Time-dependent quantum current for independent electrons driven under nonperiodic conditions

Oriols, X.; Alarcon, A.; Fernandez-Diaz, E.

doi:10.1103/physrevb.71.245322

Cited by 25 publications

(24 citation statements)

References 55 publications

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“…The quantum fluctuations of the current can be directly computed, without additional cost, because Bohm trajectories describe the transmission and reflection process as two mutually exclusive events [11]. Since the algorithm deals with time-dependent Schrödinger equations, the many-electron transmission probabilities can be computed for zero or high frequencies, under static or time-dependent external bias [12].…”

Section: Fig 1 (Color Online) Two-particle Bohm Trajectories Withmentioning

confidence: 99%

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

2007

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It is proved that many-particle Bohm trajectories can be computed from single-particle time-dependent Schrödinger equations. From this result, a practical algorithm for the computation of transport properties of many-electron systems with exchange and Coulomb correlations is derived. As a test, two-particle Bohm trajectories in a tunneling scenario are compared to exact results with an excellent agreement. The algorithm opens the path for implementing a many-particle quantum transport (Monte Carlo) simulator, beyond the Fermi liquid paradigm. DOI: 10.1103/PhysRevLett.98.066803 PACS numbers: 73.23.ÿb, 02.70.Tt, 34.10.+x From a computational point of view, the direct solution of the many-particle Schrödinger equation is inaccessible for more than very few electrons. This issue is at the heart of almost all the unsolved problems in quantum transport. The standard solution to overcome this computational barrier is assuming noninteracting (Fermi liquid) electrons and decoupling the studies of transport from those of the electronic structure (via the effective electron mass) [1]. Nowadays, ab initio many-particle quantum transport approaches, based on the density functional theory (DFT) [2], are being developed [3] to surpass the previous approximations.In this Letter, we present an alternative approach, beyond the Fermi liquid paradigm, to study many-particle quantum transport using Bohm trajectories [4,5]. Bohmian mechanics was originally presented as an interpretative tool, and it generated an intense debate about the ''reality'' of the trajectories [6]. Here, this issue becomes irrelevant because Bohm trajectories (similarly to Feynman paths) are used to reproduce the probabilistic results of standard quantum mechanics. Following this point of view, Bohmian mechanics has recently undergone a revival to develop new quantum computational algorithms [7].We study a system of N (spinless) electrons described by a (first-quantization) many-particle wave-function, x; t, solution of the Schrödinger equation:wherex fx 1 ; x 2 ; . . . ; x N g fx a ;x b g is the vector of the electron positions. For simplicity, we consider a 1D solidstate system where the lattice-electron interaction is included into the electron effective mass, m. The potential energy Ux; t takes into account the Coulomb interaction among all electrons and the role of an external battery. First, we summarize the basic many-particle de BroglieBohm development [4,5,7,8]. Equation (1) can be split into two (real) equations when the wave function is written in polar form, x; t Rx; t expiSx; t=@. The real part leads to the many-particle quantum Hamilton-Jacobi Equations (2) The vectorxt fx 1 t; . . . ; x N tg fx a t;x b tg contains the N Bohm trajectories. We omit the dependence of each trajectory on its particular initial position, x a t o .On the other hand, the imaginary part of Eq. (1) leads to a continuity equation:

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Section: Fig 1 (Color Online) Two-particle Bohm Trajectories Withmentioning

confidence: 99%

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

2007

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“…Electron transport beyond the stationary regime (AC) constitutes an extremely valuable source of information to gain insight into relevant dynamical quantum phenomena such as the AC conductance quantization [109,110], the quantum measurement back-reaction [111,112], highmoments of the electrical current [113,114], classical-toquantum transitions [115,116], Leggett inequalities [117][118][119], etc. Moreover, the prediction of the dynamic (AC, transients and noise) performance of electron devices is of crucial importance to certify the usefulness of emerging devices at a practical level.…”

Section: Nanoelectronics: From DC To the Thz Regimementioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

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Abstract. Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics to address practical problems, rather than on its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics. Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectorybased explanation of complicated quantum phenomena. Here we present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for this kind of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this work also emphasizes that the Bohmian formalism can be a useful tool in other types of (nonunitary and nonlinear) quantum problems where the influence of the environment or the nonsimulated degrees of freedom are relevant. This review contains also examples on the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory among the scientific community will be greatly influenced by its potential success in those types of problems that present nonunitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism and some of its extensions are presented in the last part of this review.

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“…which is in perfect agreement with the results observed in figure 5. There, we see that the peak values for noise at each energy, move accordingly to equation (11), which is plotted in the f requency-energy plane with a blue solid line. Therefore, the simulations performed with sinusoidal potentials provide a clear behaviour: when we move to higher frequencies, quantum noise will be increased as we move to higher energies and will achieve a maximum at the new resonant energy.…”

Section: Numerical Results For the Oscillatory Proposed Experimentsmentioning

confidence: 90%

Quantum noise with exchange and tunnelling: predictions for a two-particle scattering experiment with time-dependent oscillatory potentials

Colomés¹,

Marian²,

Oriols³

2016

J. Stat. Mech.

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Quantum noise with exchange and tunneling is studied within time-dependent wave packets. A novel expression for the quantum noise of two identical particles injected simultaneously from opposite sides of a tunneling barrier is presented. Such quantum noise expression provides a physical (non-spurious) explanation for the experimental detection of two electrons at the same side under static potentials. Numerical simulations of the two-particle scattering probabilities in a double barrier potential with an oscillatory well are performed. The dependence of the quantum noise on the electron energy and oscillatory frequency are analyzed. The peculiar behaviour of the dependence of the quantum noise on such parameters is proposed as a test about the soundness of this novel quantum noise expression, for either static or oscillatory potentials. arXiv:1511.00608v1 [quant-ph] 2 Nov 2015Quantum noise with exchange and tunneling.

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Time-dependent quantum current for independent electrons driven under nonperiodic conditions

Cited by 25 publications

References 55 publications

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

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

Applied Bohmian mechanics

Quantum noise with exchange and tunnelling: predictions for a two-particle scattering experiment with time-dependent oscillatory potentials

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