Applied Bohmian Mechanics

Abstract

Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than 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 (non-unitary and nonlinear) quantum problems where the influence of the environment or the global wave function are unknown. 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 these type of problems that present non-unitary 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.

43 pages, 16 figures

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Cited by in corpus (39)

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• Dynamics of Tunneling Ionization using Bohmian Mechanics
• Physical vacuum is a special superfluid medium
• Correlated Electron-Nuclear Dynamics with Conditional Wave Functions
• Hydrodynamics of the Physical Vacuum: II. Vorticity dynamics
• Bohmian trajectory analysis of high-order harmonic generation: ensemble averages, non-locality and quantitative aspects
• Dynamics of Current, Charge and Mass
• Hydrodynamics of the Physical Vacuum: I. Scalar quantum sector
• Hydrodynamics of Superfluid Quantum Space: de Broglie interpretation of the quantum mechanics
• Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory
• Chaos and ergodicity in an entangled two-qubit Bohmian system
• Quantum consciousness in warm, wet, and noisy brain
• Entangled Quantum Dynamics of Many-Body Systems using Bohmian Trajectories
• Natural classical limit for the center of mass of many-particle quantum systems
• Semi-classical approximations based on Bohmian mechanics
• Universal Steps in Quantum Dynamics with Time-Dependent Potential-Energy Surfaces: Beyond the Born-Oppenheimer Picture
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• On the classical Schrödinger equation
• Partial Integrability of 3-d Bohmian Trajectories
• Uncertainty Relations in Hydrodynamics
• Many-body soliton-like states of the bosonic ideal gas
• On the self-interference in electron scattering: Copenhagen, Bohmian and geometrical interpretations of quantum mechanics
• Identifying weak values with intrinsic dynamical properties in Modal theories
• Stochastic Schrödinger equations and conditional states: a general Non-Markovian quantum electron transport simulator for THz electronics
• Splitting the source term for the Einstein equation to classical and quantum parts
• Contributions to single-shot energy exchanges in open quantum systems
• Mean Value of the Quantum Potential and Uncertainty Relations
• Symmetries and singular behaviors with Bohmian trajectories
• Nonclassical polarization dynamics in classical-like states
• Bohmian trajectories for the half-line barrier
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• The Dynamics of Wave-Particle Duality
• A Review on Ab Initio Approaches for Multielectron Dynamics
• Quantum and Classical Frontiers of Noise
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