arXiv subjects

Xavier Oriols

Publications and source records attributed to Xavier Oriols.

At least 37 records · Page 2Linked to original sources

arXiv2019

Proposal for a clumsiness-free test of macroscopic realism

We propose a test of macrorealism that exploits the contextuality of two-time correlation functions to escape the so-called "clumsiness loophole" that plagues Leggett-Garg inequalities. The non-contextuality of reduced joint probability distributions is proven to be an unequivocal criterion to guarantee that measurements are carried out in the ideally-weak measurement regime of a class of generalized von Neumann measurements. In this regime, testing the so-called "no-signaling in time" condition allows to uncontextually ascertain whether a property of a given system is macrorealistic or non-macrorealistic. The resulting protocol allows for tests of macrorealism in situations where Leggett-Garg inequalities and ideal negative measurement cannot be used at all.

quant-ph↗

arXiv2019

Stochastic Schrödinger equations and conditional states: a general Non-Markovian quantum electron transport simulator for THz electronics

A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of the so-called conditional states in Markovian and non-Markovian scenarios has been a topic of recent debate in the construction of stochastic Schrödinger equations. We shed light on this discussion by acknowledging the Bohmian conditional wavefunction as the proper mathematical object to represent, in terms of state vectors, an arbitrary subset of degrees of freedom. As an example of the practical utility of these states, we present a time-dependent quantum Monte Carlo algorithm to describe electron transport in open quantum systems under general (Markovian or non-Markovian) conditions. By making the most of trajectory-based and wavefunction methods, the resulting simulation technique extends, to the quantum regime, the computational capabilities that the Monte Carlo solution of the Boltzmann transport equation offers for semi-classical electron devices.

cond-mat.mes-hall↗

arXiv2019

Coulomb and exchange interaction effects on the exact two-electron dynamics in the Hong-Ou-Mandel interferometer based on Hall edge states

The electronic Hong-Ou-Mandel interferometer in the integer quantum Hall regime is an ideal system to probe the building up of quantum correlations between charge carriers and it has been proposed as a viable platform for quantum computing gates. Using a parallel implementation of the split-step Fourier method, we simulated the antibunching of two interacting fermionic wave packets impinging on a quantum point contact. Numerical results of the exact approach are compared with a simplified theoretical model based on one-dimensional scattering formalism. We show that, for a realistic geometry, the Coulomb repulsion dominates over the exchange energy, this effect being strongly dependent on the energy broadening of the particles. We define analytically the spatial entanglement between the two regions of the quantum point contact, and obtain quantitatively its entanglement-generation capabilities.

cond-mat.mes-hall↗

arXiv2019

Overview of Bohmian Mechanics

This chapter provides a comprehensive overview of the Bohmian formulation of quantum mechanics. It starts with a historical review of the difficulties found by Louis de Broglie, David Bohm, and John S. Bell to convince the scientific community about the validity and utility of Bohmian mechanics. Then, a formal explanation of Bohmian mechanics for nonrelativistic, single-particle quantum systems is presented. The generalization to many-particle systems, where the exchange interaction and the spin play an important role, is also presented. After that, the measurement process in Bohmian mechanics is discussed. It is emphasized that Bohmian mechanics exactly reproduces the mean value and temporal and spatial correlations obtained from the standard, that is the Copenhagen or orthodox, formulation. The ontological characteristics of Bohmian mechanics provide a description of measurements as another type of interaction without the need for introducing the wave function collapse. Several solved problems are presented at the end of the chapter, giving additional mathematical support to some particular issues. A detailed description of computational algorithms to obtain Bohmian trajectories from the numerical solution of the Schrodinger or the Hamilton-Jacobi equations are presented in an appendix. The motivation of this chapter is twofold: first, as a didactic introduction to Bohmian formalism, which is used in the subsequent chapters, and second, as a self-contained summary for any newcomer interested in using Bohmian mechanics in his or her daily research activity.

quant-ph↗

arXiv2019

Quantum time-dependent Monte Carlo simulation of electron devices with 2D linear-band materials: a genuine TeraHertz signature for graphene

