Related papers: Quantum graphs with spin Hamiltonians

Since the discovery a century ago, spin describing the intrinsic angular momentum of massive elementary particles has exposed its nature and significant roles in wide ranges of (relativistic) quantum phenomena and practical applications for…

Following the quantisation of a graph with the Dirac operator (spin-1/2) we explain how additional weights in the spectral form factor K(\tau) due to spin propagation around orbits produce higher order terms in the small-\tau asymptotics in…

We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions,…

Exploiting inherent symmetries is a common and effective approach to speed up the simulation of quantum systems. However, efficiently accounting for non-Abelian symmetries, such as the $SU(2)$ total-spin symmetry, remains a major challenge.…

It is substantiated that spin is a notion associated with the group of internal symmetry that is tightly connected with the geometrical structure of spacetime. The wave equation for the description of the particles with spin one half is…

There are two main notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Both objects have a venerable history as they are related to…

We introduce a new technique for dealing with the matrix elements of the Hamiltonian operator in loop quantum gravity, based on the use of intertwiners projected on coherent states of angular momentum. We give explicit expressions for the…

Topological properties of a certain class of spinless three-band Hamiltonians are shown to be summed up by the Skyrmion number in momentum space, analogous to the case of two-band Hamiltonian. Topological tight-binding Hamiltonian on a…

Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…

In the search of a mathematical basis for quantum mechanics, in order to render it self-consistent and rationally understandable, we find that the best approach is to adopt E. Cartan's way for discovering spinors; that is to start from…

We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in R^2 with a potential having a deep strict minimum on the graph, when the width of the well shrinks to zero. For a generic…

Here we give an overview of the research on spin-based quantum dot quantum computation. In particular, we discuss the conditions for the Heisenberg exchange Hamiltonian to be a satisfactory description of two-electron interaction in a GaAs…

We study the XX model for quantum spins on the star graph with three legs (i.e., on a Y-junction). By performing a Jordan-Wigner transformation supplemented by the introduction of an auxiliary space we find a Kondo Hamiltonian of fermions,…

The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…

We derive the effective one-dimensional Schrodinger-Pauli equation for electrons constrained to move on a space curve. The electrons are confined using a double thin-wall quantization procedure with adiabatic separation of fast and slow…

We describe relativistic particles with spin as points moving in phase space $X=T^* R^{1,3}\times C^2_L\times C^2_R$, where $T^* R^{1,3}=R^{1,3}\times R^{1,3}$ is the space of coordinates and momenta, and $C^2_L$ and $C^2_R$ are the spaces…

We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube…

We define quantum observables associated with Einstein localisation in space-time. These observables are built on Poincare' and dilatation generators. Their commutators are given by spin observables defined from the same symmetry…

We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…

We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…