Related papers: Conserved geometric phase and group velocity
We discuss an extension of the velocity Verlet method that accurately approximates the kinetic-energy-conserving charged particle motion that comes from magnetic forcing. For a uniform magnetic field, the method is shown to conserve both…
In this brief report, the group velocity of the eigen-modes in sonic crystals is derived, and shown to equal the averaged energy velocity of the eigen-modes. How the group velocity can be used to describe acoustic energy flows in sonic…
Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…
Spin current of a Dirac particle is shown to be given by the geometric phase and in terms of the later, a closed form expression is obtained for the dissipationlessness of the spin current.
We introduce a nonminimal coupling into the Dirac equation as a model of describing the interaction of a Dirac neutral particle with an induced electric dipole moment with magnetic and electric fields. Then, we obtain a relativistic…
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to…
Circular motion of particles, dust grains and fluids in the vicinity of compact objects has been investigated as a model for accretion of gaseous and dusty environment. Here we further discuss, within the framework of general relativity,…
Given a vector field on a manifold M, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitable submanifolds are constant under time evolution, the…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
In experiments searching for a nonzero electric dipole moment of trapped particles, frequency shifts correlated with an applied electric field can be interpreted as a false signal. One such effect, referred to as the geometric phase effect,…
We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the…
We discuss the geometric phases and flux densities for the metastable states of hydrogen with principal quantum number n=2 being subjected to adiabatically varying external electric and magnetic fields. Convenient representations of the…
Here we make use of the Hellmann-Feynman theorem, with the aim to calculate macroscopic quantum velocities instead of forces, and we show how it is possible to derive the expression of the work per unit time, per unit volume (power density)…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
The stopping power and energy loss rate of charged particles traversing a two-dimensional Dirac plasma is investigated. The Dirac plasma considered here models a solid state system, recently realized graphene monolayer, where the conduction…
A covariant formula for conserved currents of energy, momentum and angular-momentum is derived from a general form of Noethers theorem applied directly to the Einstein-Hilbert action of classical general relativity. Energy conservation in a…
When a two-dimensional curved surface is conceived as a limiting case of a curved shell of equal thickness d, where the limit d\rightarrow0 is then taken, the well-known geometric potential is induced by the kinetic energy operator, in fact…
In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving…
A theory where the gravitational, Maxwell and Dirac fields (mathematically represented as particular sections of a convenient Clifford bundle) are supposed fields in Faraday's sense living in Minkowski spacetime is presented. In our theory…
We show that quantum particles constrained to move along curves undergoing cyclic deformations acquire, in general, geometric phases. We treat explicitly an example, involving particular deformations of a circle, and ponder on potential…