Wave-particle dualism and the interpretation of quantum mechanics

The realist interpretations of quantum theory, proposed by de Broglie and by Bohm, are re-examined and their differences, especially concerning many-particle systems and the relativistic regime, are explored. The impact of the recently proposed experiments of Vigier et al. and of Ghose et al. on the debate about the interpretation of quantum mechanics is discussed. An indication of how de Broglie and Bohm would account for these experimental results is given.     

Particle Trajectories for Quantum Field Theory

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic quantum field theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm’s approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic quantum field theory. In the present paper, Bell’s formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of (stochastic) trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model.     

Protective measurements and Bohm trajectories

We consider a protective measurement on a particle in a box and find that the particle participates in a local interaction although its Bohm trajectory never comes near the interaction region. This confirms earlier results to the same extent for von Neumann measurements and weak measurements, and challenges any realistic interpretation of Bohm trajectories.     

Three-dimensional modelling of dissipative quantum transport in quantum dots and atomistic scale devices using nonHermitian generalized potentials

In this paper we introduce a phenomenology for inserting dissipation into the single-particle Schrödinger equation for carrier transport by utilizing appropriate nonHermitian additions to the Hamiltonian. The nonHermitian terms are determined by incorporating model particle trapping/de-trapping, momentum gain/loss, energy gain/loss into the quantum continuity equations derived within the Bohm picture and then reconstructing the full Hamiltonian by reversing the Bohm projection. The new phenomenology is designed to obtain quantum velocity flows using the Bohm projection of solutions to the nonHermitian Schrödinger equation for applications in 2D and 3D quantum dots and mesoscopic MOSFETs. For this purpose we introduce a novel fast algorithm to compute the wave function in 2D and 3D based on a two time step iteration and direct integration.     

Stochasticity in a many-particle system with finite time of interaction

The statistical characteristics of a many-particle system with finite time of interaction under different kinds of instability of trajectories in the phase space are studied.     

Quantum cosmology with varying speed of light and Bohmian trajectories

The classical trajectories for FLRW universe with varying speed of light are obtained for the cases in which the cosmological constant depends or not depend on the velocity of light. The theory is then quantized and the corresponding WDW equation is solved. It is shown that the method of causal interpretation of Bohm can be applied successfully to the theory. Finally the Bohmian trajectories are obtained and compared with the classical ones.     

Position measurements in the de Broglie–Bohm interpretation of quantum mechanics

The de Broglie–Bohm interpretation of quantum mechanics assigns positions and trajectories to particles. We analyze the validity of a formula for the velocities of Bohmian particles which makes the analysis of these trajectories particularly simple. We apply it to particle detectors of four different types and show that the detectors of three of these types lead to “surrealistic trajectories”, i.e., leave a trace where the Bohmian particle was not present.     

Quantum trajectories and the Bohm time constant

This work proposes a new logarithmic nonlinear Schrödinger equation to describe the dynamics of a wave packet under continuous measurement. Via the method of quantum trajectories formalism of the Bohmian model of quantum mechanics, it is shown that this continuous measurement alters the dynamical properties of the measured system. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge asymptotically in time to classical trajectories. So, continuous measurements not only disturb the particle but compel it to eventually converge to a Newtonian regime. The rate of convergence depends on what is defined here as the Bohm time constant which characterizes the resolution time of the measurement. If the initial wave packet width is taken to be equal to 2.8×10⁻¹⁵ m (the approximate size of an electron) then the Bohm time constant is found to be about 6.8×10⁻²⁶ s.     

Quintom Potentials from Quantum Cosmology Using the FRW Cosmological Model

We construct the quintom potential of dark energy models in the framework of spatially flat Friedmann–Robertson Walker universe in the inflationary epoch, using the Bohm like approach, known as amplitude-real-phase. We find some potentials for which the wave function of the universe is found analytically and we have obtained the classical trajectories in the inflation era.     

An Approach to Construct Wave Packets with Complete Classical-Quantum Correspondence in Non-relativistic Quantum Mechanics

We introduce a method to construct wave packets with complete classical and quantum correspondence in one-dimensional non-relativistic quantum mechanics. First, we consider two similar oscillators with equal total energy. In classical domain, we can easily solve this model and obtain the trajectories in the space of variables. This picture in the quantum level is equivalent with a hyperbolic partial differential equation which gives us a freedom for choosing the initial wave function and its initial slope. By taking advantage of this freedom, we propose a method to choose an appropriate initial condition which is independent from the form of the oscillators. We then construct the wave packets for some cases and show that these wave packets closely follow the whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm interpretation of quantum mechanics to quantify this correspondence and show that the resulting Bohmian trajectories are also in complete agreement with their classical counterparts.     

