Related papers: Bohmian particle trajectories in relativistic boso…
According to Bohmian dynamics, the particles of a quantum system move along trajectories, following a velocity field determined by the wave-function Psi(x,t). We show that for simple one-dimensional systems any initial probability…
We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form $\Psi=a\Psi_{m_1,n_1}(x,y)+b\Psi_{m_2,n_2}(x,y)+c\Psi_{m_3,n_3}(x,y)$. We first find the…
Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
Recently, there has been progress in developing interior-boundary conditions (IBCs) as a technique of avoiding the problem of ultraviolet divergence in non-relativistic quantum field theories while treating space as a continuum and…
So-called hidden variables introduced in quantum mechanics by de Broglie and Bohm have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The start viewpoint was the…
The prediction of arrival time or first passage time statistics of a quantum particle is an open problem, which challenges the foundations of quantum theory. One of the most promising and insightful approaches to this problem stems from the…
Quantum mechanics is the most successful theory to describe microscopic phenomena. It was derived in different ways over the past 100 years by Heisenberg, Schr\"{o}dinger, and Feynman. At the same time, other interpretations have been…
The proposal that the one-parameter solutions of the real part of the Schrodinger equation (quantum Hamilton-Jacobi equation) can be regarded as `quantum particle trajectories' has received considerable attention recently. Opinions as to…
The similarity between the energy spectra of relativistic particles and that of quasi-particles in super-conductivity BCS theory makes us conjecture that the relativistic physical vacuum medium as the ground state of the background field is…
We develop an extension of Bohmian mechanics to a curved background space-time containing a singularity. The present paper focuses on timelike singularities. We use the naked timelike singularity of the super-critical Reissner-Nordstrom…
We present a Bohmian description of a decaying quantum system. A particle is initially confined in a region around the origin which is surrounded by a repulsive potential barrier. The particle leaks out in time tunneling through the…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…
"Particle"-trajectories are defined as integrable $dx_\mu dp^\mu = 0$ paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalise in $(x, p)$ projection, the phase associated with the…
We study the Quantum Brownian motion of a charged particle moving in a harmonic potential in the presence of an uniform external magnetic field and linearly coupled to an Ohmic bath through momentum variables. We analyse the growth of the…
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
We investigate both ordered and chaotic Bohmian trajectories within the Born distribution of Bohmian particles of an anisotropic 2d quantum harmonic oscillator. We compute the average values of energy, momentum, angular momentum, and…
We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite…
Initial momenta of de Broglie-Bohm trajectories generally do not obey quantum mechanical momentum distributions. The solution to this problem presented in the following leads to an extended hydrodynamic interpretation of quantum mechanics.…