Related papers: Relativistic pendulum and invariant curves
In this paper, we study the existence of solutions for generalized vector quasi-equilibrium problems. Firstly, we prove that in the case of Banach spaces, the assumptions of continuity over correspondences can be weakened. The theoretical…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
We consider two different relativistic versions of the Kepler problem in the plane: the first one involves the relativistic differential operator, the second one involves a correction for the usual gravitational potential due to…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…
A manifestly covariant expression for the current matrix elements of three quark bound systems is derived in the framework of the Point Form Relativistic Hamiltonian Dynamics. The relativistic impulse approximation is assumed in the model.…
We construct a relativistic quantum mechanics for a boson. To do this we exploit two component wave functions in Dirac type equations of motion. In our formalism we fix the pathological aspect of particle probability density which appears…
Unexpected accelerator modes were recently observed experimentally for cold cesium atoms when driven in the presence of gravity. A detailed theoretical explanation of this quantum effect is presented here. The theory makes use of invariance…
We study the quantization of many-body systems in three dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear gauge conditions, and discuss their Gribov…
It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order…
Introduce several KAM theorems for infinite dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori. Especially, introduce a KAM theorem in the paper(Cummun. Math.…
We prove a reducibility result for a linear Klein-Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving, however we require it to be fast…
Starting from the Keldysh theory, for a general low energy $N$-band Hamiltonian in the clean limit, we perform a manifestly $\smash{U(1) \times SU(N)}$ gauge invariant semiclassical expansion. A generalized Berry curvature tensor is shown…
Quantum mechanical transition amplitudes directly tells the probability of each transition and which one is more favourable. Path-integrals offers a systematic methodology to compute this quantum mechanical process in a consistent manner.…
The equations of General Relativity are recast in the form of a wave equation for the Weyl tensor. This allows to reformulate gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
In the framework of KAM theory, the persistence of invariant tori in quasi-integrable systems is proved by assuming a non-resonance condition on the frequencies, such as the standard Diophantine condition or the milder Bryuno condition. In…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
We introduce an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible Schr\"odinger systems. Using this KAM theorem together with partial Birkhoff normal form method, we find the existence of quasi-periodic…