Michael Ridley | Bar-Ilan University (original) (raw)
Papers by Michael Ridley
arxiv, 2025
We study stochastic resonance in molecular junctions driven by a periodically-varying external fi... more We study stochastic resonance in molecular junctions driven by a periodically-varying external field. This is done using the time-dependent Landauer-B{ĂŒ}ttiker formalism, which follows from exact analytical solutions to the Kadanoff-Baym equations describing the molecular junction subject to an arbitrary time-dependent bias. We focus on a double quantum dot nanojunction and compare the effects of the temperature with the fluctuating bias in the statically-driven case. We then consider the combined effect of AC-driving and white noise fluctuations on the rectified current through the nanojunction, and find a stochastic resonance effect, where at certain driving conditions the bias fluctuations enhance the current signal. The study is then extended to include the color noise in the applied bias, so that the combined effect of the color noise correlation time and driving frequency on stochastic resonance is investigated. We thereby demonstrate that photon-assisted transport can be optimized by a suitably tuned environment.
We investigate two types of temporal symmetry in quantum mechanics. The first type, time symmetry... more We investigate two types of temporal symmetry in quantum mechanics. The first type, time symmetry, refers to the inclusion of opposite time orientations on an equivalent physical footing. The second, event symmetry, refers to the inclusion of all time instants in a history sequence on an equivalent physical footing. We find that recent time symmetric interpretations of quantum mechanics fail to respect event symmetry. Building on the recent fixed-point formulation (FPF) of quantum theory, we formulate the notion of an event precisely as a fixed point constraint on the Keldysh time contour. Then, considering a sequence of measurement events in time, we show that both time and event symmetry can be retained in this multiple-time formulation of quantum theory. We then use this model to resolve conceptual paradoxes with time symmetric quantum mechanics within an 'all-at-once', atemporal picture.
Quantum Reports, 2023
The Born probability measure describes the statistics of measurements in which observers self-loc... more The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In đ
-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified using fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics, with a network of âfixed pointsâ defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre- and postselection.
The Born probability measure describes the statistics of measurements in which observers selfloca... more The Born probability measure describes the statistics of measurements in which observers selflocate themselves in some region of reality. In Ï-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified with fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics with a network of âfixed pointsâ defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with preand post-selection.
, sincerely affirm that the work contained in this thesis is my own. Where the work of others has... more , sincerely affirm that the work contained in this thesis is my own. Where the work of others has been used in the process of obtaining my results, I have thoroughly referenced the original source material.
Physical Review B, 2021
Using the recently developed time-dependent Landauer-B\"uttiker formalism and Jefimenko'... more Using the recently developed time-dependent Landauer-B\"uttiker formalism and Jefimenko's retarded solutions to the Maxwell equations, we show how to compute the time-dependent electromagnetic field produced by the charge and current densities in nanojunctions out of equilibrium. We then apply this formalism to a benzene ring junction, and show that geometry-dependent quantum interference effects can be used to control the magnetic field in the vicinity of the molecule. Then, treating the molecular junction as a quantum emitter, we demonstrate clear signatures of the local molecular geometry in the non-local radiated power.
Physics Letters A, 2021
A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup vio... more A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS 113, 532 (2016)] is refuted. The quantum nature of the violation of the pigeonhole principle with pre-and postselection is clarified.
Entropy, 2019
Using the partition-free time-dependent LandauerâBĂŒttiker formalism for transient current correla... more Using the partition-free time-dependent LandauerâBĂŒttiker formalism for transient current correlations, we study the traversal times taken for electrons to cross graphene nanoribbon (GNR) molecular junctions. We demonstrate electron traversal signatures that vary with disorder and orientation of the GNR. These findings can be related to operational frequencies of GNR-based devices and their consequent rational design.
The Journal of Chemical Physics, 2019
We present a numerically exact study of charge transport and its uctuations through a molecular j... more We present a numerically exact study of charge transport and its uctuations through a molecular junction driven out of equilibrium by a bias voltage, using the Inchworm quantum Monte Carlo (iQMC) method. After showing how the technique can be used to address any lead geometry, we concentrate on one dimensional chains as an example. The nite bandwidth of the leads is shown to aect transport properties in ways that cannot be fully captured by quantum master equations: in particular, we reveal an interactioninduced broadening of transport channels that is visible at all voltages, and show how uctuations of the current are a more sensitive probe of this eect than the mean current. I.
