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M R Wegewijs - One of the best experts on this subject based on the ideXlab platform.
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time dependent quantum transport causal superfermions exact fermion parity protected decay modes and pauli exclusion principle for mixed quantum states
Physical Review B, 2014Co-Authors: R B Saptsov, M R WegewijsAbstract:We extend the recently developed causal superfermion approach to the real-time transport theory to time-dependent decay problems.Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to the ferromagnetic electrodes and/or spin polarization of the tunnel junction. We set up a second quantization scheme for density operators in the Liouville-Fock space constructing causal field Superoperators using the fundamental physical principles of causality/probability conservation and the fermion-parity superselection (univalence). The time-dependent perturbation series for the time-evolution is renormalized by explicitly performing the wide-band limit on the Superoperator level. The short and long-time reservoir correlations are shown to be tightly linked to the occurrence of causal field destruction and creation Superoperators, respectively. The effective theory takes as a reference a damped local system, providing an interesting starting point for numerical calculations of memory kernels in real-time. A remarkable feature of this approach is the natural appearance of a measurable fermion-parity protected decay mode. It already can be calculated exactly in the Markovian, infinite temperature limit by leading order perturbation theory, yet persists unaltered for the finite temperature, interaction and tunneling spin polarization. Furthermore, we show how a Liouville-space analog of the Pauli principle directly leads to the exact result in the noninteracting limit: surprisingly, it is obtained in finite (second) order renormalized perturbation theory, both for the self-energy as well as the time-evolution propagator. For this limit we calculate the time-evolution of the full density operator starting from an arbitrary initial state on the quantum dot, including spin and pairing coherences and two-particle correlations.
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time dependent quantum transport causal superfermions exact fermion parity protected decay modes and pauli exclusion principle for mixed quantum states
Physical Review B, 2014Co-Authors: R B Saptsov, M R WegewijsAbstract:We extend the recently developed causal superfermion approach to the real-time diagrammatic transport theory to time-dependent decay problems. Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to ferromagnetic electrodes and/or spin polarization of the tunnel junction. This approach naturally leads to an exact result for one of the time-dependent decay modes for any value of the Coulomb interaction compatible with the wideband limit. We generalize these results to multilevel Anderson models and indicate constraints they impose on renormalization-group schemes in order to recover the exact noninteracting limit.(i) We first set up a second quantization scheme in the space of density operators constructing ``causal'' field Superoperators using the fundamental physical principles of causality/probability conservation and fermion-parity superselection (univalence). The time-dependent perturbation series for the time evolution is renormalized by explicitly performing the wideband limit on the Superoperator level. As a result, the occurrence of destruction and creation Superoperators are shown to be tightly linked to the physical short- and long-time reservoir correlations, respectively. This effective theory takes as a reference a damped local system, which may also provide an interesting starting point for numerical calculations of memory kernels in real time. (ii) A remarkable feature of this approach is the natural appearance of a fermion-parity protected decay mode which can be measured using a setup proposed earlier [Phys. Rev. B 85, 075301 (2012)]. This mode can be calculated exactly in the fully Markovian, infinite-temperature limit by leading-order perturbation theory, but surprisingly persists unaltered for finite temperature, for any interaction and tunneling spin polarization. (iii) Finally, we show how a Liouville-space analog of the Pauli principle directly leads to an exact expression in the noninteracting limit for the time evolution, extending previous works by starting from an arbitrary initial mixed state including spin and pairing coherences and two-particle correlations stored on the quantum dot. This exact result is obtained already in finite-order renormalized perturbation theory, which surprisingly is not quadratic but quartic in the field Superoperators, despite the absence of Coulomb interaction. The latter fact we relate to the time evolution of the two-particle component of the mixed state, which is just the fermion-parity operator, a cornerstone of the formalism. We illustrate how the super-Pauli-principle also simplifies problems with nonzero Coulomb interaction.
