Related papers: Commuting Position and Momentum Operators, Exact D…
Using the Gell-Mann and Hartle formalism of generalized quantum mechanics of closed systems, we study coarse-grained decoherent histories. The system under consideration is one-dimensional and consists of a particle coupled to a von Neumann…
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
This paper discusses the relation between the decoherent histories approach to quantum mechanics that is based on coarse-grained decoherent histories of a closed system, and the approximate quantum mechanics of measured subsystems, as in…
Some ambiguities have recently been found in the definition of the partial derivative (in the case of presence of both explicit and implicit dependencies of the function subjected to differentiation). We investigate the possible influence…
Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…
A theory recently proposed by the author aims to explain decoherence and the thermodynamical behaviour of closed systems within a conservative, unitary, framework for quantum gravity by assuming that the operators tied to the gravitational…
Whether an almost-commuting pair of operators must be close to a commuting pair is a central question in operator and matrix theory. We investigate this problem for pairs of $C^*$-subalgebras $\mathcal{A}$ and $\mathcal{B}$ of…
Quantum decoherence provides a framework to study the emergence of classicality from quantum systems by showing how interactions with the environment suppress interferences and select robust states known as pointer states. Earlier studies…
A commuting pair of operators (S, P) on a Hilbert space H is said to be a Gamma-contraction if the symmetrized bidisc is a spectral set of the tuple (S, P). In this paper we develop some operator theory inspired by Agler and Young's results…
A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system.…
In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…
In this paper, the quantization and generalized uncertainty relation for some quantum deformed algebras are investigated. For several deformed algebras, the commutation relation between the position and the momentum operator is shown to be…
Lueders theorem states that two observables commute if measuring one of them does not disturb the measurement outcomes of the other. We study measurements which are described by continuous positive operator-valued measurements (or POVMs)…
We consider the decoherence of phase space histories in a class of quantum Brownian motion models, consisting of a particle moving in a potential $V(x)$ in interaction with a heat bath at temperature $T$ and dissipation gamma, in the…
We study the phase space structure of exact quantum Wightman functions in spatially homogeneous, temporally varying systems. In addition to the usual mass shells, the Wightman functions display additional coherence shells around zero…
The assumption that an ensemble of classical particles is subject to nonclassical momentum fluctuations, with the fluctuation uncertainty fully determined by the position uncertainty, has been shown to lead from the classical equations of…
Recently, some problems have been found in the definition of the partial derivative in the case of the presence of both explicit and implicit functional dependencies in the classical analysis. In this talk we investigate the influence of…
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…