Journal of Low Temperature Physics, 2018
In this paper we review the partitioned and partition-free approaches to the calculation of the t... more In this paper we review the partitioned and partition-free approaches to the calculation of the time-dependent response of a molecular junction to the switch-on of an arbitrary time-dependent bias. Using the non equilibrium Green's function formalism on different time contours, we derive a formal equivalence between these two approaches. This clarifies a recent result of [PRB 95, 104301 (2017)], which is valid for a static bias and single level molecular structure, and extends it to arbitrary time-dependent biases and arbitrarily large molecular structures.
Physical Review B, 2017
We apply the recently-developed partition-free time-dependent Landauer-BĂŒttiker (TD-LB) formalism... more We apply the recently-developed partition-free time-dependent Landauer-BĂŒttiker (TD-LB) formalism to the study of periodically-driven transport in graphene nanoribbons (GNR). When an AC driving is applied, this formalism can be used to prove generic conditions for the existence of a nonzero DC component of the net current (pump current) through the molecular device. Time-reversal symmetry breaking in the driving field is investigated and found to be insufficient for a non-zero pump current. We then derive explicit formulas for the current response to a particular biharmonic bias. We calculate the pump current through different GNR configurations and find that the sign and existence of a non-zero pump current can be tuned by simple alterations to the static parameters of the TD bias. Further, we investigate transient currents in different GNR configurations. We find a selection rule of even and odd harmonic response signal depending on a broken dynamical inversion symmetry in the bias.
Physical Review B, 2018
The time dependent full counting statistics of charge transport through an interacting quantum ju... more The time dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron-electron interactions on the time-dependent charge cumulants, first-passage time distributions and n-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade-to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single electron transfer events.
Physical Review B, 2017
Partition-free theory of time-dependent current correlations in nanojunctions in response to an a... more Partition-free theory of time-dependent current correlations in nanojunctions in response to an arbitrary time-dependent bias.
Journal of Physics: Conference Series, 2016
If citing, it is advised that you check and use the publisher's definitive version for pagination... more If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections.
Physical Review B, 2015
We apply the nonequilibrium Green's function formalism to the problem of a multiterminal nanojunc... more We apply the nonequilibrium Green's function formalism to the problem of a multiterminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide-band-limit approximation, it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et al. [Phys. Rev. B 50, 5528 (1994)] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et al. [Phys. Rev. B 89, 085131 (2014)] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally varying bias. At certain frequencies of the driving bias, we observe "ringing" oscillations of the current, whose dependence on the dot level, level width, oscillation amplitude, and temperature is also investigated.
Physical Review B, 2016
If citing, it is advised that you check and use the publisher's definitive version for pagination... more If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections.
The Born probability measure describes the statistics of measurements in which observers selfloca... more The Born probability measure describes the statistics of measurements in which observers selflocate themselves in some region of reality. In Ï-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified with fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics with a network of 'fixed points' defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre-and post-selection.
We review one of the most versatile theoretical approaches to the study of time-dependent correla... more We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium tra...
arXiv: Mesoscale and Nanoscale Physics, 2014
We apply the Nonequilibrium Green's Function (NEGF) formalism to the problem of a multi-termi... more We apply the Nonequilibrium Green's Function (NEGF) formalism to the problem of a multi-terminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide band limit approximation (WBLA), it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et. al. [doi:10.1103/PhysRevB.50.5528] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et. al. [doi:10.1088/1742-6596/427/1/012014] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally-varying bias. At certain frequencies ...
We review one of the most versatile theoretical approaches to the study of time-dependent correla... more We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss nonequilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive-encompassing pump-probe scenarios as well as driven quantum systems-we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one-and two-dimensional electronic systems, systems with electron-phonon couplings, topological superconductors, and optically responsive molecular junctions where electron-photon couplings are relevant.
arxiv, 2025
We study stochastic resonance in molecular junctions driven by a periodically-varying external fi... more We study stochastic resonance in molecular junctions driven by a periodically-varying external field. This is done using the time-dependent Landauer-B{ĂŒ}ttiker formalism, which follows from exact analytical solutions to the Kadanoff-Baym equations describing the molecular junction subject to an arbitrary time-dependent bias. We focus on a double quantum dot nanojunction and compare the effects of the temperature with the fluctuating bias in the statically-driven case. We then consider the combined effect of AC-driving and white noise fluctuations on the rectified current through the nanojunction, and find a stochastic resonance effect, where at certain driving conditions the bias fluctuations enhance the current signal. The study is then extended to include the color noise in the applied bias, so that the combined effect of the color noise correlation time and driving frequency on stochastic resonance is investigated. We thereby demonstrate that photon-assisted transport can be optimized by a suitably tuned environment.
