Related papers: Simple Proof for Global Existence of Bohmian Traje…
Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they…
The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to…
We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same…
After summarizing three versions of trajectory-based quantum mechanics, it is argued that only the original formulation due to Bohm, which uses the Schr\"odinger wave function to guide the particles, can be readily extended to particles…
The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown, that the necessary and sufficient condition for there to be a…
In this paper, we prove the global existence of H\"older continuous solutions for the Cauchy problem of a family of partial differential equations, named as $\lambda$-family equations, where $\lambda$ is the power of nonlinear wave speed.…
In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…
We consider discrete nonlinear Schr\"odinger equations of n sites with periodic boundary conditions. These equations have n branches of standing waves that bifurcate from zero. Traveling waves appear as a symmetry-breaking from the standing…
The global existence of classical solutions to strongly coupled parabolic systems is shown to be equivalent to the availability of an iterative scheme producing a sequence of solutions with uniform continuity in the BMO norms. Amann's…
We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, near the continuous limit.We construct a family of solutions…
Since particle such as molecule, atom and nucleus are composite particle, it is important to recognize that physics must be invariant for both the composite particle and its constituent particles, this requirement is called particle…
We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for quantum particles in a curved background space-time containing a spacelike singularity. As an example of such a metric we use the Schwarzschild metric,…
In this paper, we study the global existence and uniqueness, Gaussian lower bound, and moment estimates in the spatially homogeneous Boltzmann equation for Fermi-Dirac particles for hard potential ($0\leq \gamma\leq 2$) with angular cutoff…
We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaitre-Robertson-Walker model and investigate the question whether or not there are singularities, in the sense that the universe reaches zero volume. We…
In this paper we intend to extend some ideas of a recently proposed Lorentz-invariant Bohmian model, obeying Klein-Gordon equations, but considering particles with a spin different than zero. First we build a Bohmian model for a single…
The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid…
We show global existence of classical solutions for the nonlinear Nordstr\"om theory with a source term and a cosmological constant under the assumption that the source term is small in an appropriate norm, while in some cases no smallness…
We prove an existence theorem for the Boltzmann-Fermi-Dirac equation for integrable collision kernels in possibly bounded domains with specular reflection at the boundaries, using the characteristic lines of the free transport. We then…
In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…
Recently, Bohmian mechanics has been challenged [Nature 643, 67 (2025)] by studying a system in which the motion of particles cannot be associated only with the gradient of phase of the wave function. We point out that, in general, Bohmian…