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We propose an algorithm based on modulable hidden variables and adaptive step lengths, inspired by heuristic statistical physics and the replica method, to study the effect of mutual correlations and the emergent Wigner-Dyson distribution…
Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant…
Exact solutions of model problems are elusive but potent tools for understanding many body interacting systems. We study a system of dissipative qubits with the Heisenberg interaction and obtain, for qubits under a certain condition, an…
A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves first integrals of the system. The idea is that given an initial point in the manifold…
Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in non-equilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly…
We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to…
We develop a discrete truncated Wigner method to analyze the real-time evolution of dissipative SU(${\cal N}$) spin systems coupled with a Markovian environment. This semiclassical approach is not only numerically efficient but also…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a…
Time-resolved photoemission spectroscopy provides a unique and direct way to explore the real-time nonequilibrium dynamics of electrons and holes. The formal theory of the spectral function evolution requires inclusion of electronic…
A time-dependent approach for the kinetic energy release (KER) spectrum is developed for a fragmentation of a diatomic molecule after an electronic decay process, e.g. Auger process. It allows one to simulate the time-resolved spectra and…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of…
Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding…
We study quantum quenches in the $S=1$ Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum…
We consider a model of two harmonically driven damped harmonic oscillators that are coupled linearly and with a cross-Kerr coupling. We show how to distinguish this combination of coupling types from the case where a coupling of…
We numerically study a model convection system of a suspension of self-propelled particles, motivated by recent experimental findings of localized and bistable bioconvection pattern, being distinct from classical Rayleigh--B\'{e}nard…
We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the…
We conduct an analysis of a one-dimensional linear problem that describes the vibrations of a connected suspension bridge. In this model, the single-span roadbed is represented as a thermoelastic Shear beam without rotary inertia. We…
In driven-dissipative bosonic systems, the interplay between coherent driving, inter-particle interactions and dissipation leads to a rich variety of non-equilibrium stationary states (NESS). In the semiclassical limit, the flow topology of…
A stochastic simulation algorithm for the computation of multitime correlation functions which is based on the quantum state diffusion model of open systems is developed. The crucial point of the proposed scheme is a suitable extension of…