Related papers: Spin-other-orbit operator in the tensorial form of…
The relativistic treatment of spin is a fundamental subject which has an old history. In various physical contexts it is necessary to separate the relativistic total angular momentum into an orbital and spin contribution. However, such…
This work is a sequel to our work "The Spin Density Matrix I: General Theory and Exact Master Equations" (eprint arXiv:0708.0644 [cond-mat]). Here we compare pure- and pseudo-spin dynamics using as an example a system of two quantum dots, a…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
We present a simple method to count the number of hadronic form factors based on the partial wave formalism and crossing symmetry. In particular, we show that the number of independent nucleon form factors of spin-n, twist-2 operators (the…
A second-order formalism for the theory of 3D spin-3 gravity is considered. Such a formalism is obtained by solving the torsion-free condition for the spin connection \omega^a_{\mu}, and substituting the result into the action integral. In…
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…
A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a…
One of the most fundamental properties of electromagnetism and special relativity is the coupling between the spin of an electron and its orbital motion. This is at the origin of the fine structure in atoms, the spin Hall effect in…
In a previous paper, field theory in curved space was considered, and a formula that expresses the first order variation of correlation functions with respect to the external metric was postulated. The formula is given as an integral of the…
We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$. We can obtain the exact and analytical…
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
As a follow-up to a recent study in the spin-0 case [J. Bunao and E. A. Galapon, Ann. Phys. 353, 83-106 (2015)], we construct a one-particle Time of Arrival (TOA) operator conjugate to a Hamiltonian describing a free relativistic spin-1/2…
We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density…
Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…
Trapped atomic ion qubits or effective spins are a powerful quantum platform for quantum computation and simulation, featuring densely connected and efficiently programmable interactions between the spins. While native interactions between…
A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function defining the Sundman…
The product of local operators in a topological quantum field theory in dimension greater than one is commutative, as is more generally the product of extended operators of codimension greater than one. In theories of cohomological type…
We discuss generic spin squeezing operators (quadratic in angular momentum operators) capable of squeezing out quantum mechanical noise from a system of two-level atoms (spins) in a coherent state. Such systems have been considered by…