Related papers: The Attractor and the Quantum States
Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…
Exceptional point in non-Hermitian system possesses fascinating properties. We present an exactly solvable attractor dynamics for the first time from a two-level time dependent non-Hermitian Hamiltonian. It allows a way to evolve to the…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
Quantum mechanics is considered to arise from an underlying classical structure (``hidden variable theory'', ``sub-quantum mechanics''), where quantum fluctuations follow from a physical noise mechanism. The stability of the hydrogen ground…
In our bouncer-walker model a quantum is a nonequilibrium steady-state maintained by a permanent throughput of energy. Specifically, we consider a "particle" as a bouncer whose oscillations are phase-locked with those of the energy-momentum…
In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant behave as attractors independently of the initial values. We develop a general…
The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the…
We study the emergent dynamics of quantum self-sustained oscillators induced by the simultaneous presence of attraction and repulsion in the coupling path. We consider quantum Stuart-Landau oscillators under attractive-repulsive coupling…
We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
The Liouville theorem is a fundamental concept in understanding the properties of systems that adhere to Hamilton's equations. However, the traditional notion of the theorem may not always apply. Specifically, when the entropy gradient in…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by the authors, we exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics in…
In this work, using Jacobson's idea: '$\delta$Q=TdS hold for all the local Rindler causal horizons through each spacetime point', we found that the transitions between the excited and ground state of a particle in a linear acceleration…