Related papers: Conserved geometric phase and group velocity
A new representation of electromagnetic gyrokinetic Vlasov-Maxwell theory is presented in which the gyrocenter equations of motion are expressed solely in terms of the perturbed electric and magnetic fields. In this representation, the…
We parameterize the phase space density by time dependent diffeomorphic, Poisson preserving transformations on phase space acting on a reference density solution. We can look at these as transformations which fix time on the extended space…
We propose a coordinate-invariant geometric formulation of the GENERIC stochastic differential equation, unifying reversible Hamiltonian and irreversible dissipative dynamics within a differential-geometric framework. Our construction…
We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we identify the Reeb vector field as the intrinsic generator…
We consider a classical Dirac field in flat Minkowski spacetime. We perform a Gordon decomposition of its canonical energy-momentum and spin currents, respectively. Thereby we find for each of these currents a convective and a polarization…
For geodesic motion of a particle in a stationary spacetime the $U_0$ component of particle 4-velocity is constant and is considered to be a conserved mechanical energy. We show that this concept of a conserved mechanical energy can be…
We present a model of (double) kinetic theory which paves the way to describe matter in a Double Field Theory background. Generalized diffeomorphisms acting on double phase space tensors are introduced. The generalized covariant derivative…
The study of the evolution of the dynamics of a massive or massless particle shows that in special relativity theory, the energy is not conserved. From the law of evolution of the velocity over time of a particle subjected to a constant…
In two-dimensional space-time, point particles can experience a geometric, dimension-specific gravity force, which modifies the usual geodesic equation of motion and provides a link between the cosmological constant and the vacuum…
We predict a geometric quantum phase shift of a moving electric dipole in the presence of an external magnetic field at a distance. On the basis of the Lorentz-covariant field interaction approach, we show that a geometric phase appears…
This paper devoted to proof the existence of stable quasi-periodic motions of the magnetic dipole that is under the action of the external magnetic field and homogeneous field of gravity. For proof this we used the group-theoretic methods…
The long-standing resolution of the Abraham--Minkowski electromagnetic momentum controversy is predicated on a decomposition of the total momentum of a closed continuum electrodynamic system into separate field and matter components. Using…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
We present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state…
In order to clarify common assumptions on the form of energy and momentum in elasticity, a generalized conservation format is proposed for finite elasticity, in which total energy and momentum are not specified a priori. Velocity, stress,…
The retarded vector potential of a point magnetic dipole with an arbitrary time dependence undergoing accelerated relativistic motions is derived. A novel expression for the angular distribution of the radiated power of an arbitrary moving…
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
Using confocal microscopy we investigate the effect of attraction on the packing of polydisperse emulsions under gravity. We find that the distributions of neighbors, coordination number, and local packing fraction as a function of…
The global in time existence of solutions of a system describing the interaction of gravitationally attracting particles with a general diffusion term and fixed energy is proved. The presented theory covers the case of the model with…
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…