Related papers: Nonlinear evolution as a possible explanation for …
This note starts with a recapitulation of what people call the ``Measurement Problem'' of Quantum Mechanics (QM). The dissipative nature of the quantum-mechanical time-evolution of averages of states over large ensembles of identical…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
Considering what the world would be like if backwards causation were possible is usually mind-bending. Here I discuss something that is easier to study: a toy model that incorporates a very restricted sort of backwards causation. It defines…
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian,…
The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic…
A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the…
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…
The advantages and disadvantages of some pedagogical non-relativistic quantum-mechanical models, used to illustrate spontaneous symmetry breakdown, are discussed. A simple quantum-mechanical toy model (a spinor on the line, subject to a…
It is generally expected that in a non-singular cosmological model a cyclic evolution is straightforward to obtain on introduction of a suitable choice of a scalar field with a negative potential or a negative cosmological constant which…
The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix…
It is shown that the classical book by von Neumann proposing dynamics of measured systems with "reduction (or collapse) of system's wave packet" contains also hints how to avoid this discontinuity in time evolution of the measured system…
It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…
Quantum measurement is a process that involves the interaction between a quantum system and a macroscopic measurement apparatus containing many degrees of freedom. The photodetector is such an apparatus with many electrons interacting with…
Driven many-body quantum systems where some parameter in the Hamiltonian is varied quasiperiodically in time may exhibit nonequilibrium steady states that are qualitatively different from their periodically driven counterparts. Here we…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
Dynamical evolution of the quantum ground state (vacuum) is analyzed for time variant harmonic oscillators characterized by asymptotically constant frequency. The oscillatory density matrix in the asymptotic future is uniquely determined by…
We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterisation of when it is consistent to treat a quantum subsystem…
We describe the classical and quantum two dimensional nonlinear dynamics of large blue-detuned eveanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is…