Damiano Marian

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.

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.

Time-dependent exchange and tunneling: detection at the same place of two electrons emitted simultaneously from different sources

Two-particle scattering probabilities in tunneling scenarios with exchange interaction are analyzed with quasi-particle wave packets. Two initial one-particle wave packets (with opposite central momentums) are spatially localized at each side of a barrier. After impinging upon a tunneling barrier, each wave packet splits into transmitted and reflected components. When the initial two-particle anti-symmetrical state is defined as a Slater determinant of any type of (normalizable) one-particle wave packet, it is shown that the probability of detecting two (identically injected) electrons at the same side of the barrier is different from zero in very common (single or double barrier) scenarios. In some particular scenarios, the transmitted and reflected components become orthogonal and the mentioned probabilities reproduce those values associated to distinguishable particles. These unexpected non-zero probabilities are still present when non-separable Coulomb interaction or non-symmetrical potentials are considered. On the other hand, for initial wave packets close to Hamiltonian eigenstates, the usual zero two-particle probability for electrons at the same side of the barrier found in the literature is recovered. The generalization to many-particle scattering probabilities with quasi-particle wave packets for low and high phase-space density are also analyzed. The far-reaching consequences of these non-zero probabilities in the accurate evaluation of quantum noise in mesoscopic systems are briefly indicated.

Quantum dissipation with conditional wave functions: Application to the realistic simulation of nanoscale electron devices

Without access to the full quantum state, modelling dissipation in an open system requires approximations. The physical soundness of such approximations relies on using realistic microscopic models of dissipation that satisfy completely positive dynamical maps. Here we present an approach based on the use of the Bohmian conditional wave function that, by construction, ensures a completely positive dynamical map for either Markovian or non-Markovian scenarios, while allowing the implementation of realistic dissipation sources. Our approach is applied to compute the current-voltage characteristic of a resonant tunnelling device with a parabolic-band structure, including electron-lattice interactions. A stochastic Schrodinger equation is solved for the conditional wave function of each simulated electron. We also extend our approach to (graphene-like) materials with a linear band-structure using Bohmian conditional spinors for a stochastic Dirac equation.

Time-dependent simulation of particle and displacement currents in THz graphene transistors

Although time-independent models provide very useful dynamical information with a reduced computational burden, going beyond the quasi-static approximation provides enriched information when dealing with terahertz (THz) frequencies. In this work, the THz noise of dual-gate graphene transistors with DC polarization is analyzed from a careful simulation of the time-dependent particle and displacement currents. From such currents, the power spectral density (PSD) of the total current fluctuations are computed at the source, drain and gate contacts. The role of the lateral dimensions of the transistors, the Klein tunneling and the positive–negative energy injection on the PSD are analyzed. Through the comparison of the PSD with and without band-to-band tunneling and graphene injection, it is shown that the unavoidable Klein tunneling and positive–negative energy injection in graphene structures imply an increment of noise without similar increment on the current, degrading the (either low or high frequency) signal-to-noise ratio. Finally, it is shown that the shorter the vertical height (in comparison with the length of the active region in the transport direction), the larger the maximum frequency of the PSD. As a byproduct of this result, an alternative strategy (without length scaling) to optimize the intrinsic cut-off frequency of graphene transistors is envisioned.

Dissipative quantum transport using one-particle time-dependent (conditional) wave functions

An effective single-particle Schrodinger equation to include dissipation into quantum devices is presented. This effective equation is fully understood in the context of Bohmian mechanics, a theory of particles and waves, where it is possible to define unambiguously the wave function of a subsystem, the so-called conditional wave function. In particular the change in energy and momentum of an electron when interacting with a phonon is presented, both theoretically and numerically. This work is a first step to include dissipation into the fully-quantum simulator BITLLES.

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 a THz quantum measurement process can be modeled as a weak measurement: the systems suffer 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).

On the back-action of THz measurement on the total current of quantum devices

Measuring a quantum system implies some kind of perturbation of the system itself. A novel approach to include the perturbation of the quantum electron device, i.e. the back-action, due to the TeraHertz (THz) measurement of the total current is presented. The approach is based on a microscopic description of the interaction between the quantum system and the measuring apparatus, in terms of conditional (Bohmian) wave functions. The disturbance of the quantum system due to measurements at THz frequencies and the (perturbed) value of the total current is numerically computed for a simple two-terminal device. Contrarily to traditional strong (i.e. projective) measurements, it is shown that the measurement of the total current at THz frequencies can be modeled by a weak measurement. An additional unavoidable source of fluctuations of the current is predicted at THz frequencies due to the back-action (i.e. the quantum measurement).

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

Quantum noise with exchange and tunnelling 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 tunnelling 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 is analysed. 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.

Noise in Quantum Devices: A Unified Computational Approach for Different Scattering Mechanisms

When talking about noise in quantum devices two issues must be faced: how to model the evolution of an electronic system with scattering and how this noise is practically computed in a quantum device simulator. In the present paper, we address both problems from a practical and computational point of view. In particular, as the electronic quantum subsystem is an open (normally far from equilibrium) system, we use the notion of conditional wave function, the wave function of a subsystem in Bohmian mechanics, an alternative version of quantum mechanics which along with the wave function posited definite positions for the particles. This allows us to define an effective equation in several physical situations, ranging from the simple tunneling barrier to the interaction with a bath of phonons. Finally, we present how this development can be used to compute quantum noise in a quantum device simulator.