Related papers: Structured Gaussians From Geometric Quantisation
In this paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with "complex Poincar\'e group" ISO(4,C).
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
The geometric phase of light is a fascinating phenomenon in optics and arises whenever there is a change in the polarization state of light. It is a fundamentally well-established concept and has recently found extensive applications,…
We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) Chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After…
Using a PT symmetric regularization technique we reminad the reader that and how (a) the SUSY is re-established between the two shifted harmonic oscillator potentials $ V(q)=q^2+{G}/{q^2}+ const$ and (b) many non-equivalent Hermitian and…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
We study both manipulation and detection of two-mode spatial quantum states of light by means of a reconfigurable integrated device built in an electro-optical material in a Kolgelnik-Schmidt configuration, which provides higher error…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
Setting off from the classic input-output formalism, we develop a theoretical framework to characterise the Gaussian quantum channels relating the initial correlations of an open bosonic system to those of properly identified output modes.…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
We present a general construction of a geometric notion of circuit complexity for Gaussian states (both bosonic and fermionic) in terms of Riemannian geometry. We lay out general conditions that a Riemannian metric function on the space of…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
We consider the Bose-Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes - a nonlinear generalisation of the (symmetric and antisymmetric)…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
The ${\mathcal D}$-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group ${\rm GL}(2,{\mathbb C})$ of…
Nonlinear optics is crucial for shaping the spatial structure of shortwave light and its interactions with matter, but achieving this through simple harmonic generation with a single pump is challenging. This study demonstrates nonlinear…