Related papers: Aperiodicity in Quantum Wang Tilings
Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary…
Unlike random potentials, quasi-periodic modulation can induce localisation-delocalisation transitions in one dimension. In this article, we analyse the implications of this for symmetry breaking in the quasi-periodically modulated quantum…
We examine the dependence of quantization on global properties of a classical system. Quantization based on local properties may lead to ambiguities and inconsistency between local and global symmetries of a quantum system. Our quantization…
Quantum Electrodynamics (QED) has been so successful a theory that it is taken as a model for the production of further quantum theories. However, when the prescription for quantising electromagnetic interactions that so successfully…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…
A finite set of integers $A$ tiles the integers by translations if $\mathbb{Z}$ can be covered by pairwise disjoint translated copies of $A$. Restricting attention to one tiling period, we have $A\oplus B=\mathbb{Z}_M$ for some…
Frauchiger and Renner recently cast doubt on the universal applicability of Quantum Mechanics [1]. In the following, it is pointed out that their conclusion of one of three common-sense conditions, demanded for Quantum Mechanics, being…
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…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…
We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple…
We generalize the formerly proposed relationship between a special complex geometry (originating from the structure of biquaternion algebra) and induced real geometry of (extended) space-time. The primordial dynamics in complex space allows…
We analyse and develop the recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalised form of quantum theory based on…
Enforcing the periodicity hypothesis of the "old" formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a Deterministic Field Theory [arXiv:0903.3680]. A…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated…
A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices…