This chapter discusses how Bohmian mechanics can help us to understand and model the behavior of novel electron device prototypes at the nanometer and picosecond scales. It shows that how Bohmian mechanics can help us in the understanding and designing the upcoming electron device prototypes. The chapter also discusses how Bohmian mechanics can help us to study many-particle quantum electron transport phenomena in nanoelectronic devices and an important advantage of Bohmian mechanics: its ability to treat many-particle systems. It explains the birth of the electronics and its evolution towards nanoelectronics. The chapter also shows that the Bohmian perspective provides useful tools when dealing with the continuous measurement of the electrical current in nanodevices. The former appears at nonzero temperature, where the thermal agitation causes the occupation of energy states to fluctuate. The practical expressions for the computation of the current fluctuations within Bohmian mechanics are quite simple.
This chapter discusses how Bohmian mechanics can help us to understand and model the behavior of novel electron device prototypes at the nanometer and picosecond scales. It shows that how Bohmian mechanics can help us in the understanding and designing the upcoming electron device prototypes. The chapter also discusses how Bohmian mechanics can help us to study many-particle quantum electron transport phenomena in nanoelectronic devices and an important advantage of Bohmian mechanics: its ability to treat many-particle systems. It explains the birth of the electronics and its evolution towards nanoelectronics. The chapter also shows that the Bohmian perspective provides useful tools when dealing with the continuous measurement of the electrical current in nanodevices. The former appears at nonzero temperature, where the thermal agitation causes the occupation of energy states to fluctuate. The practical expressions for the computation of the current fluctuations within Bohmian mechanics are quite simple.
The necessity of faster and smaller devices is pushing the electronic industry into developing electron devices with solid-state structures of a few nanometers driven by picosecond signals. Electron dynam- ics in such scenarios is in general governed by quantum mechanical laws. This chapter is devoted to discuss how Bohmian mechanics can help us to understand and model the behavior of novel electron devices at the nanometer and picosecond scales. The adaptation of Bohmian mechanics to electron transport in open systems leads to a quantum Monte Carlo algorithm, where randomness appears because of the uncertainties in the number of electrons, their energies, and the initial positions of the (Bohmian) trajectories. A general, versatile, and time-dependent three-dimensional (3D) elec- tron transport simulator for nanoelectronic devices, namedBITLLES (Bohmian Interacting Transport for nonequiLibrium eLEctronic Structures), is presented, showing its ability for a full prediction (direct current [DC], alternating current [AC], fluctuations, etc.) of the electrical characteristics of any nanoelectronic device. See the website http://europe.uab.es/bitlles . As a typical example of the BITLLES capabilities, we discuss the performance of a resonant tunneling diode.
Today, the necessity of faster and smaller devices is pushing the electronic industry into developing electron devices with solid-state structures of few nanometers. In these dimensions electron dynamics are in general governed by quantum mechanical laws. We have recently shown that Bohmian trajectories allow a direct treatment of the many-particle interaction among electrons with an accuracy comparable to DFT techniques. In this article we present a general, versatile and time-dependent 3D quantum electron transport simulator, named BITLLES (Bohmian Interacting Transport in Electronic Structures), based on Bohmian trajectories for nanoelectronic devices. As a numerical example, we show the ability of BITLLES simulator to predict the electrical characteristics (DC, AC and fluctuations) of a Resonant Tunneling Diode.
