Related papers: Simple Proof for Global Existence of Bohmian Traje…

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our…

Since the pioneering work of James E. Broadwell, discrete velocity models (DVMs) have played a fundamental role in approximating the Boltzmann equation and in the analysis of non-equilibrium gas dynamics. Despite their apparent simplicity,…

We analyze finite-sample statistics of Bohmian trajectories for single spinless and spin-1/2 particles. Equivariance ensures agreement with $|\psi|^2$ in the quantum equilibrium limit, yet experiments and simulations necessarily use finite…

We prove the existence of periodic travelling wave solutions for general discrete nonlinear Klein-Gordon systems, considering both cases of hard and soft on-site potentials. In the case of hard on-site potentials we implement a fixed point…

By studying the linearization of contour dynamics equation and using implicit function theorem, we prove the existence of co-rotating and travelling global solutions for the gSQG equation, which extends the result of Hmidi and Mateu…

We are interested in nonlocal Eikonal Equations arising in the study of the dynamics of dislocations lines in crystals. For these nonlocal but also non monotone equations, only the existence and uniqueness of Lipschitz and local-in-time…

In this paper, we establish global existence of smooth solutions for the Cauchy problem of the critical nonlinear wave equation with time dependent variable coefficients in three space dimensions…

Bohmian mechanics solves the wave-particle duality paradox by introducing the concept of a physical particle that is always point-like and a separate wavefunction with some sort of physical reality. However, this model has not been…

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which in particular ascribes trajectories to…

We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave…

In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann…

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…

We find that real and complex Bohmian quantum trajectories resulting from well-localized Klauder coherent states in the quasi-Poissonian regime possess qualitatively the same type of trajectories as those obtained from a purely classical…

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…

We consider smooth solutions of the Burgers-Hilbert equation that are a small perturbation $\delta$ from a global periodic traveling wave with small amplitude $\epsilon$. We use a modified energy method to prove the existence time of smooth…

We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and…

For certain non linear evolution equations, existence of global in time flows for large data is a fundamental and difficult question. In general, for dispersive and wave equations high regularity of the data does not automatically guarantee…

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…

The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep water under gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a…

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to QFT. By means of the Dirac sea model -- exemplified in the electron sector of…