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A thought experiment is described and the probability of a particular type of results is predicted according to the quantum formalism. Then, the assumption is made that there exists a particle that travels from the source to one of the…
This paper is devoted to the analysis of massive particle in general and Newton-Cartan Background in de Broglie-Bohm Theory. We find classical and quantum version of Hamilton-Jacobi equations and find their relations to wave equations. We…
A quantum model based on a Euler-Lagrange variational approach is proposed. In analogy with the classical transport, our approach maintain the description of the particle motion in terms of trajectories in a configuration space. Our method…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Under purification and irreducibility assumptions, these Markov processes admit a unique invariant measure…
The Bridge Theory that is based on the role that the transversal component of the Pointing vector has in the localisation in the neighbourhood of a dipole of an amount of energy and momentum equal to ones of a photon of same frequency, if…
A usual assumption in the so-called {\it de Broglie - Bohm} approach to quantum dynamics is that the quantum trajectories subject to typical `guiding' wavefunctions turn to be quite irregular, i.e. {\it chaotic} (in the dynamical systems'…
The concepts of quantile position, trajectory, and velocity are defined. For a tunneling quantum mechanical wave packet, it is proved that its quantile position always stays behind that of a free wave packet with the same initial…
Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has mainly been restricted to…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case,…
A common knowledge suggests that trajectories of particles in quantum mechanics always have quantum uncertainties. These quantum uncertainties set by the Heisenberg uncertainty principle limit precision of measurements of fields and forces,…
The de Broglie-Bohm theory is about non-relativistic point-particles that move deterministically along trajectories. The theory reproduces the predictions of standard quantum theory, given that the distribution of particles over an ensemble…
Relativistic quantum transport theory has begun to play an important role in the space-time description of matter under extreme conditions of high energy density in out-of-equilibrium situations. The following introductory lectures on some…
We show that the average trajectories of relativistic quantum particles in Schwarzschild spacetime, obtained via quantum mechanical weak measurements of momentum and energy, are equivalent to the predicted flow lines of probability current…
Several recent arguments purport to show that there can be no relativistic, quantum-mechanical theory of localizable particles and, thus, that relativity and quantum mechanics can be reconciled only in the context of quantum field theory.…
Distributed quantum networks will allow users to perform tasks and to interact in ways which are not possible with present-day technology. Their implementation is a key challenge for quantum science and requires the development of…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
We show that the conductance of neutral atoms through a tightly confining waveguide constriction is quantized in units of lambda_dB^2/pi, where lambda_dB is the de Broglie wavelength of the incident atoms. Such a constriction forms the atom…
Quantum trajectory calculations for electrons are a useful tool in the field of molecular dynamics, e.g. to understand processes in ultrafast spectroscopy. They have, however, two limitation: On the one hand, such calculations are typically…