相关论文: Projective Limits of State Spaces III. Toy-Models

An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…

The $f(T)$ theory is recently proposed to explain the present cosmic accelerating expansion of the universe. $f(T)$ theory is an extension of Teleparallel theory of gravity, where $T$ is the torsion scalar. This paper contains the…

This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…

Recent progress in mathematical theory of random processes provides us with non-Fock product systems (continuous tensor products of Hilbert spaces) used here for constructing a toy model for fermions. Some state vectors describe infinitely…

We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative…

Open quantum systems are powerful effective descriptions of quantum systems interacting with their environments. Studying changes of Fock state probabilities can be intricate in this context since the prevailing description of open quantum…

We consider the kinematic axioms of quantum mechanics projectively. Instead of normalized (pure) states up to global phase, states become one-dimensional subspaces of vector spaces. This process of projectivization is functorial and lax…

New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the…

Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current…

Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…

We first prove that ontological models of the quantum state which are capable of reproducing the Born probability rule and fall in the class of $\psi$-epistemic models are inconsistent with the Sch{\"o}dinger time evolution. We then model…

The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…

The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by…

We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new…

Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…

In the first part of the thesis we construct models, called integrable, in which we can perform exact computations of physical quantities. We introduce several new out-of-equilibrium models that are obtained by solving, in specific cases,…

We derive and analyze the perturbation series for the classical effective action in quantum statistical mechanics, treated as a toy model for the dimensionally reduced effective action in quantum field theory at finite temperature. The…

Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees…

In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems…

In this paper we construct a solvable toy model of the quantum dynamics of the interior of a spherical black hole with falling spherical scalar field excitations. We first argue about how some aspects of the quantum gravity dynamics of…