Moore’s law has been the milestone for electronics improvement, and the cause for the exponential growth in our computational abilities and for reaching nanoscale electron devices. At such dimensions, classical simulation tools must be substituted by quantum ones. Such substitution implies to tackle new fundamental problems. First, the many-body problem makes (almost) impossible the exact simulation of many particles scenarios. Second, the measurement problem is especially relevant in high-frequency scenarios where multi-time measurements are mandatory. Alternatively to the orthodox theory, Bohmian mechanics emerges as a quantum theory which is specially well-equipped for the simulation of high-frequency characteristic of quantum electron devices. The Bohmian theory provides the conditional wave function that guides particles with well-defined positions. In this thesis, I explored quantum transport using Bohmian mechanics, putting special emphasis to graphene, a 2D material with linear bandstructure, which is expected to play an important role in the next future electronics. Differently from other materials, graphene obeys the bispinor Dirac equation, electrons behave as massless particles, exhibiting exotic behaviors, such as the Klein Tunneling effect. During the thesis, the quantum BITLLES simulator has been improved to correctly model electron nanodevices with either linear (by the inclusion of the complex bispinor Dirac equation) or parabolic bandstructures in either ballistic or dissipative (by the inclusion of the complete positive Bohmian scattering approach) systems. Thus, the BITLLES has become the candidate for substituting the versatile semiclassical Monte Carlo approach in the quantum regime, while keeping the versatility to predict DC, AC and noise performances. As practical applications, during the thesis, unexpected scattering probabilities in a Hong-Ou-Mandel experiment were predicted. In addition, different current-voltage characteristics were analyzed. Finally, a new limit (due to the discrete nature of charge) for ultra-small logic applications working at THz frequencies was predicted.
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book explains the historical development of Bohmian mechanics, Bohmian mechanics for single particle and for many particle systems. It discusses the dynamics of a single hydrogen atom interacting with a strong laser and presents a clear example on how a Bohmianthinking on superluminal velocities and nonlocal interactions helps in extending the quantum theory towards relativity and quantum field theory. The book also explains model nanoscale electron devices and their Bohmiancomputing development for knowing the ab initio quantum mechanical structure, energetics and thermodynamics of multiatoms systems. It deals with new cosmological models describing the accelerating universe in the spatially flat case. The book describes how many conceptual problems that appear in a description of gravity in quantum mechanical terms, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian perspective.
With the aim of manufacturing faster and smaller devices, the electronic industry is today entering into the nanoscale and the high frequency regimes. In this particular scenario, the dynamics of the electron charge becomes affected by quantum mechanical laws, both, for its spatial or temporal description. We have recently shown that Bohmian trajectories allow a direct treatment of the time-dependent many-particle interaction among electrons with an accuracy comparable to Density Functional Theory techniques. In addition, Bohmian mechanics, by combining wave functions and trajectories, provides a very simple description on how to describe multi-time measurements in quantum scenarios. Using the previous formalism, in this work we present a general purpose time-dependent 3D quantum electron transport simulator named BITLLES (Bohmian Interacting Transport in large low-dimensional Electronic Structures) especially indicated for AC, transients and noise predictions. As a numerical example of its capabilities, we compute the full electrical characteristics (DC, High frequency and fluctuations) of a Resonant Tunneling Diode.
Mesoscopic physics and nanoelectronics concentrate on systems with dimensions somewhere between atomic and everyday macroscopic scale. Modern technology enables construction of submicron nanostructures where modeling based on classical physics has proven inadequate. It is possible to design electric circuits where dynamics of single electrons and photons are controlled using state-of-the-art experimental methods. For quantitative understanding of these systems it is necessary to resort to a quantum-mechanical description. Quantum phenomena, such as tunneling and a wave-like interference of particles, are essential ingredients of physics in mesoscopic systems. Field of mesoscopic physics contains a rich variety of topics ranging from fundamental condensed matter physics to quantum information processing and possible future technological applications. \n \nThis thesis presents theoretical studies of mesoscopic quantum phenomena in nanostructures and small electronic devices. We have focused on effects of environment fluctuations and investigated connections between fluctuations and transport phenomena. Decoherence in quantum bits (qubits) and quantum state engineering in superconducting circuits are also studied. The theoretical analysis in each case requires an open-system treatment. \n \nEffects of current fluctuations on quantum probe systems have been studied in detail. We have calculated transitions induced by current noise and discussed how these could be used for characterization of fluctuations. We have also shown that electric fluctuations play a key role in radiation and photon heat transport in nanostructures. Motivated by recent advances in mesoscopic electron-photon systems, we have studied a response of a coupled resonator-qubit system, squeezing of quantum fluctuations in small superconducting circuits and investigated decoherence in Josephson flux qubits.