Related papers: Classical Oscilators in General Relativity
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on…
In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with…
Stationary rotating strings can be viewed as geodesic motions in appropriate metrics on a two-dimensional space. We obtain all solutions describing stationary rotating strings in flat spacetime as an application. These rotating strings have…
Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that…
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This…
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…
The classical rotation is not self-consistent in the framework of the special theory of relativity. the Relativistic rotation is obtained, which takes the relativistic effect into account. It is demonstrated that the angular frequency of…
We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities…
Were studied classical oscillations of background metric in the multidimensional anisotropic model of Kazner in the de-Sitter stage. Obtained dependence of fluctuations on dimension of space-time with infinite expansion. Stability of the…
For a time-dependent classical quadratic oscillator we introduce pairs of real and complex invariants that are linear in position and momentum. Each pair of invariants realize explicitly a canonical transformation from the phase space to…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
A model is proposed to demonstrate that classical general relativity can emerge from loop quantum gravity, in a relational description of gravitational field in terms of the coordinates given by matter. Local Dirac observables and coherent…
For a nonrelativistic classical particle undergoing arbitrary oscillations, the generalized effective potential Y is derived from nonlinear eigenfrequencies of the particle-field system. Specifically, the ponderomotive potential is extended…
We consider a class of three parameter static and axially symmetric metrics that reduce to the Janis-Newman-Winicour (JNW) and $ \gamma$-metrics in certain limits of the parameters. We obtain rotating form of the metrics that are…
Neutrino oscillations are studied in the general framework of open quantum systems by means of extended dynamics that take into account possible dissipative effects. These new phenomena induce modifications in the neutrino oscillation…