We investigate two types of temporal symmetry in quantum mechanics. The first type, time symmetry... more We investigate two types of temporal symmetry in quantum mechanics. The first type, time symmetry, refers to the inclusion of opposite time orientations on an equivalent physical footing. The second, event symmetry, refers to the inclusion of all time instants in a history sequence on an equivalent physical footing. We find that recent time symmetric interpretations of quantum mechanics fail to respect event symmetry. Building on the recent fixed-point formulation (FPF) of quantum theory, we formulate the notion of an event precisely as a fixed point constraint on the Keldysh time contour. Then, considering a sequence of measurement events in time, we show that both time and event symmetry can be retained in this multiple-time formulation of quantum theory. We then use this model to resolve conceptual paradoxes with time symmetric quantum mechanics within an 'all-at-once', atemporal picture.
Quantum Reports, 2023
The Born probability measure describes the statistics of measurements in which observers self-loc... more The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In đ
-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified using fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics, with a network of âfixed pointsâ defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre- and postselection.
The Born probability measure describes the statistics of measurements in which observers selfloca... more The Born probability measure describes the statistics of measurements in which observers selflocate themselves in some region of reality. In Ï-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified with fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics with a network of âfixed pointsâ defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with preand post-selection.
, sincerely affirm that the work contained in this thesis is my own. Where the work of others has... more , sincerely affirm that the work contained in this thesis is my own. Where the work of others has been used in the process of obtaining my results, I have thoroughly referenced the original source material.
Physical Review B, 2021
Using the recently developed time-dependent Landauer-B\"uttiker formalism and Jefimenko'... more Using the recently developed time-dependent Landauer-B\"uttiker formalism and Jefimenko's retarded solutions to the Maxwell equations, we show how to compute the time-dependent electromagnetic field produced by the charge and current densities in nanojunctions out of equilibrium. We then apply this formalism to a benzene ring junction, and show that geometry-dependent quantum interference effects can be used to control the magnetic field in the vicinity of the molecule. Then, treating the molecular junction as a quantum emitter, we demonstrate clear signatures of the local molecular geometry in the non-local radiated power.
Physics Letters A, 2021
A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup vio... more A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS 113, 532 (2016)] is refuted. The quantum nature of the violation of the pigeonhole principle with pre-and postselection is clarified.
Entropy, 2019
Using the partition-free time-dependent LandauerâBĂŒttiker formalism for transient current correla... more Using the partition-free time-dependent LandauerâBĂŒttiker formalism for transient current correlations, we study the traversal times taken for electrons to cross graphene nanoribbon (GNR) molecular junctions. We demonstrate electron traversal signatures that vary with disorder and orientation of the GNR. These findings can be related to operational frequencies of GNR-based devices and their consequent rational design.
The Journal of Chemical Physics, 2019
We present a numerically exact study of charge transport and its uctuations through a molecular j... more We present a numerically exact study of charge transport and its uctuations through a molecular junction driven out of equilibrium by a bias voltage, using the Inchworm quantum Monte Carlo (iQMC) method. After showing how the technique can be used to address any lead geometry, we concentrate on one dimensional chains as an example. The nite bandwidth of the leads is shown to aect transport properties in ways that cannot be fully captured by quantum master equations: in particular, we reveal an interactioninduced broadening of transport channels that is visible at all voltages, and show how uctuations of the current are a more sensitive probe of this eect than the mean current. I.
Journal of Low Temperature Physics, 2018
In this paper we review the partitioned and partition-free approaches to the calculation of the t... more In this paper we review the partitioned and partition-free approaches to the calculation of the time-dependent response of a molecular junction to the switch-on of an arbitrary time-dependent bias. Using the non equilibrium Green's function formalism on different time contours, we derive a formal equivalence between these two approaches. This clarifies a recent result of [PRB 95, 104301 (2017)], which is valid for a static bias and single level molecular structure, and extends it to arbitrary time-dependent biases and arbitrarily large molecular structures.
