state is independent of the initial state of the inner sample. Closed formulae for the NESS two-point correlation functions (Green-Keldysh functions), in the form of a convergent expansion, are derived. In the partitioning approach, we show that the 0th order term in the interaction strength of the charge current leads to the Landauer-Buettiker formula, while the 1st order correction contains the mean-field (Hartree-Fock) results.We address the existence of steady state Green-Keldysh correlation functions of interacting fermions in mesoscopic systems for both the partitioning and partition-free scenarios. Under some spectral assumptions on the non-interacting model and for sufficiently small interaction strength, we show that the system evolves to a NESS which does not depend on the profile of the time-dependent coupling strength/bias. For the partitioned setting we also show that the steady state is independent of the initial state of the inner sample. Closed formulae for the NESS two-point correlation functions (Green-Keldysh functions), in the form of a convergent expansion, are derived. In the partitioning approach, we show that the 0th order term in the interaction strength of the charge current leads to the Landauer-Buettiker formula, while the 1st order correction contains the mean-field (Hartree-Fock) results.

Jan 1, 201315 citations

Nonequilibrium steady states for interacting open systems: Exact results

Valeriu Moldoveanu, Horia D. Cornean, Claude‐Alain Pillet

Under certain conditions, we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our time-dependent scattering approach is exact and proves, among other things, the independence of the steady-state quantities from the initial state of the sample. Closed formulas for the steady-state current amenable for perturbative calculations with regard to the interaction strength are also derived. In the partitioning case, we calculate the first-order correction and recover the mean-field (Hartree-Fock) results.Under certain conditions, we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our time-dependent scattering approach is exact and proves, among other things, the independence of the steady-state quantities from the initial state of the sample. Closed formulas for the steady-state current amenable for perturbative calculations with regard to the interaction strength are also derived. In the partitioning case, we calculate the first-order correction and recover the mean-field (Hartree-Fock) results.

arXiv:1104.5399Physical Review BAug 11, 201126 citations

Landauer transport as a quasisteady state on finite chains under unitary quantum dynamics

J. P. Santos Pires, Bruno Amorim, João M. Viana Parente Lopes

In this paper, we study the emergence of a Landauer transport regime from the quantum-mechanical dynamics of free electrons in a disordered tight-binding chain, which is coupled to finite leads with open boundaries. Both partitioned and partition-free initial conditions are analyzed and seen to give rise, for large enough leads, to the same spatially uniform quasisteady-state current, which agrees with the Landauer value. The quasisteady-state regime is preceded by a transient regime, which lasts for a time proportional to the length of the disordered sample, and followed by recursions, after a time that is proportional to the lead size. These theoretical predictions may be of interest to future experiments on transport of fermionic ultracold atoms across optical lattices. We also observe finite-size current oscillations, superimposed on the quasisteady state, whose behavior depends crucially on the conditions initially imposed on the system. Finally, we show how a time-resolved Kubo formula is able to reproduce this Landauer transport regime, as the leads grow bigger.In this paper, we study the emergence of a Landauer transport regime from the quantum-mechanical dynamics of free electrons in a disordered tight-binding chain, which is coupled to finite leads with open boundaries. Both partitioned and partition-free initial conditions are analyzed and seen to give rise, for large enough leads, to the same spatially uniform quasisteady-state current, which agrees with the Landauer value. The quasisteady-state regime is preceded by a transient regime, which lasts for a time proportional to the length of the disordered sample, and followed by recursions, after a time that is proportional to the lead size. These theoretical predictions may be of interest to future experiments on transport of fermionic ultracold atoms across optical lattices. We also observe finite-size current oscillations, superimposed on the quasisteady state, whose behavior depends crucially on the conditions initially imposed on the system. Finally, we show how a time-resolved Kubo formula is able to reproduce this Landauer transport regime, as the leads grow bigger.

arXiv:1909.12402Physical review. B./Physical review. BMar 31, 202010 citations

Numerical method for nonlinear steady-state transport in one-dimensional correlated conductors

