Related papers: On some algebraic problems arising in quantum mech…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
Nature can be seen as informational structure with computational dynamics (info-computationalism), where an (info-computational) agent is needed for the potential information of the world to actualize. Starting from the definition of…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts…
Our understanding of the physics of biological molecules, such as proteins and DNA, is limited because the approximations we usually apply to model inert materials are not in general applicable to soft, chemically inhomogeneous systems. The…
A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently,…
Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
The quantum mechanics of a simple mechanical system is considered. A group of gears can serve as a model for several different systems such as an artifically constructed nanomechanical device or a group of ring molecules. It is shown that…
The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…
This paper explores the idea that information is an essential and distinctive feature of living systems. Unlike non-living systems, living systems actively acquire, process, and use information about their environments to respond to…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
To maintain homeostasis, living cells process information with networks of interacting molecules. Traditional models for cellular information processing have focused on networks of chemical reactions between molecules. Here, we describe how…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems…
Biology has taken strong steps towards becoming a computer science aiming at reprogramming nature after the realisation that nature herself has reprogrammed organisms by harnessing the power of natural selection and the digital prescriptive…
A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with…
It is shown how configuration space, possibly encompassing ordinary spatial structures, Born's rule, and ontological states aiming to address an underlying reality beyond Quantum Mechanics relate to each other in models of Hamiltonian…
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits. The class of quantum…