Related papers: Mirror potentials in classical mechanics
The paper reviews some parts of classical potential theory with applications to two dimensional fluid dynamics, in particular vortex motion. Energy and forces within a system of point vortices are similar to those for point charges when the…
Periodically-modulated potentials in the form of light fields have previously been applied to induce reversible phase transitions in dilute colloidal systems with long-range interactions. Here we investigate whether similar transitions can…
Properties of the magnetic translation operators for a charged particle moving in a crystalline potential and a uniform magnetic field show that it is necessary to consider all inequivalent irreducible projective representations of the the…
It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and…
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and…
We show that the logarithmically rising static potential between opposite-charged sources in two dimensions is screened by dynamical fields even if the probe charges are fractional, in units of the charge of the dynamical fields. The effect…
Examples are worked out using a new equation proposed in the previous paper to show that it has new physical predictions for mesoscopic systems.
A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle…
The concept of partnership of potentials is studied in detail and in particular the non-uniqueness due to the ambiguity in the election of the factorization energy and in the choice of the solution of certain Riccati equation. We generate…
We introduce the notion of a cross-frame potential function, which takes one frame as input and returns its cross-frame potential value with respect to another frame. We analyze the behavior of this new function to determine what…
Scanning gate microscopy measurements in a circular ballistic cavity with a tip placed near its center yield a non-monotonic dependence of the conductance on the tip voltage. Detailed numerical quantum calculations reproduce these…
We introduce a notion of super-potential for positive closed currents of bidegree (p,p) on projective spaces. This gives a calculus on positive closed currents of arbitrary bidegree. We define in particular the intersection of such currents…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
We study the situation where two point like mirrors are placed in the vacuum state of a scalar field in a two-dimensional spacetime. Describing the scattering upon the mirrors by transmittivity and reflectivity functions obeying unitarity,…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
The formulation of a generalized classical electromagnetism that includes both electric and magnetic charges, is explored in the framework of two potential approach. It is shown that it is possible to write an action integral from which one…
We consider superintegrability in classical mechanics in the presence of magnetic fields. We focus on three-dimensional systems which are separable in Cartesian coordinates. We construct all possible minimally and maximally superintegrable…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
We consider the motion of a classical particle under the influence of a random potential on R^d, in particular the distribution of asymptotic velocities and the question of ergodicity of time evolution.