Related papers: A transformational approach to collective behavior
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
This work introduces a novel model of quantum entities as unified, physically extended wavefields, forming the basis for a testable realist, holist framework for quantum measurement and collapse. Unlike interpretations that postulate hidden…
A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…
Envariance -- entanglement assisted invariance -- is a recently discovered symmetry of composite quantum systems. We show that thermodynamic equilibrium states are fully characterized by their envariance. In particular, the microcanonical…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
Human social behavior is structured by relationships. We form teams, groups, tribes, and alliances at all scales of human life. These structures guide multi-agent cooperation and competition, but when we observe others these underlying…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to…
The well known and oft-quoted Feynman's expression, entered the title, leading at a loss and even being objectionable, has not yet a clear explanation. The hidden parameters problem in quantum mechanics is considered here on the base of…
The simplest prescription for building a patterned structure from its constituents is to add particles, one at a time, to an appropriate template. However, self-organizing molecular and colloidal systems in nature can evolve in much more…
We present a new theory for the hierarchical clustering of dark matter (DM) halos based on stochastic differential equations, that constitutes a change of perspective with respect to existing frameworks (e.g., the excursion set approach);…
The quantum dynamics of a particle in the Modified P\"oschl-Teller potential is derived from the group $SL(2,R)$ by applying a Group Approach to Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder operators is…
The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical operators are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then,…
Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group…
A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…
We consider several Hamiltonian systems perturbed by external agents, that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…