Malcolm Einhellinger, Alex Cojuhovschi, Eric Jeckelmann

We present a method for investigating the steady-state transport properties of one-dimensional correlated quantum systems. Using a procedure based on our analysis of finite-size effects in a related classical model ( $LC$ line) we show that stationary currents can be obtained from transient currents in finite systems driven out of equilibrium. The nonequilibrium dynamics of correlated quantum systems is calculated using the time-evolving block decimation method. To demonstrate our method we determine the full $I$ - $V$ characteristic of the spinless fermion model with nearest-neighbor hopping ${t}_{\text{H}}$ and interaction ${V}_{\text{H}}$ using two different setups to generate currents (turning on/off a potential bias). Our numerical results agree with exact results for noninteracting fermions ( ${V}_{\text{H}}=0$ ). For interacting fermions we find that in the linear regime $eV\ensuremath{\ll}4{t}_{\text{H}}$ the current $I$ is independent from the setup and our numerical data agree with the predictions of the Luttinger liquid theory combined with the Bethe Ansatz solution. For larger potentials $V$ the steady-state current depends on the current-generating setup and as $V$ increases we find a negative differential conductance with one setup while the currents saturate at finite values in the other one. Both effects are due to finite renormalized bandwidths.We present a method for investigating the steady-state transport properties of one-dimensional correlated quantum systems. Using a procedure based on our analysis of finite-size effects in a related classical model ($LC$ line) we show that stationary currents can be obtained from transient currents in finite systems driven out of equilibrium. The nonequilibrium dynamics of correlated quantum systems is calculated using the time-evolving block decimation method. To demonstrate our method we determine the full $I$-$V$ characteristic of the spinless fermion model with nearest-neighbor hopping ${t}_{\text{H}}$ and interaction ${V}_{\text{H}}$ using two different setups to generate currents (turning on/off a potential bias). Our numerical results agree with exact results for noninteracting fermions (${V}_{\text{H}}=0$). For interacting fermions we find that in the linear regime $eV\ensuremath{\ll}4{t}_{\text{H}}$ the current $I$ is independent from the setup and our numerical data agree with the predictions of the Luttinger liquid theory combined with the Bethe Ansatz solution. For larger potentials $V$ the steady-state current depends on the current-generating setup and as $V$ increases we find a negative differential conductance with one setup while the currents saturate at finite values in the other one. Both effects are due to finite renormalized bandwidths.

arXiv:1201.5323Physical Review BJun 21, 201224 citations

Many-body approach to time-dependent quantum transport

Anna-Maija Uimonen

In this thesis the electron transport through interacting quantum wires is studied.The time-dependent properties of the system are investigated by using the non-equilibrium Green function technique.This technique provides a way to include ultra-fast timedependent processes, arbitrary strong external fields and also brings forward an effective treatment of electron-electron and electron-phonon interactions.The electronelectron interactions are included via various self-energy approximations at Hartree-Fock, second-order Born and GW levels.These approximations are called conserving since they fulfill the physical conservation laws like the charge conservation law.The interacting central system is coupled to one-dimensional tight-binding leads, which are considered effectively as noninteracting.The system is perturbed by a bias voltage after which the time-evolution of the system is followed by Kadanoff-Baym equations.The non-equilibrium steady-state value of the current depends on the used self-energy approximation, which indicates the importance of the history-dependence in the calculation of current.This is an important observation in the aspect of time-dependent density functional theory, since it is one indication for the need of functionals with memory.The steady-state current is independent of the initial state, which is in accordance with the memory-loss theorem.The transient current shows small oscillations, which are consequence of the density oscillations especially in the first and last site.The density oscillations in the sites are effect of the electron transition from the lead to the central system and vice versa.In this thesis the electron transport through interacting quantum wires is studied.The time-dependent properties of the system are investigated by using the non-equilibrium Green function technique.This technique provides a way to include ultra-fast timedependent processes, arbitrary strong external fields and also brings forward an effective treatment of electron-electron and electron-phonon interactions.The electronelectron interactions are included via various self-energy approximations at Hartree-Fock, second-order Born and GW levels.These approximations are called conserving since they fulfill the physical conservation laws like the charge conservation law.The interacting central system is coupled to one-dimensional tight-binding leads, which are considered effectively as noninteracting.The system is perturbed by a bias voltage after which the time-evolution of the system is followed by Kadanoff-Baym equations.The non-equilibrium steady-state value of the current depends on the used self-energy approximation, which indicates the importance of the history-dependence in the calculation of current.This is an important observation in the aspect of time-dependent density functional theory, since it is one indication for the need of functionals with memory.The steady-state current is independent of the initial state, which is in accordance with the memory-loss theorem.The transient current shows small oscillations, which are consequence of the density oscillations especially in the first and last site.The density oscillations in the sites are effect of the electron transition from the lead to the central system and vice versa.

Jan 1, 20090 citations

LC

line) we show that stationary currents can be obtained from transient currents in finite systems driven out of equilibrium. The nonequilibrium dynamics of correlated quantum systems is calculated using the time-evolving block decimation method. To demonstrate our method we determine the full

I

V

characteristic of the spinless fermion model with nearest-neighbor hopping

{t}_{\text{H}}

and interaction

{V}_{\text{H}}

using two different setups to generate currents (turning on/off a potential bias). Our numerical results agree with exact results for noninteracting fermions (

{V}_{\text{H}}=0

). For interacting fermions we find that in the linear regime $eV\ensuremath{\ll}4{t}_{\text{H}}$ the current

I

is independent from the setup and our numerical data agree with the predictions of the Luttinger liquid theory combined with the Bethe Ansatz solution. For larger potentials

V

the steady-state current depends on the current-generating setup and as

V

increases we find a negative differential conductance with one setup while the currents saturate at finite values in the other one. Both effects are due to finite renormalized bandwidths.