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fermionic Superoperators for zero temperature nonlinear transport real time perturbation theory and renormalization group for anderson quantum dots
Physical Review B, 2012Co-Authors: R B Saptsov, M R WegewijsAbstract:We study the transport through a strongly interacting Anderson quantum dot at zero-temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic equation for the reduced density operator. We further develop the general finite temperature real-time transport formalism by introducing field Superoperators that obey fermionic statistics. This direct second quantization in Liouville-Fock space strongly simplifies the construction of operators and Superoperators which transform irreducibly under the Anderson-model symmetry transformations. The fermionic field Superoperators naturally arise from the univalence (fermion-parity) superselection rule for the total system. Expressed in these field Superoperators, the causal structure of the perturbation theory for the effective time-evolution Superoperator-kernel becomes explicit. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling. Furthermore, in the WBL the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. We perform a complete 2-loop RG analysis at finite voltage and magnetic field, while systematically accounting for the dependence on both the quantum dot and reservoir frequencies. Using the second quantization in Liouville-space and symmetry restrictions we obtain analytical RT-RG equations with an efficient numerical solution and we extensively study the model parameter space, excluding the Kondo regime. The incorporated renormalization effects result in an enhancement of the inelastic cotunneling peak. Moreover, we find a tunnel-induced non-linearity of the stability diagrams at finite voltage, both in the SET and ICT regime.
R B Saptsov - One of the best experts on this subject based on the ideXlab platform.
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time dependent quantum transport causal superfermions exact fermion parity protected decay modes and pauli exclusion principle for mixed quantum states
Physical Review B, 2014Co-Authors: R B Saptsov, M R WegewijsAbstract:We extend the recently developed causal superfermion approach to the real-time transport theory to time-dependent decay problems.Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to the ferromagnetic electrodes and/or spin polarization of the tunnel junction. We set up a second quantization scheme for density operators in the Liouville-Fock space constructing causal field Superoperators using the fundamental physical principles of causality/probability conservation and the fermion-parity superselection (univalence). The time-dependent perturbation series for the time-evolution is renormalized by explicitly performing the wide-band limit on the Superoperator level. The short and long-time reservoir correlations are shown to be tightly linked to the occurrence of causal field destruction and creation Superoperators, respectively. The effective theory takes as a reference a damped local system, providing an interesting starting point for numerical calculations of memory kernels in real-time. A remarkable feature of this approach is the natural appearance of a measurable fermion-parity protected decay mode. It already can be calculated exactly in the Markovian, infinite temperature limit by leading order perturbation theory, yet persists unaltered for the finite temperature, interaction and tunneling spin polarization. Furthermore, we show how a Liouville-space analog of the Pauli principle directly leads to the exact result in the noninteracting limit: surprisingly, it is obtained in finite (second) order renormalized perturbation theory, both for the self-energy as well as the time-evolution propagator. For this limit we calculate the time-evolution of the full density operator starting from an arbitrary initial state on the quantum dot, including spin and pairing coherences and two-particle correlations.
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time dependent quantum transport causal superfermions exact fermion parity protected decay modes and pauli exclusion principle for mixed quantum states
Physical Review B, 2014Co-Authors: R B Saptsov, M R WegewijsAbstract:We extend the recently developed causal superfermion approach to the real-time diagrammatic transport theory to time-dependent decay problems. Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to ferromagnetic electrodes and/or spin polarization of the tunnel junction. This approach naturally leads to an exact result for one of the time-dependent decay modes for any value of the Coulomb interaction compatible with the wideband limit. We generalize these results to multilevel Anderson models and indicate constraints they impose on renormalization-group schemes in order to recover the exact noninteracting limit.(i) We first set up a second quantization scheme in the space of density operators constructing ``causal'' field Superoperators using the fundamental physical principles of causality/probability conservation and fermion-parity superselection (univalence). The time-dependent perturbation series for the time evolution is renormalized by explicitly performing the wideband limit on the Superoperator level. As a result, the occurrence of destruction and creation Superoperators are shown to be tightly linked to the physical short- and long-time reservoir correlations, respectively. This effective theory takes as a reference a damped local system, which may also provide an interesting starting point for numerical calculations of memory kernels in real time. (ii) A remarkable feature of this approach is the natural appearance of a fermion-parity protected decay mode which can be measured using a setup proposed earlier [Phys. Rev. B 85, 075301 (2012)]. This mode can be calculated exactly in the fully Markovian, infinite-temperature limit by leading-order perturbation theory, but surprisingly persists unaltered for finite temperature, for any interaction and tunneling spin polarization. (iii) Finally, we show how a Liouville-space analog of the Pauli principle directly leads to an exact expression in the noninteracting limit for the time evolution, extending previous works by starting from an arbitrary initial mixed state including spin and pairing coherences and two-particle correlations stored on the quantum dot. This exact result is obtained already in finite-order renormalized perturbation theory, which surprisingly is not quadratic but quartic in the field Superoperators, despite the absence of Coulomb interaction. The latter fact we relate to the time evolution of the two-particle component of the mixed state, which is just the fermion-parity operator, a cornerstone of the formalism. We illustrate how the super-Pauli-principle also simplifies problems with nonzero Coulomb interaction.