An intrinsic electron injection model for linear band two-dimensional (2D) materials, like graphene, is presented and its coupling to a recently developed quantum time-dependent Monte Carlo simulator for electron devices, based on the use of stochastic Bohmian conditional wave functions, is explained. The simulator is able to capture the full (DC, AC, transient and noise) performance of 2D electron devices. In particular, we demonstrate that the injection of electrons with positive and negative kinetic energies is mandatory when investigating high frequency performance of linear band materials with Klein tunneling, while traditional models dealing with holes (defined as the lack of electrons) can lead to unphysical results. We show that the number of injected electrons is bias-dependent, implying that an extra charge is required to get self-consistent results. Interestingly, we provide a successful comparison with experimental DC data. Finally, we predict that a genuine high-frequency signature due to a roughly constant electron injection rate in 2D linear band electron devices (which is missing in 2D parabolic band ones) can be used as a band structure tester.

cond-mat.mes-hall↗

arXiv2019

Implications of the Klein tunneling times on high frequency graphene devices using Bohmian trajectories

Because of its large Fermi velocity, leading to a great mobility, graphene is expected to play an important role in (small signal) radio frequency electronics. Among other, graphene devices based on Klein tunneling phenomena are already envisioned. The connection between the Klein tunneling times of electrons and cut-off frequencies of graphene devices is not obvious. We argue in this paper that the trajectory-based Bohmian approach gives a very natural framework to quantify Klein tunneling times in linear band graphene devices because of its ability to distinguish, not only between transmitted and reflected electrons, but also between reflected electrons that spend time in the barrier and those that do not. Without such distinction, typical expressions found in the literature to compute dwell times can give unphysical results when applied to predict cut-off frequencies. In particular, we study Klein tunneling times for electrons in a two-terminal graphene device constituted by a potential barrier between two metallic contacts. We show that for a zero incident angle (and positive or negative kinetic energy), the transmission coefficient is equal to one, and the dwell time is roughly equal to the barrier distance divided by the Fermi velocity. For electrons incident with a non-zero angle smaller than the critical angle, the transmission coefficient decreases and dwell time can still be easily predicted in the Bohmian framework. The main conclusion of this work is that, contrary to tunneling devices with parabolic bands, the high graphene mobility is roughly independent of the presence of Klein tunneling phenomena in the active device region.

cond-mat.mes-hall↗

arXiv2017

Dynamics of Current, Charge and Mass

Electricity plays a special role in our lives and life. Equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term the displacement current (of vacuum). Displacement current allows electrical signals to propagate through space. Displacement current guarantees that current is exactly conserved from inside atoms to between stars, as long as current is defined as Maxwell did, as the entire source of the curl of the magnetic field. We show how the Bohm formulation of quantum mechanics allows easy definition of current. We show how conservation of current can be derived without mention of the polarization or dielectric properties of matter. Matter does not behave the way physicists of the 1800's thought it does with a single dielectric constant, a real positive number independent of everything. Charge moves in enormously complicated ways that cannot be described in that way, when studied on time scales important today for electronic technology and molecular biology. Life occurs in ionic solutions in which charge moves in response to forces not mentioned or described in the Maxwell equations, like convection and diffusion. Classical derivations of conservation of current involve classical treatments of dielectrics and polarization in nearly every textbook. Because real dielectrics do not behave in a classical way, classical derivations of conservation of current are often distrusted or even ignored. We show that current is conserved exactly in any material no matter how complex the dielectric, polarization or conduction currents are. We believe models, simulations, and computations should conserve current on all scales, as accurately as possible, because physics conserves current that way. We believe models will be much more successful if they conserve current at every level of resolution, the way physics does.

physics.gen-ph↗

arXiv2017

Natural classical limit for the center of mass of many-particle quantum systems

We discuss the conditions for the classicality of quantum states with a very large number of identical particles. By treating the center of mass as a Bohmian particle, we show that it follows a classical trajectory when the distribution of the Bohmian positions in just one experiment is always equal to the marginal distribution of the quantum state in physical space. This result can also be interpreted as a unique-experiment generalization of the well-known Ehrenfest theorem. We also demonstrate that the classical trajectory of the center of mass is fully compatible with a conditional wave function solution of a classical non-linear Schrödinger equation. Our work shows clear evidence for a quantum-classical inter-theory unification and opens new possibilities for practical quantum computations with decoherence.

