Related papers: Statistical geometry of random weave states
Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
An alternative methodology to investigate indirect polyatomic processes with quasi-classical trajectories is proposed, which effectively avoids any binning or weighting procedure while provides rovibrational resolution. Initial classical…
An analog of classical "hidden variables" for qubit states is presented. The states of qubit (two-level atom, spin-1/2 particle) are mapped onto the states of three classical--like coins. The bijective map of the states corresponds to the…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
A classical spin network consists of a ribbon graph (i.e., an abstract graph with a cyclic ordering of the vertices around each edge) and an admissible coloring of its edges by natural numbers. The standard evaluation of a spin network is…
A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different…
Loop quantum gravity has provided us with a canonical framework especially devised for background independent and diffeomorphism invariant gauge field theories. In this quantization the fundamental excitations are called spin network…
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…
Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional…
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
We use spin-coherent states as a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of…
The semiclassical propagation of spin coherent states is considered in complex phase space. For two time-independent systems we find the appropriate classical trajectories and show that their combined contributions are able to describe…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
These lectures discuss the formulation of quantum mechanics with fractional spin and statistics in 2+1 dimensions in a relativistic setting, emphasizing the path-integral approach. The non-relativistic theory is reviewed from a…