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fermionic Superoperators for zero temperature nonlinear transport real time perturbation theory and renormalization group for anderson quantum dots
Physical Review B, 2012Co-Authors: R B Saptsov, M R WegewijsAbstract:We study the transport through a strongly interacting Anderson quantum dot at zero-temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic equation for the reduced density operator. We further develop the general finite temperature real-time transport formalism by introducing field Superoperators that obey fermionic statistics. This direct second quantization in Liouville-Fock space strongly simplifies the construction of operators and Superoperators which transform irreducibly under the Anderson-model symmetry transformations. The fermionic field Superoperators naturally arise from the univalence (fermion-parity) superselection rule for the total system. Expressed in these field Superoperators, the causal structure of the perturbation theory for the effective time-evolution Superoperator-kernel becomes explicit. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling. Furthermore, in the WBL the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. We perform a complete 2-loop RG analysis at finite voltage and magnetic field, while systematically accounting for the dependence on both the quantum dot and reservoir frequencies. Using the second quantization in Liouville-space and symmetry restrictions we obtain analytical RT-RG equations with an efficient numerical solution and we extensively study the model parameter space, excluding the Kondo regime. The incorporated renormalization effects result in an enhancement of the inelastic cotunneling peak. Moreover, we find a tunnel-induced non-linearity of the stability diagrams at finite voltage, both in the SET and ICT regime.
Shaul Mukamel - One of the best experts on this subject based on the ideXlab platform.
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probing electronic and vibrational dynamics in molecules by time resolved photoelectron auger electron and x ray photon scattering spectroscopy
Faraday Discussions, 2015Co-Authors: Kochise Bennett, Markus Kowalewski, Shaul MukamelAbstract:We present a unified description for time-resolved electron and photon scattering spectroscopies from molecules prepared in nonstationary states. Signals are expressed in terms of Superoperator Green's functions and a systematic procedure for treating various degrees of freedom consistently at different levels of theory is developed. The standard Fermi Golden Rule expressions for photoelectron spectra, which are limited to broad, slowly-varying signals, are obtained as a limiting case of our more general theory that applies to broader parameter regimes.
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Superoperator nonequilibrium green s function theory of many body systems applications to charge transfer and transport in open junctions
Physics Reports, 2008Co-Authors: Upendra Harbola, Shaul MukamelAbstract:Abstract Nonequilibrium Green’s functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and introduce Superoperator algebra that greatly simplifies the derivation and the physical interpretation of all quantities. Expressions for various observables are derived directly in real time in terms of Superoperator nonequilibrium Green’s functions (SNGF), rather than the artificial time-loop required in Schwinger’s Hilbert-space formulation. Applications for computing interaction energies, charge densities, average currents, current induced fluorescence, electroluminescence and current fluctuation (electron counting) statistics are discussed.
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nonequilibrium Superoperator gw equations
Journal of Chemical Physics, 2006Co-Authors: Upendra Harbola, Shaul MukamelAbstract:Hedin’s equations [Phys. Rev. 139, 796 (1965)] for the one-particle equilibrium Green’s function of a many-electron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Green’s function, the self-energy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.
