Related papers: Distributed Transformations of Hamiltonian Shapes …
We show that the linear group of automorphism of Hermitian matrices which preserves the set of separable states is generated by \emph{natural} automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each…
The collective motion of self-driven agents is a phenomenon of great interest in interacting particle systems. In this paper, we develop and analyze a model of agent motion in one dimension with periodic boundaries using a stochastic…
This work presents a geometric formulation for transforming nonconservative mechanical Hamiltonian systems and introduces a new method for regularizing and linearizing central force dynamics -- in particular, Kepler and Manev dynamics --…
We consider a network of agents that locate themselves in an environment through sensor measurements and aim to transmit a message signal to a base station via collaborative beamforming. The agents' sensor measurements result in…
We analyze two simple models derived from a quantum-mechanical particle on an elliptical path. The first Hamiltonian operator is non-Hermitian but equivalent to an Hermitian operator. It appears to exhibit the same two-fold degeneracy as…
Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the…
Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics, requiring the computation of collision-free paths for multiple agents moving from their respective start to goal positions. Coordinating multiple agents in a shared…
Multi Agent Path Finding (MAPF) requires identification of conflict free paths for agents which could be point-sized or with dimensions. In this paper, we propose an approach for MAPF for spatially-extended agents. These find application in…
Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a…
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian.…
We study a distributed learning problem in which $n$ agents, each with potentially heterogeneous local data, collaboratively minimize the sum of their local cost functions via peer-to-peer communication. We propose a novel algorithm,…
We study scattering rigidity for Hamiltonian systems on $T^*M\setminus 0$, where $M$ is a manifold with boundary equipped with a positively homogeneous Hamiltonian function $H(x,\xi)$. We show that $H$ can be uniquely determined by the…
Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators etc.) as those of the original operators between the corresponding true…
This paper proposes a novel maneuvering technique for the complex-Laplacian-based formation control. We show how to modify the original weights that build the Laplacian such that a designed steady-state motion of the desired shape emerges…
We study Multi-Agent Path Finding for arrangements of labeled agents in the interior of a simply connected domain: Given a unique start and target position for each agent, the goal is to find a sequence of parallel, collision-free agent…
Motivated by concerns about diversity in social networks, we consider the following pattern formation problems in rings. Assume $n$ mobile agents are located at the nodes of an $n$-node ring network. Each agent is assigned a colour from the…
The configuration interaction approach to nuclear structure uses the effective Hamiltonian in a finite orbital space. The various parts of this Hamiltonian and their interplay are responsible for specific features of physics including the…
How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional…
In mathematical models of epidemic diffusion on networks based upon systems of differential equations, it is convenient to use the Heterogeneous Mean Field approximation (HMF) because it allows to write one single equation for all nodes of…
We construct an effective Hamiltonian of interacting bosons, based on scattered radiation off vibrational modes of designed molecular architectures. Making use of the infinite yet countable set of spatial modes representing the scattering…