Related papers: n-particle quantum statistics on graphs
We present two paradigms relating algebraic, topological and quantum computational statistics for the topological model for quantum computation. In particular we suggest correspondences between the computational power of topological quantum…
Anyons are quasiparticles with fractional statistics, bridging between fermions and bosons. We propose an experimental setup to measure the statistical angle of topological anyons emitted from a quantum point contact (QPC) source. The setup…
In contrast to classical physics, quantum mechanics divides particles into two classes-bosons and fermions-whose exchange statistics dictate the dynamics of systems at a fundamental level. In two dimensions quasi-particles known as 'anyons'…
Particle statistics impose fundamental constraints on nonequilibrium quantum dynamics, yet it remains an open question whether anyonic statistics can lead to emergent dynamical scaling beyond the conventional Bose-Fermi paradigm. Here we…
According to a basic rule of fermionic and bosonic many-body physics, known as the linked cluster theorem, physical observables are not affected by vacuum bubbles, which represent virtual particles created from vacuum and self-annihilating…
Quantum particle statistics fundamentally controls the way particles interact, and plays an essential role in determining the properties of the system at low temperature. Here we study how the quantum statistics affects the computational…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
This contribution, to be published in Imagine Math 8 to celebrate Michele Emmer's 75th birthday, can be seen as the second part of my previous considerations on the relationships between topology and physics (Mouchet, 2018). Nevertheless,…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different…
In this work we consider general fermion systems in two spatial dimensions, both with and without charge conservation symmetry, which realize a nontrivial fermionic topological order with only Abelian anyons. We address the question of…
We discuss the connection between anyons (particles with fractional statistics) and deformed Lie algebras (quantum groups). After a brief review of the main properties of anyons, we present the details of the anyonic realization of all…
In this thesis, we study Laplacian eigenfunctions on metric graphs, also known as quantum graphs. We restrict the discussion to standard quantum graphs. These are finite connected metric graphs with functions that satisfy Neumann vertex…
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory,…
We investigate a promising conformal field theory realization scheme for topological quantum computation based on the Fibonacci anyons, which are believed to be realized as quasiparticle excitations in the $\mathbb{Z}_3$ parafermion…
We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arising from certain association schemes. The main result is built…
Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a)…
Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but…
This work deals with quantum graphs, focusing on the transmission properties they engender. We first select two simple diamond graphs, and two hexagonal graphs in which the vertices are all of degree 3, and investigate their transmission…
Identifying experimental signatures of anyons, which exhibit fractional exchange statistics, remains a central challenge in the study of two-dimensional topologically ordered systems. Previous theoretical work has shown that the threshold…