quant-ph↗

arXiv2017

Limitations of the intrinsic cut-off frequency to correctly quantify the speed of nanoscale transistors

The definition of the intrinsic cut-off frequency ($f_T$) based on the current gain equals to one (0 dB) is critically analyzed. A condition for the validity of the quasi-static estimation of $f_T$ is established in terms of the temporal variations of the electric charge and electric flux on the drain, source and gate terminals. Due to the displacement current, an electron traversing the channel length generates a current pulse of finite temporal width. For electron devices where the intrinsic delay time of the current after a transient perturbation is comparable to such width, the displacement currents cannot be neglected and the quasi-static approximation becomes inaccurate. We provide numerical results for some ballistic transistors where the estimation of $f_T$ under the quasi-static approximation can be one order of magnitude larger than predictions obtained from a time-dependent numerical simulations of the intrinsic delay time (including particle and displacement currents). In other ballistic transistors, we show that the gate current phasor can be smaller than the drain one at all frequencies, giving no finite value for $f_T$.

cond-mat.mes-hall↗

arXiv2016

How does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?

Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually taken for granted and considered unproblematic that the state is, at least in principle, measurable, this is not the case in Bohmian mechanics. Due to the linearity of the quantum dynamical laws, one essential component of the Bohmian state, the wave function, is not directly measurable. Moreover, it turns out that the measurement of the other component of the state -the positions of the particles- must be mediated by the wave function; a fact that in turn implies that the positions of the particles, though measurable, are constrained by absolute uncertainty. This is the key to understanding how Bohmian mechanics, despite being deterministic, can account for all quantum predictions, including quantum randomness and uncertainty.

quant-ph↗

arXiv2016

BITLLES: Electron Transport Simulation with Quantum Trajectories

After the seminal work of R. Landauer in 1957 relating the electrical resistance of a conductor to its scattering properties, much progress has been made in our ability to predict the performance of electron devices in the DC (stationary) regime. Computational tools to describe their dynamical behavior (including the AC, transient and noise performance), however, are far from being as trustworthy as would be desired by the electronic industry. While there is no fundamental limitation to correctly modeling the high-frequency quantum transport and its fluctuations, certainly more careful attention must be paid to delicate issues such as overall charge neutrality, total current conservation, or the back action of the measuring apparatus. In this review, we will show how the core ideas behind the Bohmian formulation of quantum mechanics can be exploited to design an efficient Monte Carlo algorithm that provides a quantitative description of electron transport in open quantum systems. By making the most of trajectory-based and wave function methods, the BITLLES simulator, a free software developed by the authors, extends the capabilities that the semi-classical Monte Carlo simulation technique has offered for decades (DC, AC, noise, transients) to the quantum regime.

cond-mat.mes-hall↗

arXiv2016

On the classical Schrödinger equation

In this paper, the classical Schrödinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an additional single-valued condition for the Hamilton's principal function, the classical Schrödinger equation is obtained. This additional assumption implies inherent non-classical features on the description of the dynamics obtained from the classical Schrödinger equation: the trajectories do not cross in the configuration space. Second, departing from Bohmian mechanics and invoking the quantum-to-classical transition, the classical Schrödinger equation is obtained in a natural way for the center of mass of a quantum system with a large number of identical particles. This quantum development imposes the condition of dealing with a narrow wave packet, which implicitly avoids the non-classical features mentioned above. We illustrate all the above points with numerical simulations of the classical and quantum Schrödinger equations for different systems.

quant-ph↗

arXiv2016

Weak Values from Displacement Currents in Multiterminal Electron Devices

Weak values allow the measurement of observables associated with noncommuting operators. Up to now, position-momentum weak values have been mainly developed for (relativistic) photons. In this Letter, a proposal for the measurement of such weak values in typical electronic devices is presented. Inspired by the Ramo-Shockley-Pellegrini theorem that provides a relation between current and electron velocity, it is shown that the displacement current measured in multiterminal configurations can provide either a weak measurement of the momentum or strong measurement of position. This proposal opens new opportunities for fundamental and applied physics with state-of-the-art electronic technology. As an example, a setup for the measurement of the Bohmian velocity of (nonrelativistic) electrons is presented and tested with numerical experiments.

