Related papers: Topics on Hamiltonian Mechanics
In this paper we are concerned with energy-conserving methods for Poisson problems, which are effectively solved by defining a suitable generalization of HBVMs, a class of energy-conserving methods for Hamiltonian problems. The actual…
We couple the issue of evolution in the laws of physics with that of violations of energy conservation. We define evolution in terms of time variables canonically dual to ``constants'' (such as $\Lambda$, the Planck mass or the…
Possibility of gravitational repulsion in General Relativity is discussed and astronomical data in favor of cosmological acceleration are described. The problem of vacuum energy is emphasized and possible ways of its solution are indicated.…
We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.
A recent proposal of new sets of squeezed states is seen as a particular case of a general context admitting realistic physical Hamiltonians. Such improvements reveal themselves helpful in the study of associated squeezing effects.…
This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2-norm by some other p-norm, then there are no nontrivial norm-preserving linear…
We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
This talk reviews some recent trends in perturbative quantum chromodynamics, with emphasis on higher orders in perturbation theory, resummation and power corrections.
We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
The perturbative approach was adopted to develop a temperature-dependent version of non-relativistic quantum mechanics in the limit of low-enough temperatures. A generalized, self-consistent Hamiltonian was therefore constructed for an…
A didatic approach of the Noether's theorem in classical mechanics is derived and used to obtain the laws of conservation.
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It…
Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have tackled the problem…
We recover the relativistic kinetic energy as the result of the work of a force.
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
In this note, we analyze the relationships that should govern the use of thermodynamics in fluid mechanics in a way that we believe is understandable to mathematicians. We also aim to better define the reasons why mechanics and…
We study conservation laws of a general class of quantum many-body systems subjected to an external time dependent quasi-periodic driving. {When the frequency of the driving is large enough or the strength of the driving is small enough, we…
Nonequilibrium molecular dynamics simulations often use mechanisms called thermostats to regulate the temperature. A Hamiltonian is presented for the case of the isoenergetic (constant internal energy) thermostat corresponding to a tunable…