Related papers: Big Toy Models: Representing Physical Systems As C…
This paper concerns the absolute versus relative motion debate. The Barbour and Bertotti 1982 work may be viewed as an indirectly set up relational formulation of a portion of Newtonian mechanics. I consider further direct formulations of…
We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum…
The Consistent Histories (CH) formalism aims at a quantum mechanical framework which could be applied even to the universe as a whole. CH stresses the importance of histories for quantum mechanics, as opposed to measurements, and maintains…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Quantum typicality refers to the phenomenon that the expectation values of any given observable are nearly identical for the overwhelming majority of all normalized vectors in a sufficiently high-dimensional Hilbert (sub-)space. As a…
For general non-classical systems, we study the different classical representations that fulfill the specific context dependence imposed by the hidden measurement system formalism introduced in quant-ph/0008061. We show that the collection…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Toy models are highly idealized and deliberately simplified models that retain only the essential features of a system in order to explore specific theoretical questions. Long used in physics and other sciences, they have recently begun to…
We study model-theoretical structures for prototypical physical systems. First, a summary of the model theory of sheaves, adapted to the metric case, is presented. In particular, we provide conditions for a generalization of the generic…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
It is argued that any possible definition of a realistic physics theory -- i.e., a mathematical model representing the real world -- cannot be considered comprehensive unless it is supplemented with requirement of being computationally…
We argue that Hilbert spaces are not suitable to represent quantum states mathematically, in the sense that they require properties that are untenable by physical entities. We first demonstrate that the requirements posited by complex inner…
In this article, we continue our investigation on the role of non-commutativity in quantum theory. Using the method explained in "On non-commutativity in quantum theory (I): from classical to quantum probability", we analyze two toy models…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
Quantum thermodynamics is a powerful theoretical tool for assessing the suitability of quantum materials as platforms for novel technologies. In particular, the modeling of quantum cycles allows us to investigate the heat changes and work…
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
In order to better understand quantum field theory we present some toy models on finite dimensional Hilbert spaces. We discuss how these models converge to a discrete spacetime version of quantum field theory. We first define toy fermion,…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor…