Related papers: Riemann's theorem for quantum tilted rotors
Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If…
We present in this communication a new solving procedure for Kelvin&Kirchhoff equations, considering the dynamics of falling the rigid rotating torus in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation…
Quantum phase-space distributions (Wigner functions) for the plane rotator are defined using wave functions expressed in both angle and angular momentum representations, with emphasis on the quantum superposition between the Fourier dual…
Complex techniques of general relativity are used to determine \emph{all} the states in the two and three dimensional momentum spaces in which the equality holds in the uncertainty relations for the non-commuting basic observables of…
We study the quantum Riemannian geometry of quantum projective spaces of any dimension. In particular we compute the Riemann and Ricci tensors, using previously introduced quantum metrics and quantum Levi-Civita connections. We show that…
This two-paper series addresses and fixes the long-standing gauge invariance problem of angular momentum in gauge theories. This QED part reveals: 1) The spin and orbital angular momenta of electrons and photons can all be consistently…
Using the Hamiltonian formulation, we have attempted to obtain the equations of motion of systems with internal angular momentum that are moving with respect to a reference system when subjected to an interaction. This interaction involves…
We calculate the rotation of the inertial frames within an almost flat cylindrical region surrounded by a pulse of non-axially-symmetric gravitational waves that rotate about the axis of our cylindrical polar coordinates. Our spacetime has…
We consider superfluidity and quantum vorticity in rotating spacetimes. The system is described by a complex scalar satisfying a nonlinear Klein-Gordon equation. Rotation terms are identified and found to lead to the transfer of angular…
We consider finite-amplitude Kelvin waves on an inviscid vortex assuming that the vortex core has infinitesimal thickness. By numerically solving the governing Biot-Savart equation of motion, we study how the frequency of the Kelvin waves…
The fundamental mode of rotation in quantum fluids is given by a vortex, whose quantized value yields the orbital angular momentum (OAM) per particle. If the vortex is displaced (off-centered) from the reference point for rotation, the…
Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum…
We present an approach of the kicked rotor quantum resonances in position-space, based on its analogy with the optical Talbot effect. This approach leads to a very simple picture of the physical mechanism underlying the dynamics and to…
We study the resonances of the quantum kicked rotor subjected to an extended initial distribution. For the primary resonances we obtain the dispersion relation for the map of this system. We find an analytical dependence of the statistical…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
The circulation around any closed loop is a Lagrangian invariant for classical, smooth solutions of the incompressible Euler equations in any number of space dimensions. However, singular solutions relevant to turbulent flows need not…
Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic…
An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and has the familiar spectrum. The operator…
We elaborate an approach to quantum fluctuations of angular momentum based on the diagonalization of the covariance matrix in two versions: real symmetric and complex Hermitian. At difference with previous approaches this is SU(2) invariant…
We consider infinite random casual Lorentzian triangulations emerging in quantum gravity for critical values of parameters. With each vertex of the triangulation we associate a Hilbert space representing a bosonic particle moving in…