Related papers: Approximate integrals of motion and the quantum ch…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling…
The motion of a stellar compact object around a supermassive black hole can be approximated by the motion of a spinning test particle. The equations of motion describing such systems are in general non-integrable, and therefore, chaotic…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…
We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for…
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
A Hamiltonian system with a modified Henon-Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic ("homogeneous") and cubic ("non-homogeneous") terms…
In this paper we continue to develop our approach to the chaoticity properties of the quantum Hamiltonian systems. Our earlier suggested chaoticity criterion characterizes the initial symmetry breaking and the destruction of the…
We propose a formalism which makes the chaos to be quantized. Quantum mechanical equation is derived for describing the chaos for a particle moving in an electromagnetic field.
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to…
Studies of integrable quantum many-body systems have a long history with an impressive record of success. However, surprisingly enough, an unambiguous definition of quantum integrability remains a matter of an ongoing debate. We contribute…
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…