Related papers: A Stochastic Hamiltonian Approach for Quantum Jump…
The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schroedinger's…
We study the nonequilibrium dynamics of quantum jumps in a one-dimensional chain of atoms. Each atom is driven on a strong transition to a short-lived state and on a weak transition to a metastable state. We choose the metastable state to…
It is well-known that quantum mechanics admits two distinct evolutions: the unitary evolution, which is deterministic and well described by the Schr\"{o}dinger equation, and the collapse of the wave function, which is probablistic,…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
A recently introduced particle-based model for fluid dynamics with effective excluded volume interactions is analyzed in detail. The interactions are modeled by means of stochastic multiparticle collisions which are biased and depend on…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
A quantum trajectory is the natural response of a quantum system subject to external perturbations due to continuous indirect measurement. We completely characterize the asymptotic behavior of continuously monitored quantum systems in…
We describe a previously unexplored effect of the continuous spontaneous localization model whereby a correlation develops in the distributions of two nearby non-interacting particles following a period of diffusion. We propose the use of…
Spatially localized structures are key components of turbulence and other spatio-temporally chaotic systems. From a dynamical systems viewpoint, it is desirable to obtain corresponding exact solutions, though their existence is not…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and…
Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion…
We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result,…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on behaviour of locusts. It exhibits nontrivial…
By means of quantum stochastic calculus we construct a model for an atom with two degenerate levels and stimulated by a laser and we compute its fluorescence spectrum; let us stress that, once the model for the unitary atom-field dynamics…
In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles,…
Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a…
This work presents a quantum mechanical framework for analyzing quantization-based optimization algorithms. The sampling process of the quantization-based search is modeled as a gradient-flow dissipative system, leading to a…