Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0810.0786

Manipulation of Semiclassical Photon States

Michael VanValkenburgh
View original source ↗Read source document ↗Export metadata ↓

Abstract

Gabriel F. Calvo and Antonio Picon defined a class of operators, for use in quantum communication, that allows arbitrary manipulations of the three lowest two-dimensional Hermite-Gaussian modes {|0,0>,|1,0>,|0,1>}. Our paper continues the study of those operators, and our results fall into two categories. For one, we show that the generators of the operators have infinite deficiency indices, and we explicitly describe all self-adjoint realizations. And secondly we investigate semiclassical approximations of the propagators. The basic method is to start from a semiclassical Fourier integral operator ansatz and then construct approximate solutions of the corresponding evolution equations. In doing so, we give a complete description of the Hamilton flow, which in most cases is given by elliptic functions. We find that the semiclassical approximation behaves well when acting on sufficiently localized initial conditions, for example, finite sums of semiclassical Hermite-Gaussian modes, since near the origin the Hamilton trajectories trace out the bounded components of elliptic curves.

Explore related subjects

math-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Michael VanValkenburgh. 2008-12-14. Manipulation of Semiclassical Photon States. https://doi.org/10.1063/1.3072670

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Stacking and the triviality of invertible phases

We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework. We show in particular that all irreducible sectors of a stacked system are unitarily equivalent to a product of irreducible sectors of the factors. This naturally leads to a faithful functor between the categories for each system and the category of the stacked system. We construct an intermediate `product' category which we then show is equivalent to the stacked system category. As a consequence, the sectors associated with an invertible state are trivial, namely, invertible states support no anyonic quasi-particles.

math-ph↗
arXiv2026

Lindblad Quantum Dynamics as Euler-Poincaré Reduction on Adjoint-Coupled Semidirect Products

We present a geometric and variational derivation of the Gorini--Kossakowski--Sudarshan--Lindblad equation from Euler--Poincar'e reduction on an adjoint--coupled semidirect product (ACSP). In this construction a Lie group $G$ acts on $V=\mathfrak{g}^{\oplus m}$ by the adjoint representation together with a second, adjointly compatible action whose failure to commute defines an adjoint torsion $K(ξ,v)$. This torsion generates a canonical quadratic curvature operator on $\mathfrak{g}^*$ that survives reduction and yields a metric double--bracket term. For $G=SU(n)$ the reduced Euler--Poincar'e equation reproduces exactly the GKSL generator: the Hamiltonian part arises from the coadjoint action, while the dissipator $-\tfracγ{2}[L,[L,ρ]]$ appears as the torsion--induced metric component of an ACSP bracket. We prove a characterization theorem showing that any quadratic $SU(n)$--equivariant operator generated by torsion factorizes into a Lindblad double commutator; a uniqueness theorem establishing that, under natural structural assumptions, the only admissible dissipator is the Lindblad form; and an orbit--contraction theorem showing strict contraction toward the commutant of the Lindblad operators. For $SU(2)$ and $SU(3)$ the ACSP geometry yields explicit Bloch equations for representative dissipative channels. We also show that the ACSP bracket fits into a metriplectic and contact--geometric framework in which the Lindblad term is the metric component and the Reeb part of a contact Hamiltonian flow. In this picture, decoherence is a curvature--induced contraction generated by Euler--Poincar'e reduction rather than a phenomenological input.

math-ph↗
arXiv2026

On the Conicality of Spacetimes

The notion of conicality, recently introduced in [2403.00916], captures the extent to which the joint future of a finite set in spacetime uniquely determines the generating subset via its light cone structure. In the same paper it was mentioned that conicality holds for Minkowski spacetime of dimension $1+N$ with $N\geq 2$ and it has been conjectured that this property holds more generally. In this work, we show that neither homotopy with Minkowski space nor global hyperbolicity alone are sufficient for the spacetime to satisfy conicality. We then establish that causally simple, future cohesive spacetimes of dimension $1+N$ with $N\geq 2$ are conical. This class of spacetimes includes, in particular, TIP spacetimes, which can be understood as the timelike past of an observer. This is in line with the origin of causal modeling since the past of an observer is the natural domain for the description of experiments.

math-ph↗