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Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
We present a general theory of classical metastability in open quantum systems. Metastability is a consequence of a large separation in timescales in the dynamics, leading to the existence of a regime when states of the system appear…
There exist some boundary-driven open systems with diffusive dynamics whose particle current fluctuations exhibit universal features that belong to the Edwards-Wilkinson universality class. We achieve this result by establishing a mapping,…
Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
A modified lagrangian with causal and retrocausal momenta was used to derive a first causal wave equation and a second retrocausal wave equation using the principle of least action. The retrocausal wave function obtained through this method…
We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the "space"…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
The waiting time distribution (WTD) is a common tool for analysing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete,…
Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…