Related papers: On classical and quantum liftings
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is…
The recapture relationship is an important element to any understanding of the connexion between different systems of logic. Loosely speaking, one system of logic recaptures another if it is possible to specify a subsystem of the former…
We develop a general framework for working with structured lifting problems, establishing closure and uniqueness properties of their solutions. In a subsequent paper, we apply these results to axiomatize computation rules of cubical type…
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…
Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems…
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical…
By using a physically-relevant and theory independent definition of measurement-based equilibration, we show quantitatively that equilibration is easier for quantum systems than for classical systems, in the situation where the initial…
A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
We study the transition between quantum and classical behavior of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
This thesis covers various aspects of open systems in classical and quantum mechanics. In the first part, we deal with classical systems. The bath-of-oscillators formalism is used to describe an open system, and the phenomenological…
Recent developments in quantum computing suggest that it could be possible to make conditional changes to the state of a quantum mechanical system without resorting to classical observation. It is accomplished through collective response of…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…