Quasi-local action of curl-less vector potential on vortex dynamics in superconductors

Studies of the Abrikosov vortex motion in superconductors based on time-dependent Ginzburg–Landau equations reveal an opportunity to detect the values of the Aharonov–Bohm type curl-less vector potentials without closed-loop electron trajectories encompassing the magnetic flux.     

Evolution Equations for Fermion Systems in the Continual Representation

The quantum balance equations are derived for the number of particles, the momentum, the energy, and the magnetic moment density. These equations in the classical limit 0 transform into the well-known balance equations. The equation for the magnetic moment is a generalization of the Bloch equation. It is also shown that the spin-spin interaction Hamiltonian, conventionally used in the quantum theory of a many-particle system, yields incorrect equations for the magnetic field in a medium and that this defect can be eliminated. An important role of the Bohm quantum potential is demonstrated for a system of identical bosons and fermions.     

On the conformally coupled scalar field quantum cosmology

We propose a new initial condition for the homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces have positive curvature. After solving corresponding Wheeler–DeWitt equation, we obtain exact solutions in both classical and quantum levels. We propose appropriate initial condition for the wave packets which results in a complete classical and quantum correspondence. These wave packets closely follow the classical trajectories and peak on them. We also quantify this correspondence using de Broglie–Bohm interpretation of quantum mechanics. Using this proposal, the quantum potential vanishes along the Bohmian paths and the classical and Bohmian trajectories coincide with each other. We show that the model contains singularities even at the quantum level. Therefore, the resulting wave packets closely follow the classical trajectories from big-bang to big-crunch.     

de Broglie–Bohm interpretation for wave function of a toroidal black hole

The mass function of a toroidal black hole as a dynamical variable is given by using Kuchar’s approach. Then the toroidal black hole is investigated by using the de Broglie–Bohm approach, and its quantum potential and quantum trajectories are obtained. In our process the vector potential of the electromagnetic field in the toroidal black hole is treated as a canonical variable.     

在Bohm模式下氘氚燃烧的等离子体温度分布

在一定的等离子体密度分布下,从电子和离子能量输运方程出发,研究了氘氚燃烧下的等离子体温度分布.研究中采用了JET适用的Bohm模式下的热传导系数,考虑了α粒子的反常扩散效应,动态反馈加热.研究结果表明,Bohm模式下的热传导率从等离子体中心到边缘逐渐增加;为了维持氘氚燃烧,必须有动态反馈加热,否则,燃烧将熄灭;α粒子的反常扩散,使得加热效率因子η_α在中心区域小于1,在外层大于1;α粒子的反常扩散越强烈,中心离子温度越高,是由于中心区域的热传导小,电子温度低,反馈加热功率增加的结果;B 关键词：     

Quantization in classical mechanics and its relation to the Bohmian Ψ-field

Based on the Chetaev theorem on stable dynamical trajectories in the presence of dissipative forces, we obtain the generalized condition for stability of Hamilton systems in the form of the Schrödinger equation.It is shown that the energy of dissipative forces, which generate the Chetaev generalized condition of stability, coincides exactly with the Bohm “quantum” potential. Within the frame-work of Bohmian quantum mechanics supplemented by the generalized Chetaev theorem and on the basis of the principle of least action for dissipative forces, we show that the squared amplitude of a wave function in the Schrödinger equation is equivalent semantically and syntactically to the probability density function for the number of particle trajectories, relative to which the velocity and the position of the particle are not hidden parameters. The conditions for the correctness of trajectory interpretation of quantum mechanics are discussed.     

On Epstein’s Trajectory Model of Non-Relativistic Quantum Mechanics

In 1952 Bohm presented a theory about non-relativistic point-particles that move deterministically along trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm’s particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general very different from those in the de Broglie-Bohm theory. In certain cases they even seem bizarre and rather unphysical. Nevertheless, it is argued that the model seems to reproduce the predictions of standard quantum theory (just as the de Broglie-Bohm theory).     

The Aharonov–Bohm effect in graphene rings

This is a review of electronic quantum interference in mesoscopic ring structures based on graphene, with a focus on the interplay between the Aharonov–Bohm effect and the peculiar electronic and transport properties of this material. We first present an overview on recent developments of this topic, both from the experimental as well as the theoretical side. We then review our recent work on signatures of two prominent graphene-specific features in the Aharonov–Bohm conductance oscillations, namely Klein tunneling and specular Andreev reflection. We close with an assessment of experimental and theoretical development in the field and highlight open questions as well as potential directions of the developments in future work.