Related papers: Master Equation approach to Reversible and Conserv…
We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical…
Time-dependent renormalization was employed to derive a nonlinear quantum master equation (QME), in which the dynamics of a non-equilibrium fluctuation in an irrelevant system are fed back into that of a relevant one. In terms of…
Master equations are typically adopted to describe the dynamics of open quantum systems. Such equations are either in integro-differential or in time-local form, with the latter class more frequently adopted due to the simpler numerical…
Cellular automata and other discrete dynamical systems have long been studied as models of emergent complexity. Recently, neural cellular automata have been proposed as models to investigate the emerge of a more general artificial…
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
Via operator theoretic methods, we formalize the concentration phenomenon for a given observable `$r$' of a discrete time Markov chain with `$\mu_{\pi}$' as invariant ergodic measure, possibly having support on an unbounded state space. The…
We investigate the sensitivity of the time evolution of a kinetic Ising model with Glauber dynamics against the initial conditions. To do so we apply the "damage spreading" method, i.e., we study the simultaneous evolution of two identical…
The time-convolutionless quantum master equation is an exact description of the nonequilibrium dynamics of open quantum systems, with the advantage of being local in time. We derive a perturbative expansion to arbitrary order in the…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
We study the early time dynamics of bimodal spin systems on $2d$ lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with locally conserved order parameter (Kawasaki dynamics), the same…
We investigate the energy transfer dynamics in a donor-acceptor model by developing a time-local master equation technique based on a variational transformation of the underlying Hamiltonian. The variational transformation allows a…
We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike…
We consider a~quasilinear model arising from dynamical magnetization. This model is described by a~magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a~conducting and a~non-conducting part,…
This is a derivation of the quantum-optical master equation using coarse-graining of time, which brings new insights into a decades old technique. My derivation is quite similar to derivations using quantum stochastic methods or Kraus…
Stochastic modelling of complex systems plays an essential, yet often computationally intensive role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to…
We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schr\"odinger…
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…
We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD)…
We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a…
We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb{R}^d \times \mathcal{P}_2(\mathbb{R}^d),$ where $\mathcal{P}_2(\mathbb{R}^d)$ is the Wasserstein space of probability measures on $\mathbb{R}^d$ with…