Related papers: On relation between geometric momentum and annihil…
We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i,x_j]=2\imath\lambda_p \epsilon_{ijk}x_k$ modulo setting $\sum_i x_i^2$ to a constant, using a recently introduced 3D rotationally invariant…
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are…
We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the SU(2) Ashtekar-Barbero framework, the spectra are discrete…
Complementarity relations constrain the distribution of coherence, predictability, and openness in quantum systems. Here we show that, in open quantum systems, these local constraints acquire a geometric interpretation through quasistatic…
In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $\phi(k,E)$ is…
Three-dimensional quadratic diffeomorphisms with quadratic inverse generically have five independent parameters. When some parameters approach infinity, the diffeomorphisms may exhibit a so-called anti-integrable limit in the traditional…
The angular momentum structure and energy structure of the coherent state of a 2D isotropic harmonic oscillator were investigated. Calculations showed that the average values of angular momentum and energy (except the zero point energy) of…
This research provides algorithms and numerical methods to geometrically control the magnitude of the internal and external forces in the reciprocal diagrams of 3D/Polyhedral Graphic statics (3DGS). In 3DGS, the form of the structure and…
Static solutions of the higher dimensional Einstein-Hilbert gravity supplemented by quadratic curvature self-interactions are discussed in the presence of hedgehog configurations along the transverse dimensions. The quadratic part of the…
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle…
The connection between the intrinsic angular momentum (spin) of particles and the quantum statistics is established by considering the response of identical particles to a common background radiation field. For this purpose, the Hamiltonian…
We develop a method for computing the free-energy of a canonical ensemble of quantum fields near the horizon of a rotating black hole. We show that the density of energy levels of a quantum field on a stationary background can be related to…
We solve the stationary Schr\"odinger equation for a particle confined to a 3D spherical wedge -- the region $\{(r,\theta,\phi): 0 \leq r \leq R,\, 0 \leq \theta \leq \pi,\, 0 \leq \phi \leq \Phi\}$ with Dirichlet BCs on all surfaces. This…
Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical…
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
Direct numerical simulations of two-dimensional decaying MHD turbulence in bounded domains show the rapid generation of angular momentum in nonaxisymmetric geometries. It is found that magnetic fluctuations enhance this mechanism. On a…
The nature of intrinsic/extrinsic character of angular momentum is defined in terms of the kind of the associated rotational energy of the light. The salient features of the spin energy of light and photon are highlighted. Spin angular…
Orbital angular momentum eigenfunctions are readily understood in terms of spherical harmonic wavefunctions. However, the quantum mechanical phenomenon of spin is often said to be mysterious and hard to visualize, with no classical…