Related papers: Simple New Axioms for Quantum Mechanics
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
Given a rigid C*-tensor category C with simple unit and a probability measure $\mu$ on the set of isomorphism classes of its simple objects, we define the Poisson boundary of $(C,\mu)$. This is a new C*-tensor category P, generally with…
We present an approach for teaching quantum physics at high school level based on the simplest quantum system - the single quantum bit (qubit). We show that many central concepts of quantum mechanics, including the superposition principle,…
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…
We consider the quantum-to-classical transition for macroscopic systems coupled to their environments. By applying Born's Rule, we are led to a particular set of quantum trajectories, or an unravelling, that describes the state of the…
We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…
Dynamics of a particle is formulated from classical principles that are amended by the uncertainty principle. Two best known quantum effects: interference and tunneling are discussed from these principles. It is shown that identical to…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and…
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from…
In a quantum theory of gravity spacetime behaves classically when quantum probabilities are high for histories of geometry and field that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This…
The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course,…