Related papers: Classical and Quantum Nambu Mechanics
Phase Space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective hamiltonian invariants. The power and simplicity of the method is fully illustrated through new…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Nambu Quantum Mechanics, proposed in Phys. Lett. B536, 305 (2002), is a deformation of canonical Quantum Mechanics in which the manifold over which the "phase" of an energy eigenstate time evolves is modified. This generalization affects…
In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum…
The phenomenological Landau theory of the spin precession has been used to reproduce the out-of-equilibrium properties of many magnetic systems. However, such an approach suffers from some serious limitations. The main reason is that the…
Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number forms of the time-dependent quantum…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
This paper proposes a novel approach to quantizing Nambu brackets in classical mechanics using operator formalism. The approach employs the ``Planck derivative'' to represent Nambu brackets, from which we derive a commutation relation for…
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity.…
Using the framework of Nambu's generalised mechanics, we obtain a new description of constrained Hamiltonian dynamics, involving the introduction of another degree of freedom in phase space, and the necessity of defining the action integral…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…
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''…
We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
Quantum mechanics is nonlocal. Classical mechanics is local. Consequently classical mechanics can not explain all quantum phenomena. Conversely, it is cumbersome to use quantum mechanics to describe classical phenomena. Not only are the…
We argue that in contrast to the classical physics, the measurements in the quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant…
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…