Guillermo Albareda

Applied Bohmian mechanics

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 trajectory-based 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.

Time-Dependent Many-Particle Simulation for Resonant Tunneling Diodes: Interpretation of an Analytical Small-Signal Equivalent Circuit

A full many-particle (beyond the mean-field approximation) electron quantum-transport simulator, which is named BITLLES, is used to analyze the transient current response of resonant tunneling diodes (RTDs). The simulations have been used to test an analytical (free-fitting parameters) small-signal equivalent circuit for RTDs under stable direct-current-biased conditions. The comparison provides an excellent agreement and furnishes a way to physically interpret each circuit element. In addition, a nonlinear novel RTD behavior in the negative differential conductance region has been established, i.e. asymmetric time constants in the RTD current response when high-low or low-high voltage steps are considered.

Robust weak-measurement protocol for Bohmian velocities

We present a protocol for measuring Bohmian - or the mathematically equivalent hydrodynamic - velocities based on an ensemble of two position measurements, defined from a Positive Operator Valued Measure, separated by a finite time interval. The protocol is very accurate and robust as long as the first measurement uncertainty divided by the finite time interval between measurements is much larger than the Bohmian velocity, and the system evolves under flat potential between measurements. The difference between the Bohmian velocity of the unperturbed state and the measured one is predicted to be much smaller than 1% in a large range of parameters. Counter-intuitively, the measured velocity is that at the final time and not a time-averaged value between measurements.

Improving the intrinsic cut-off frequency of gate-all-around quantum-wire transistors without channel length scaling

Progress in high-frequency transistors is based on reducing electron transit time, either by scaling their lengths or by introducing materials with higher electron mobility. For gate-all-around quantum-wire transistors with lateral dimensions similar or smaller than their length, a careful analysis of the displacement current reveals that a time shorter than the transit time controls their high-frequency performance. Monte Carlo simulations of such transistors with a self-consistent solution of the 3D Poisson equation clearly show an improvement of the intrinsic cut-off frequency when their lateral areas are reduced, without length scaling.

Correlated Electron-Nuclear Dynamics with Conditional Wave Functions

The molecular Schrödinger equation is rewritten in terms of nonunitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear) trajectories. This scheme is exact and does not rely on the tracing out of degrees of freedom. Hence, the use of trajectory-based statistical techniques can be exploited to circumvent the calculation of the computationally demanding Born-Oppenheimer potential-energy surfaces and nonadiabatic coupling elements. The concept of the potential-energy surface is restored by establishing a formal connection with the exact factorization of the full wave function. This connection is used to gain insight from a simplified form of the exact propagation scheme.

COMPUTATION OF QUANTUM ELECTRICAL CURRENTS THROUGH THE RAMO–SHOCKLEY–PELLEGRINI THEOREM WITH TRAJECTORIES

Motivated by a recent approach to solve quantum dynamics with full Coulomb correlations [X. Oriols, Phys. Rev. Lett.98 (2007) 066803], we present here an extension of the Ramo–Shockley–Pellegrini theorem for quantum systems to compute the total (conduction plus displacement) current in terms of quantum (Bohmian) trajectories. By way of test, we derive an extension of the Ramo-Shockley-Pellegrini theorem using standard quantum mechanics and we compare it to our former result. As expected, both formulations give identical results, however we emphasize the numerical viability of computing self-consistently the total current by means of quantum trajectories in front of the difficulties to do it in terms of standard quantum mechanics.

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

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.

EFFECT OF GATE-ALL-AROUND TRANSISTOR GEOMETRY ON THE HIGH-FREQUENCY NOISE: ANALYTICAL DISCUSSION

By means of the Ramo–Shockley–Pellegrini theorem, an analytical discussion on how different geometries of gate-all-around 1D ballistic transistors affect their time-dependent current and their (intrinsic) high-frequency noise spectrum is presented. In particular, it is shown that the frequency range where the high-frequency noise spectrum is meaningful increases when the lateral area is decreased.

Many-particle transport in the channel of quantum wire double-gate field-effect transistors with charged atomistic impurities

One of the most reported causes of variations in electron devices characteristics (coming from the atomistic nature of matter) are discrete doping induced fluctuations. In this work we highlight the importance of accurately accounting for (time-dependent) coulomb correlations among (transport) electrons in the analysis of such fluctuations. In particular, we study the effect of single ionized dopants on the performance of a quantum wire double-gate metal-oxide-semiconductor field-effect transistor, mainly when its lateral dimensions approach the effective cross section of the charged impurities. In this regard, we use a recently developed many-particle semiclassical simulation approach by Albareda et al. [Phys. Rev. B 79, 075315 (2009)] which provides an accurate treatment of electron–electron and electron–impurity interactions (avoiding the mean-field approximation). We reveal the significant impact of the sign and position of the impurity along the transistor channel on the on-current, the threshold vol...

Universal steps in quantum dynamics with time-dependent potential-energy surfaces: Beyond the Born-Oppenheimer picture

It was recently shown [G. Albareda, et al., Phys. Rev. Lett. 113, 083003 (2014)] that within the conditional decomposition approach to the coupled electron-nuclear dynamics, the electron-nuclear wave function can be exactly decomposed into an ensemble of nuclear wavepackets effectively governed by nuclear conditional time-dependent potential-energy surfaces (C-TDPESs). Employing a one-dimensional model system we show that for strong nonadiabatic couplings the nuclear C-TDPESs exhibit steps that bridge piecewise adiabatic Born-Oppenheimer PESs. The nature of these steps is identified as an effect of electron-nuclear correlation. Furthermore, a direct comparison with similar discontinuities recently reported in the context of the exact factorization framework allows us to draw conclusions about the universality of these discontinuities, viz. they are inherent to all nonadiabatic nuclear dynamics approaches based on (exact) time-dependent potential energy surfaces.