Quantum-Trajectory Approach to Time-Dependent Transport in Mesoscopic Systems with Electron-Electron Interactions

Oriols, X.

doi:10.1103/physrevlett.98.066803

Cited by 139 publications

(268 citation statements)

References 20 publications

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“…The BITLLES simulator allows to perform both classical [32] and quantum [33] simulations of electronic devices, respectively using a classical Monte Carlo technique to solve the Boltzmann transport equation [34], and a quantum Monte Carlo algorithm to solve the many-body Schrödinger equation based on the use of conditional wavefunctions [35]. In both cases the self-consistency of the electronic equations of motion and the many-body Poisson equation is fulfilled [36] in combination with a proper set of time-dependent boundary conditions [37] and injection algorithms [38].…”

Section: A Resonant Tunneling Device Under Continuous Monitoring Of Tmentioning

confidence: 99%

Sequential Measurement of Displacement and Conduction Currents in Electronic Devices

2016

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Abstract. The extension of the Ramo-Schockley-Pellegrini theorem for quantum systems allows to define a positive-operator valued measure (POVM) for the total conduction plus displacement electrical current. The resulting current operator is characterized by two parameters, viz. the width of the associated Gaussian functions and the lapse of time between consecutive measurements. For large Gaussian dispersions and small time intervals, the operator obeys to a continuous weakmeasurement scheme. Contrarily, in the limit of very narrow Gaussian widths and a single-shot measurement, the operator corresponds to a standard von Neumann (projective) measurement. We have implemented the resulting measurement protocol into a quantum electron transport simulator. Numerical results for a resonant tunneling diode show the great sensibility of current-voltage characteristics to different parameter configurations of the total current operator.

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Section: A Resonant Tunneling Device Under Continuous Monitoring Of Tmentioning

confidence: 99%

Sequential Measurement of Displacement and Conduction Currents in Electronic Devices

2016

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“…In practice, the reconstruction of the full nuclear phase S(R, t) can be avoided at the expense of solving N times the number of equations of motion. 16,17,21 In this way, quantum trajectories can be computed as…”

Section: The Journal Of Physical Chemistry Lettersmentioning

confidence: 99%

Conditional Born–Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine

Albareda

Bofill

Tavernelli

et al. 2015

J. Phys. Chem. Lett.

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We report a new theoretical approach to solve adiabatic quantum molecular dynamics halfway between wave function and trajectory-based methods. The evolution of a N-body nuclear wave function moving on a 3N-dimensional Born− Oppenheimer potential-energy hyper-surface is rewritten in terms of single-nuclei wave functions evolving nonunitarily on a 3-dimensional potential-energy surface that depends parametrically on the configuration of an ensemble of generally defined trajectories. The scheme is exact and, together with the use of trajectory-based statistical techniques, can be exploited to circumvent the calculation and storage of many-body quantities (e.g., wave function and potential-energy surface) whose size scales exponentially with the number of nuclear degrees of freedom. As a proof of concept, we present numerical simulations of a 2-dimensional model porphine where switching from concerted to sequential double proton transfer (and back) is induced quantum mechanically. O n the basis of the Born−Huang expansion of the molecular wave function, 1 an exact description of adiabatic molecular dynamics requires the propagation of a nuclear wavepacket on the ground-state Born−Oppenheimer potential-energy surface (gs-BOPES). This propagation scheme is, somehow, computationally doubly prohibitive. Besides the computational burden associated with the propagation of the (many-body) nuclear wave function, the calculation of the gs-BOPES constitutes, per se, a time-independent problem that grows exponentially with the number of electrons and nuclei. In this respect, two main classes of computational methods have emerged depending on whether the knowledge of the gs-BOPES is required in the full configuration space, that is, fullquantum methods, 2,3 or only at certain reduced number of points, namely trajectory-based or direct methods.4,5 While methods for computing the energy of any configuration of nuclei have become quicker and more accurate, full-quantum dynamics calculations still become rapidly unfeasible for large molecules. Alternatively, direct dynamics notably reduce the computational cost of the simulations by avoiding partially, sometimes completely, the calculation of the full gs-BOPES (this can be done, for instance, by the use of reaction-path Hamiltonians 6,7 ). Nuclear quantum effects, however, can be hardly included systematically in this second class of methods. Up to date, only quantum-trajectory methods have the particularity of being able to describe all nuclear quantum effects (just as full-quantum methods) and being on-the-fly simultaneously.8−11 Unfortunately, these methods have serious problems in dealing with the so-called quantum potential, which gathers, by definition, all quantum information on the system. The mathematical structure of the quantum potential depends on the inverse of the quantum probability density, and thus, its manipulation entails serious instability problems. 12−14We report here an exact theoretical approach to solve adiabatic quantum molecular dynamics based o...

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“…Although most of these studies are restricted to the steady-state regime, more recently there has been increasing activity to describe the time evolution towards the steady state as the system is driven out of equilibrium by applying a bias in the leads. These studies use a range of methods such as, e.g., TDDFT [2,[17][18][19][20], generalized master equations [21], many-body perturbation theory [22][23][24], the timedependent density-matrix renormalization group [25][26][27], a quantum trajectory approach [28], or real-time path integral [29] and Monte Carlo approaches [30].…”

Section: Model Hamiltonian For Time-dependent Transportmentioning

confidence: 99%

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

Kurth

Stefanucci

2011

Chemical Physics

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The cornerstone of time-dependent (TD) density functional theory (DFT), the Runge-Gross theorem, proves a one-to-one correspondence between TD potentials and TD densities of continuum Hamiltonians. In all practical implementations, however, the basis set is discrete and the system is effectively described by a lattice Hamiltonian. We point out the difficulties of generalizing the Runge-Groos proof to the discrete case and thereby endorse the recently proposed TD bond-current functional theory (BCFT) as a viable alternative. TDBCFT is based on a one-to-one correspondence between TD Peierl's phases and TD bond-currents of lattice systems. We apply the TDBCFT formalism to electronic transport through a simple interacting device weakly coupled to two biased non-interacting leads. We employ Kohn-Sham Peierls phases which are discontinuous functions of the density, a crucial property to describe Coulomb blockade. As shown by explicit time propagations, the discontinuity may prevent the biased system from ever reaching a steady state.

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Quantum-Trajectory Approach to Time-Dependent Transport in Mesoscopic Systems with Electron-Electron Interactions

Cited by 139 publications

References 20 publications

Sequential Measurement of Displacement and Conduction Currents in Electronic Devices

Sequential Measurement of Displacement and Conduction Currents in Electronic Devices

Conditional Born–Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

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