Related papers: Could Spontaneous Transitions be Spontaneous?
We consider a random walk with death in $[-N,N]$ moving in a time dependent environment. The environment is a system of particles which describes a current flux from $N$ to $-N$. Its evolution is influenced by the presence of the random…
Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more…
A thought experiment is considered on observation of instantaneous collapse of an extended wave packet. According to relativity of simultaneity, such a collapse being instantaneous in some reference frame must be a lasting process in other…
The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat…
Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to…
Some important rigorous results on phase transitions accompanied by the spontaneous breaking of symmetries in statistical mechanics and relativistic quantum field theory are reviewed. Basic ideas, mainly inspired by quantum field theory,…
We develop a rigorous treatment of discontinuous stochastic unitary evolution for a system of quantum particles that interacts singularly with quantum "bubbles" at random instants of time. This model of a "cloud chamber" allows to watch and…
Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
We outline the solution of a fundamental problem in quantum theory which has hitherto lacked a proper solution, namely finding the requisite quantum theoretical framework guaranteeing that the calculated inverse spontaneous emission rate of…
The dynamics of open quantum systems is often modelled using master equations, which describe the expected outcome of an experiment (i.e., the average over many realizations of the same dynamics). Quantum trajectories, instead, model the…
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
Tunneling is an important physical process. The observation that particles surmount a high mountain in spite of the fact that they don't have the necessary energy cannot be explained by classical physics. However, this so called tunneling…
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies…
I discuss three proposed experiments that could in principle locate the boundary between the classical and quantum worlds, as well as distinguish the Hamiltonian theory presented in the first paper of this series from the…
The inability of Schrodinger's unitary time evolution to describe measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrodinger dynamics can be spontaneously broken,…
We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…
We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum…
We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with one-band isotropic model,…