Physical Review B, 2017
We apply the recently-developed partition-free time-dependent Landauer-BĂŒttiker (TD-LB) formalism... more We apply the recently-developed partition-free time-dependent Landauer-BĂŒttiker (TD-LB) formalism to the study of periodically-driven transport in graphene nanoribbons (GNR). When an AC driving is applied, this formalism can be used to prove generic conditions for the existence of a nonzero DC component of the net current (pump current) through the molecular device. Time-reversal symmetry breaking in the driving field is investigated and found to be insufficient for a non-zero pump current. We then derive explicit formulas for the current response to a particular biharmonic bias. We calculate the pump current through different GNR configurations and find that the sign and existence of a non-zero pump current can be tuned by simple alterations to the static parameters of the TD bias. Further, we investigate transient currents in different GNR configurations. We find a selection rule of even and odd harmonic response signal depending on a broken dynamical inversion symmetry in the bias.
Physical Review B, 2018
The time dependent full counting statistics of charge transport through an interacting quantum ju... more The time dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron-electron interactions on the time-dependent charge cumulants, first-passage time distributions and n-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade-to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single electron transfer events.
Physical Review B, 2017
Partition-free theory of time-dependent current correlations in nanojunctions in response to an a... more Partition-free theory of time-dependent current correlations in nanojunctions in response to an arbitrary time-dependent bias.
Journal of Physics: Conference Series, 2016
If citing, it is advised that you check and use the publisher's definitive version for pagination... more If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections.
Physical Review B, 2015
We apply the nonequilibrium Green's function formalism to the problem of a multiterminal nanojunc... more We apply the nonequilibrium Green's function formalism to the problem of a multiterminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide-band-limit approximation, it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et al. [Phys. Rev. B 50, 5528 (1994)] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et al. [Phys. Rev. B 89, 085131 (2014)] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally varying bias. At certain frequencies of the driving bias, we observe "ringing" oscillations of the current, whose dependence on the dot level, level width, oscillation amplitude, and temperature is also investigated.
Physical Review B, 2016
If citing, it is advised that you check and use the publisher's definitive version for pagination... more If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections.
The Born probability measure describes the statistics of measurements in which observers selfloca... more The Born probability measure describes the statistics of measurements in which observers selflocate themselves in some region of reality. In Ï-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified with fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics with a network of 'fixed points' defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre-and post-selection.
We review one of the most versatile theoretical approaches to the study of time-dependent correla... more We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium tra...
arXiv: Mesoscale and Nanoscale Physics, 2014
We apply the Nonequilibrium Green's Function (NEGF) formalism to the problem of a multi-termi... more We apply the Nonequilibrium Green's Function (NEGF) formalism to the problem of a multi-terminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide band limit approximation (WBLA), it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et. al. [doi:10.1103/PhysRevB.50.5528] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et. al. [doi:10.1088/1742-6596/427/1/012014] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally-varying bias. At certain frequencies ...
We review one of the most versatile theoretical approaches to the study of time-dependent correla... more We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss nonequilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive-encompassing pump-probe scenarios as well as driven quantum systems-we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one-and two-dimensional electronic systems, systems with electron-phonon couplings, topological superconductors, and optically responsive molecular junctions where electron-photon couplings are relevant.
The Born probability measure describes the statistics of measurements in which observers selfloca... more The Born probability measure describes the statistics of measurements in which observers selflocate themselves in some region of reality. In Ï-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified with fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics with a network of 'fixed points' defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre-and post-selection.
Using the recently developed time-dependent Landauer-BĂŒttiker formalism and Jefimenko's retarded ... more Using the recently developed time-dependent Landauer-BĂŒttiker formalism and Jefimenko's retarded solutions to the Maxwell equations, we show how to compute the time-dependent electromagnetic field produced by the charge and current densities in nanojunctions out of equilibrium. We then apply this formalism to a benzene ring junction, and show that geometry-dependent quantum interference effects can be used to control the magnetic field in the vicinity of the molecule. Then, treating the molecular junction as a quantum emitter, we demonstrate clear signatures of the local molecular geometry in the non-local radiated power.
We use the inchworm Quantum Monte Carlo method to investigate the full counting statistics of par... more We use the inchworm Quantum Monte Carlo method to investigate the full counting statistics of particle and energy currents in a strongly correlated quantum dot. Our method is used to extract the heat fluctuations and entropy production of a quantum thermoelectric device, as well as cumulants of the particle and energy currents. The energy-particle current cross correlations reveal information on the preparation of the system and the interplay of thermal and electric currents. We furthermore demonstrate the signature of a crossover from Coulomb blockade to Kondo physics in the energy current fluctuations, and show how the conventional master equation approach to full counting statistics systematically fails to capture this crossover.