We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface, by modeling it with a discrete time quantum walk. During the evolution, the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles...

Schumpeter's theory of democracy can be read through the lens of the cognitive approach to rationality. Schumpeter himself constructed his theory on the basis of his (neglected) conception of conscious rationality, which considers the process of thinking as composed of conscious/deliberate and unconscious/automatic components. The prevalence of the deliberate over the automatic component can oc...

It is shown that two stochastic electromagnetic beams that propagate from the source plane z = 0 into the half-space z > 0 may have different degrees of polarization throughout the half-space, even though they have the same sets of Stokes parameters in the source plane. This fact is due to a possible difference in the coherence properties of the field in that plane, but other reasons are also p...

We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through an exchange term with strength inversely proportional to the square of their distance. We achieve this by viewing the Haldane-Shastry system as a high-interac...

We study the spin-1/2 quantum Heisenberg antiferromagnet on a Bethe lattice diluted to the percolation threshold. Dilution creates areas of even or odd sublattice imbalance resulting in "dangling spins" [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006); Phys. Rev. B 81, 054417 (2010)]. These collectively act as "emergent" spin-1/2 degrees of freedom and are responsible for the crea...

Within an asset allocation framework, when the number of assets is larger than the sample dimension, mean-variance approaches cannot be used due to the limited number of degrees of freedom. In such a situation, performance measures could be used to rank assets, and then select a subset of them for further analysis. However, the financial economics literature proposes dozens of measures, and the...

In this paper we determined all of the possible self mapping degrees of the manifolds with S-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self mapping degrees of all closed orientable 3-manifold in Thurston’s picture.

We review some old and new methods of reduction of the number of degrees of freedom from ∼ N 2 to ∼ N in the multi-matrix integrals.

We introduce a novel property of bipartite quantum states, which we call faithfulness, and we say that a state is faithful when acting with a channel on one of the two quantum systems; the output state carries complete information about the channel. The concept of faithfulness can also be extended to sets of states, when the output states altogether carry a complete imprinting of the channel. M...