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We seek an extension to Schrodinger's equation that incorporates the macroscopic measurement-induced wavefunction collapse phenomenon. We find that a suitable hybrid between two leading approaches, the Bohm-de Broglie pilot-wave and…
We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr\"odinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this…
We introduce a new self-interacting random walk on the integers in a dynamic random environment and show that it converges to a pure diffusion in the scaling limit. We also find a lower bound on the diffusion coefficient in some special…
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: the mobility of particles depends on the configuration of their neighbors and…
It is demonstrated that the collapse of the wave function is equivalent to the continuity of measurement outcomes. The latter states that a second measurement has to result in the same outcome as the first measurement of the same observable…
The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex valued Gaussian, looking for relevance to quantum mechanics. Here we show that the…
Some experimental implications of the recent progress on wave function collapse are calculated. Exact results are derived for the center-of-mass wave function collapse caused by random scatterings and applied to a range of specific…
Macroscopic quantum optical effects (Schrodinger cat states, squeezing, collapse and revival) for light beams propagating in an inhomogeneous linear medium are demonstrated using exact analytical solutions of wave equation. It is shown that…
It has been hypothesized that the time evolution of wave functions might include collapses, rather than being governed by the Schroedinger equation. The leading models of such an evolution, GRW and CSL, both have two parameters (or new…
The von Neumann collapse of the quantum mechanical wavefunction after a position measurement is derived by a purely probabilistic mechanism in the context of Nelson's stochastic mechanics.
Though classical random walks have been studied for many years, research concerning their quantum analogues, quantum random walks, has only come about recently. Numerous simulations of both types of walks have been run and analyzed, and are…
We analyze data from confocal microscopy experiments of a colloidal suspension to validate predictions of rapid sporadic events responsible for structural relaxation in a glassy sample. The trajectories of several thousand colloidal…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
Proximity measurements probe whether pairs of particles are close to one another. We consider the impact of post-selected random proximity measurements on a quantum fluid of many distinguishable particles. We show that such measurements…
The review is concerned with the nonlinear Schr\"odinger equation (NLSE) in the presence of disorder. Disorder leads to localization in the form of the localized Anderson modes (AM), while nonlinearity is responsible for the interaction…
Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
Despite the widespread adoption of deterministic samplers in diffusion models (DMs), their potential limitations remain largely unexplored. In this paper, we identify collapse errors, a previously unrecognized phenomenon in ODE-based…
Collapse models postulate that space is filled with a collapse noise field, inducing quantum Brownian motions which are dominant during the measurement, thus causing collapse of the wave function. An important manifestation of collapse…
Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of the walker grows non-linearly with time in contrast to the diffusive motion described by simple random walks…