Related papers: Plane Pendulum and Beyond by Phase Space Geometry
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal…
In this paper, we handle the problem of the motion of the Foucault pendulum. We explore a new method induced from the De Alembert Principle giving the motional equations without small-amplitude oscillation approximation. The result of the…
The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity. In particular, we focus on perturbations in the form of power laws and calculate…
This conference talk elaborates on a recently discovered mapping procedure by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed correctly into those in curved space. This procedure…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for…
Quantum devices, such as quantum simulators, quantum annealers, and quantum computers, may be exploited to solve problems beyond what is tractable with classical computers. This may be achieved as the Hilbert space available to perform such…
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for…
We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and…
As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…
Operational definition of space-time in light of quantum mechanics and general relativity inevitably indicates an intrinsic imprecision in space-time structure which has to do with space-time dimension as well. The operational dimension of…
Jarzynski's identity for the free energy difference between two equilibrium states can be viewed as a special case of a more general procedure based on phase space mappings. Solving a system's equation of motion by approximate means…
A time dependent variational approach is used to derive the equations of motion for the \lambda \phi^4 model. The simultaneous evolution of the quantum fluctuations and of the classical part of the field is considered in a lattice of 1+1…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation…
In the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of any planar analytic Hamiltonian system. We apply it to several…
Properties of inertial modes of Jupiter are investigated for an n=1 polytropic description of the planet interior. We use the anelastic approximation to overcome the usual handicap of a severe spherical harmonics truncation. A powerful…