We investigate the orgin of ``quantum superarrivals'' in the reflection and transmission probabilities of a Gaussian wave packet for a rectangular potential barrier while it is perturbed by either reducing or increasing its height. There exists a finite time interval during which the probability of reflection is {\it larger} (superarrivals) while the barrier is {\it lowered} compared to the unperturbed case. Similarly, during a certain interval of time, the probability of transmission while the barrier is {\it raised} {\it exceeds} that for free propagation. We compute {\it particle trajectories} using the Bohmian model of quantum mechanics in order to understand {\it how} this phenomenon of superarrivals occurs.
Scattering of a Gaussian wavepacket from rectangular potential barriers with increasing widths or heights is studied numerically. It is seen that during a certain time interval the time-evolving transmission probability increases compared to the corresponding unperturbed cases. In the literature this effect is known as superarrival in transmission probability. We present a trajectory-based explanation for this effect by using the concept of quantum potential energy and computing a selection of Bohmian trajectories. Relevant parameters in superarrivals are determined for the case that the barri…
Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a theory known as Bohmian mechanics, to which this article is an introduction.
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 tak…
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 t…
This work is about Bohmian mechanics, a non-relativistic quantum theory about the motion of particles and their trajectories, named after its inventor David Bohm (Bohm,1952). This mechanics resolves all paradoxes associated with the measurement problem in nonrelativistic quantum mechanics. It accounts for quantum randomness, absolute uncertainty, the meaning of the wave function of a system, collapse of the wave function, and familiar (macroscopic) reality. We review the purpose for which Bohmian trajectories were invented: to serve as the foundation of quantum mechanics, i.e., to explain quan…
In the Entropic Dynamics (ED) derivation of the Schroedinger equation the physical input is introduced through constraints that are implemented using Lagrange multipliers. There is one constraint involving a "drift" potential that correlates the motions of different particles and is ultimately responsible for entanglement. The purpose of this work is to deepen our understanding of the corresponding multiplier. Its main effect is to control the strength of the drift relative to the fluctuations. We show that ED exhibits a symmetry: models with different values of the multiplier can lead to the …
The reality of Bohm's intellectual journey is very different from what is often claimed by the proponents of "Bohmian Mechanics" and others as we will explain in this paper. He did not believe a mechanical explanation of quantum phenomena was possible. Central to his thinking, and incidentally to Bohr's also, was the notion of 'unbroken wholeness', a notion that is crucial for understanding quantum properties like quantum nonlocality. His proposals were based on a primitive notion of `process' or `activity', producing a more 'organic' approach to quantum phenomena. He published many papers out…
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears naturally in classical statistical mechanics of relativistic particles, with scalar time being identified with the proper time along particle trajectories. The conceptual understanding of relativistic Bohmian mechanics is significantly enriched by this classical insight. In particular, the analogy between classical and Bohmian mechanics suggests the interpretation o…
In this review we deal with open (dissipative and stochastic) quantum systems within the Bohmian mechanics framework which has the advantage to provide a clear picture of quantum phenomena in terms of trajectories, originally in configuration space. The gradual decoherence process is studied from linear and nonlinear Schrödinger equations through Bohmian trajectories as well as by using the so-called quantum-classical transition differential equation through scaled trajectories. This transition is governed by a continuous parameter, the transition parameter, covering these two extreme open dyn…
The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple mathematical idea of linearly combining vectors in a Hilbert space. Specifically, the discussion turns around the connection between symmetries characterizing the wave function and the behavior in time displayed by the quantum flux when the latter is analyzed in terms of streamlines (Bohmian trajectories). This is illustrated with a series of analytical results an…
The ontological aspect of Bohmian mechanics, as a hidden-variable theory that provides us with an objective description of a quantum world without observers, is widely known. Yet its practicality is getting more and more acceptance and relevance, for it has proven to be an efficient and useful resource to tackle, explore, describe and explain such phenomena. This practical aspect emerges precisely when the pragmatic application of the formalism prevails over any other interpretational question, still a matter of debate and controversy. In this regard, the purpose here is to show and discuss ho…
Bohmian mechanics, a hydrodynamic formulation of the quantum theory, constitutes a useful tool to understand the role of the phase as the mechanism responsible for the dynamical evolution displayed by quantum systems. This role is analyzed and discussed here in the context of quantum interference, considering to this end two well-known scenarios, namely Young's two-slit experiment and Wheeler's delayed choice experiment. A numerical implementation of the first scenario is used to show how interference in a coherent superposition of two counter-propagating wave packets can be seen and explained…
What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function (representing a pure state) but by a density matrix (representing a mixed state). I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with a fundamental density matrix. The Past …
