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This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
It is often argued that measurable predictions of Bohmian mechanics cannot be distinguished from those of a theory with arbitrarily modified particle velocities satisfying the same equivariance equation. By considering the wave function of…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
We present a local-realistic description of both wave-particle duality and Bohmian trajectories. Our approach is relativistic and based on Hamilton's principle of classical mechanics, but departs from its standard setting in two respects.…
A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and…
Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation. Although the…
We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the…
It is shown that Bohmian mechanics is internally consistent in the sense that the equations of motion typically have global solutions despite the fact that the velocity field is singular at the nodes of the wave function and at other…
The transport and continuum equations exhibit a number of conservation laws. For example, scalar multiplication is conserved by the transport equation, while positivity of probabilities is conserved by the continuum equation. Certain…
We explain the approximate nature of particle trajectories in Bohm's quantum mechanics. They are streamlines of a superfluid in Madelung's reformulation of the Schr\"{o}dinger wave function, around which the proper particle trajectories…
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…
We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the…
In this study, we use the concept of Bohmian trajectories to present a dynamical and deterministic interpretation for the gravity induced wave function reduction. We shall classify all possible regimes for the motion of a particle, based on…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
In this paper the relations between the asymptotic velocity operators of a quantum system and the asymptotic velocities of the associated Bohmian trajectories are studied. In particular it is proved that, under suitable conditions of…
In this paper I describe the history of the surreal trajectories problem and argue that in fact it is not a problem for Bohm's theory. More specifically, I argue that one can take the particle trajectories predicted by Bohm's theory to be…
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…
The violation of Bell type inequalities in quantum systems manifests that quantum states cannot be described by classical probability distributions. Yet, Bohmian mechanics is a realistic, non-local theory of classical particle trajectories…
We consider the problem of whether there are deterministic theories describing the evolution of an individual physical system in terms of the definite trajectories of its constituent particles and which stay in the same relation to Quantum…
The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…