Related papers: Algebraic topology and the quantization of fluctua…

In this paper we study the controllability of networked systems with static network topologies using tools from algebraic graph theory. Each agent in the network acts in a decentralized fashion by updating its state in accordance with a…

Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…

Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a…

At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…

We apply the adiabatic approximation to slow but finite-time thermodynamic processes and obtain the full counting statistics of work. The average work consists of change in free energy and the dissipated work, and we identify each term as a…

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…

Soft current algebras capture the infrared structure of scattering in asymptotically flat spacetimes, but an analogous algebraic description of finite-energy dynamics has been missing. We uncover an infinite-dimensional hard current algebra…

Topological boundary and interface modes are generated in an acoustic waveguide by simple quasi-periodic patternings of the walls. The procedure opens many topological gaps in the resonant spectrum and qualitative as well as quantitative…

A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approximate approach is offerred that effectively propagates the statistics in time. Loss of…

We consider the hydrodynamic origin of anomalous current fluctuations in a family of stochastic charged cellular automata. Using ballistic macroscopic fluctuation theory, we study both typical and large fluctuations of the charge current…

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…

Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…

A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approach is offered that effectively propagates the statistics in time. Loss of sensitivity to an…

The ALEA Coq library formalizes measure theory based on a variant of the Giry monad on the category of sets. This enables the interpretation of a probabilistic programming language with primitives for sampling from discrete distributions.…

Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…

We identify the conditions under which a stochastic driving inducing energy changes on a system coupled to a thermal bath can be treated as a work source. When these conditions are met, the work statistics satisfies the Crooks fluctuation…

Current fluctuations in a dissipative two-state system have been studied using a novel quantum dynamics simulation method. After a transformation of the path integrals, the tunneling dynamics is computed by deterministic integration over…

Turbulence in quantum fluids has, surprisingly, a lot in common with its classical counterpart. Recently, cold atomic gases has emerged as a well controlled experimental platform to study turbulent dynamics. In this work, we introduce a…