quant-ph↗

arXiv2016

On the noise induced by the measurement of the THz electrical current in quantum devices

From a quantum point of view, it is mandatory to include the measurement process when predicting the time-evolution of a quantum system. In this paper, a model to treat the measurement of the (TeraHertz) THz electrical current in quantum devices is presented. The explicit interaction of a quantum system with an external measuring apparatus is analyzed through the unambiguous notion of the Bohmian conditional wave function, the wave function of a subsystem. It it shown that such THz quantum measurement process can be modeled as a weak measurement: The systems suffers a small perturbation due to the apparatus, but the current is measured with a great uncertainty. This uncertainty implies that a new source of noise appears at THz frequencies. Numerical (quantum Monte Carlo) experiments are performed confirming the weak character of this measurement. This work also indicates that at low frequencies this noise is negligible and it can be ignored. From a classical point of view, the origin of this noise due to the measurement at THz frequencies can be attributed to the plasmonic effect of those electrons at the contacts (by interpreting the contacts themselves as part of the measuring apparatus).

quant-ph↗

arXiv2016

Local energy and power for many-particle quantum systems driven by an external electrical field

We derive expressions for the expectation values of the local energy and the local power transferred by an external electrical field to a many-particle system of interacting spinless electrons. In analogy with the definition of the (local) presence and current probability densities, we construct a local energy operator such that the time-rate of change of its expectation value provides information on the spatial distribution of power. Results are presented as functions of an arbitrarily small volume $Ω$, and physical insights are discussed by means of the quantum hydrodynamical representation of the wavefunction, which is proven to allow for a clear-cut separation into contributions with and without classical correspondence. Quantum features of the local power are mainly manifested through the presence of non-local sources/sinks of power and through the action of forces with no classical counterpart. Many-particle classical-like effects arise in the form of current-force correlations and through the inflow/outflow of energy across the boundaries of the volume $Ω$. Interestingly, such intriguing features are only reflected in the expression for the local power when the volume $Ω$ is finite. Otherwise, for closed systems with $Ω\to \infty$, we recover a classical-like single-particle expression.

quant-ph↗

arXiv2015

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

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.

quant-ph↗

arXiv2015

Quantum Noise from a Bohmian perspective: fundamental understanding and practical computation in electron devices

In the literature, the study of electron transport in quantum devices is mainly devoted to DC properties. The fluctuations of the electrical current around these DC values, the so-called quantum noise, are much less analyzed. The computation of quantum noise is intrinsically linked (by temporal correlations) to our ability to understand/compute the time-evolution of a quantum system that is measured several times. There are several quantum theories that provide different (but empirically equivalent) ways of understanding/computing the perturbation of the wave function when it is measured. In this work, quantum noise associated to an electron impinging upon a semitransparent barrier is explained using Bohmian mechanics (which deals with wave functions and point-like particles). From this result, the fundamental understanding and practical computation of quantum noise with Bohmian trajectories are discussed. Numerical simulations of low and high frequency features of quantum shot noise in a resonant tunneling diode are presented (through the BITLLES simulator), showing the usefulness of the Bohmian approach.

quant-ph↗

arXiv2014

Can the wave function in configuration space be replaced by single-particle wave functions in physical space?

The ontology of Bohmian mechanics includes both the universal wave function (living in 3N-dimensional configuration space) and particles (living in ordinary 3-dimensional physical space). Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated -- replaced by a set of single-particle pilot-wave fields living in ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields (living in 3-dimensional space) which influence the particles' motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy (like that enjoyed by GRW type theories) with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the (once popular but prematurely-abandoned) program of trying to replace the (philosophically puzzling) configuration space wave function with a (totally unproblematic) set of fields in ordinary physical space.

quant-ph↗