Related papers: A transformational approach to collective behavior
We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between the…
This chapter provides a comprehensive overview of controlling collective behavior in complex systems comprising large ensembles of interacting dynamical agents. Building upon traditional control theory's foundation in individual systems, we…
Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different…
Collective motion is found in various animal systems, active suspensions and robotic or virtual agents. This is often understood using high level models that directly encode selected empirical features, such as co-alignment and cohesion.…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a…
The mass spectrum problem (the 14th Ginzburg's problem) is analyzed in terms of the conventional reductional and alternative holistic frameworks. From the holistic viewpoint, substance (the same as energy) is the primary concept and…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
One of the most important concepts in non-equilibrium physics is relaxation. In the vicinity of a classical critical point, the relaxation time can diverge and result in a universal power-law for the relaxation dynamics; the emerging…
We develop an action formulation of stochastic dynamics in the Hilbert space. By generalizing the Wiener process into 1+3-dimensional spacetime, we define a Lorentz-invariant random field. By coupling the random to quantum fields, we obtain…
In the framework of the stochastic theory for hierarchical clustering, we investigate the time-dependent solutions of the Fokker-Planck equation describing the statistics of dark matter halos, and discuss the typical timescales needed for…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
The process algebra HYPE was recently proposed as a fine-grained modelling approach for capturing the behaviour of hybrid systems. In the original proposal, each flow or influence affecting a variable is modelled separately and the overall…
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model…