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Superoperator many body theory of molecular currents non equilibrium green functions in real time
arXiv: Quantum Physics, 2005Co-Authors: Upendra Harbola, Shaul MukamelAbstract:Publisher Summary This chapter discusses development of the nonequilibrium Superoperator green function theory (NESGFT) and applied it to the computation of molecular current. The Liouville space-time ordering operator provides an elegant way for performing calculations in real time, thus avoiding the artificial backward and forward time evolution required in Hilbert space (Keldysh loop). Wick's theorem for Superoperators is used to compute the self-energies perturbatively to the second order in phonon–electron coupling. Recently, Galperin et al. have used a fully self-consistent solution to study the influence of different interactions on molecular conductivity for a strong electron–phonon coupling. The main aim of the present work is to demonstrate that by doing calculations in Liouville space one can avoid the backward/forward time evolution (Keldysh loop) required in Hilbert space. This originates from the fact that in Liouville space both ket and bra evolve forward in time. Thus, one can couple the system with two independent, “left” and “right” fields. This property of Liouville space can be used to construct real (physical) time generating functionals for the nonperturbative calculation of the self-energies. The present model ignores electron-electron interactions. These may be treated using the GW technique formulated in terms of the Superoperators and extended to nonequilibrium situations. All nonequilibrium observables can be obtained from a single generating functional in terms of “left” and “right” operators.
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chapter 14 Superoperator many body theory of molecular currents non equilibrium green functions in real time
Theory and Applications of Computational Chemistry#R##N#The First Forty Years, 2005Co-Authors: Upendra Harbola, Shaul MukamelAbstract:Publisher Summary This chapter discusses development of the nonequilibrium Superoperator green function theory (NESGFT) and applied it to the computation of molecular current. The Liouville space-time ordering operator provides an elegant way for performing calculations in real time, thus avoiding the artificial backward and forward time evolution required in Hilbert space (Keldysh loop). Wick's theorem for Superoperators is used to compute the self-energies perturbatively to the second order in phonon–electron coupling. Recently, Galperin et al. have used a fully self-consistent solution to study the influence of different interactions on molecular conductivity for a strong electron–phonon coupling. The main aim of the present work is to demonstrate that by doing calculations in Liouville space one can avoid the backward/forward time evolution (Keldysh loop) required in Hilbert space. This originates from the fact that in Liouville space both ket and bra evolve forward in time. Thus, one can couple the system with two independent, “left” and “right” fields. This property of Liouville space can be used to construct real (physical) time generating functionals for the nonperturbative calculation of the self-energies. The present model ignores electron-electron interactions. These may be treated using the GW technique formulated in terms of the Superoperators and extended to nonequilibrium situations. All nonequilibrium observables can be obtained from a single generating functional in terms of “left” and “right” operators.
Upendra Harbola - One of the best experts on this subject based on the ideXlab platform.
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Superoperator nonequilibrium green s function theory of many body systems applications to charge transfer and transport in open junctions
Physics Reports, 2008Co-Authors: Upendra Harbola, Shaul MukamelAbstract:Abstract Nonequilibrium Green’s functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and introduce Superoperator algebra that greatly simplifies the derivation and the physical interpretation of all quantities. Expressions for various observables are derived directly in real time in terms of Superoperator nonequilibrium Green’s functions (SNGF), rather than the artificial time-loop required in Schwinger’s Hilbert-space formulation. Applications for computing interaction energies, charge densities, average currents, current induced fluorescence, electroluminescence and current fluctuation (electron counting) statistics are discussed.
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nonequilibrium Superoperator gw equations
Journal of Chemical Physics, 2006Co-Authors: Upendra Harbola, Shaul MukamelAbstract:Hedin’s equations [Phys. Rev. 139, 796 (1965)] for the one-particle equilibrium Green’s function of a many-electron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Green’s function, the self-energy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.
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Superoperator many body theory of molecular currents non equilibrium green functions in real time
arXiv: Quantum Physics, 2005Co-Authors: Upendra Harbola, Shaul MukamelAbstract:Publisher Summary This chapter discusses development of the nonequilibrium Superoperator green function theory (NESGFT) and applied it to the computation of molecular current. The Liouville space-time ordering operator provides an elegant way for performing calculations in real time, thus avoiding the artificial backward and forward time evolution required in Hilbert space (Keldysh loop). Wick's theorem for Superoperators is used to compute the self-energies perturbatively to the second order in phonon–electron coupling. Recently, Galperin et al. have used a fully self-consistent solution to study the influence of different interactions on molecular conductivity for a strong electron–phonon coupling. The main aim of the present work is to demonstrate that by doing calculations in Liouville space one can avoid the backward/forward time evolution (Keldysh loop) required in Hilbert space. This originates from the fact that in Liouville space both ket and bra evolve forward in time. Thus, one can couple the system with two independent, “left” and “right” fields. This property of Liouville space can be used to construct real (physical) time generating functionals for the nonperturbative calculation of the self-energies. The present model ignores electron-electron interactions. These may be treated using the GW technique formulated in terms of the Superoperators and extended to nonequilibrium situations. All nonequilibrium observables can be obtained from a single generating functional in terms of “left” and “right” operators.
