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We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
Any decomposition of the total trajectory entropy production for Markovian systems has a joint probability distribution satisfying a generalized detailed fluctuation theorem, when all the contributing terms are odd with respect to time…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
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…
Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space-time scale. In these…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approximate approach is offerred that effectively propagates the statistics in time. Loss of…
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…
Process of dynamical tunneling in two-dimensional coupled potentials is considered within Bohmian approach to quantum mechanics. Quantum trajectories tend to go along the paths where potential energy increases and then decreases. It leads…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…
We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical…
The Bohm interpretation of quantum mechanics is applied to a transmission and reflection process in a double potential well. We consider a time dependent periodic wave function and study the particle trajectories. The average time,…
We analyze data from direct numerical simulations of homogeneous and isotropic turbulence (at Re_\lambda \approx 280) and study the statistics of curvature and torsion of Lagrangian trajectories in order to extract informations on the…
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…
Within the framework of Bohmian mechanics dwell times find a straightforward formulation. The computation of associated probabilities and distributions however needs the explicit knowledge of a relevant sample of trajectories and therefore…
We investigate dynamics of activated escape in periodically modulated systems. The trajectories followed in escape form diffusion broadened tubes, which are periodically repeated in time. We show that these tubes can be directly observed…
In our recent work (Sharoglazova et al., Nature 643, 67 (2025)), we reported the measurement of the speed of tunnelling particles using a coupled waveguide system. The measured speed was found to disagree with the standard guiding equation…
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…
It is shown that the Bohmian mechanics and the Madelung quantum hydrodynamics are different theories and the latter is a better ontological interpretation of quantum mechanics. A new stochastic interpretation of quantum mechanics is…
Being able to accurately model and predict the dynamics of dispersed inclusions transported by a turbulent flow, remains a challenge with important scientific, environmental and economical issues. One critical and difficult point is to…