Related papers: Quantum Systems as results of Geometric Evolutions
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent…
We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
Is the dynamical evolution of physical systems objectively a manifestation of information processing by the universe? We find that an affirmative answer has important consequences for the measurement problem. In particular, we calculate the…
The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation…
While in relativity theory space evolves over time into a single entity known as spacetime, quantum theory lacks a standard notion of how to encapsulate the dynamical evolution of a quantum state into a single "state over time". Recently it…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
Process of formation of the universe with its further expansion in the first evolution stage is investigated in the framework of Friedmann-Robertson-Walker metrics on the basis of quantum model, where a new type of matter is introduced,…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…