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chapter 14 Superoperator many body theory of molecular currents non equilibrium green functions in real time
Theory and Applications of Computational Chemistry#R##N#The First Forty Years, 2005Co-Authors: Upendra Harbola, Shaul MukamelAbstract:Publisher Summary This chapter discusses development of the nonequilibrium Superoperator green function theory (NESGFT) and applied it to the computation of molecular current. The Liouville space-time ordering operator provides an elegant way for performing calculations in real time, thus avoiding the artificial backward and forward time evolution required in Hilbert space (Keldysh loop). Wick's theorem for Superoperators is used to compute the self-energies perturbatively to the second order in phonon–electron coupling. Recently, Galperin et al. have used a fully self-consistent solution to study the influence of different interactions on molecular conductivity for a strong electron–phonon coupling. The main aim of the present work is to demonstrate that by doing calculations in Liouville space one can avoid the backward/forward time evolution (Keldysh loop) required in Hilbert space. This originates from the fact that in Liouville space both ket and bra evolve forward in time. Thus, one can couple the system with two independent, “left” and “right” fields. This property of Liouville space can be used to construct real (physical) time generating functionals for the nonperturbative calculation of the self-energies. The present model ignores electron-electron interactions. These may be treated using the GW technique formulated in terms of the Superoperators and extended to nonequilibrium situations. All nonequilibrium observables can be obtained from a single generating functional in terms of “left” and “right” operators.
V. V. Dodonov - One of the best experts on this subject based on the ideXlab platform.
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how to verify the form of quantum jump Superoperator
2007Co-Authors: A. V. Dodonov, S S Mizrahi, V. V. DodonovAbstract:We propose an experimental scheme to probe the form of quantum jump Superoperator used in the theory of continuous photodetection in cavities. Two main steps are as follows: 1) a resonance absorption of a single photon by a Rydberg atom passing through a high-Q cavity filled in with the electromagnetic field in a thermal or coherent state with a small mean photon number, 2) a subsequent quantum nondemolition measurement of the photon statistics in the new field state arising after the photon absorption, using the interaction with Rydberg atoms in other (off-resonance) quantum states. Then comparing the probabilities of finding 0 and 1 photons in the initial and final states of the field, one can make conclusions on the form of the quantum jump Superoperator.
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Microscopic models of quantum-jump Superoperators
Physical Review A, 2005Co-Authors: A. V. Dodonov, Salomon S. Mizrahi, V. V. DodonovAbstract:We discuss the quantum-jump operation in an open system and show that jump Superoperators related to a system under measurement can be derived from the interaction of that system with a quantum measurement apparatus. We give two examples for the interaction of a monochromatic electromagnetic field in a cavity (the system) with two-level atoms and with a harmonic oscillator (representing two different kinds of detectors). We show that the derived quantum-jump Superoperators have a 'nonlinear' form J{rho}={gamma} diag[F(n)a{rho}a{sup {dagger}}F(n)], where the concrete form of the function F(n) depends on assumptions made about the interaction between the system and detector. Under certain conditions the asymptotical power-law dependence F(n)=(n+1){sup -{beta}} is obtained. A continuous transition to the standard Srinivas-Davies form of the quantum-jump Superoperator (corresponding to {beta}=0) is shown.
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quantum photodetection distributions with nonlinear quantum jump Superoperators
Journal of Optics B-quantum and Semiclassical Optics, 2005Co-Authors: A. V. Dodonov, S S Mizrahi, V. V. DodonovAbstract:We address the issue of the detection and counting of photons. We assume an electromagnetic field enclosed in an ideal cavity, which together with the detector constitute a closed system, so no photon is lost to the environment. Basing ourselves on a microscopic model consisting of a set of two-level atoms (the detector) interacting with the field, we derive a 'nonlinear' jump Superoperator. We compare the count statistics calculated within our model with those obtained from previous models, such as the coincidence probability density, two-count conditional probability density, waiting times and the second order correlation function, for several field states.