Related papers: Partial Integrability of 3-d Bohmian Trajectories
Chaos in Bohmian Quantum Mechanics is an open field of research. In general, most of the 3-d Bohmian trajectories are free to wander around the 3-d space. However there are cases where the evolution of the trajectories is dictated by exact…
We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found…
In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems…
In the present paper we study the classical and the quantum H\'enon-Heiles systems. In particular we make a comparison between the classical and the quantum trajectories of the integrable and of the non integrable H\'enon Heiles…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are…
We analyze the dynamics of a quantum particle in a one-dimensional bistable potential within the framework of Bohm's quantum mechanics. We give arguments that evidence the fallacy of certain claims found in the literature dealing with the…
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:…
Bohmian mechanics is a non-relativistic quantum theory based on a particle approach. In this paper we study the Schr\"odinger equation with rapidly oscillating potential and the associated Bohmian trajectory. We prove that the corresponding…
Claims have been made that, in two-particle interference experiments involving bosons, Bohmian trajectories may entail observable consequences incompatible with standard quantum mechanics. By general arguments and by an examination of…
In this paper we examine the evolution of Bohmian trajectories in the presence of quantum entanglement. We study a simple two-qubit system composed of two coherent states and investigate the impact of quantum entanglement on chaotic and…
We describe the advantages and disadvantages of numerical methods when Bohmian trajectory-grids are used for numerical simulations of quantum dynamics. We focus on the crucial non crossing property of Bohmian trajectories, which numerically…
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…
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is…
A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of…
Bohmian trajectories are considered for a particle that is free (i.e. the potential energy is zero), except for a half-line barrier. On the barrier, both Dirichlet and Neumann boundary conditions are considered. The half-line barrier yields…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
We determine approximate numerical integrals of motion of 2D symmetric Hamiltonian systems. We detail for a few gravitational potentials the conditions under which quasi-integrals are obtained as polynomial series. We show that each of…
The quantum trajectories in the de Broglie-Bohm formulation of quantum mechanics depend on an additional quantum potential derived from the full wave solution of Schr\"odinger's equation. The task of supplying collectively all the correct…
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…