arXiv subjects
Publications and source records attributed to Mario A. Castagnino.
When $t\to \infty $ any wave packet in the liouvillian representation of the density matrices, becomes a Hardy class function from below. This fact, in the global frame of Reichenbach diagram, is used to explain the observed global time asymmetry of the universe.
064 There are two schools, or lines of thought, that try to unify the apparently divergent laws of dynamics and thermodynamics and to explain the observed time-asymmetry of the universe, and most of its sub-systems, in spite of the fact that these systems are driven by time-symmetric evolution equations. They will be called the coarse-graining and the fine-graining schools (even if these names describe only a part of their philosophy). Coarse-graining school obtains time-asymmetry via a projection of the state space on a space of ''relevant'' states. The corresponding projection of the primitive reversible evolution laws yields effective irreversible evolution laws for the relevant states. Fine-graining always use the same primitive reversible evolution laws. But these laws (in adequate extensions of the usual spaces where these laws are formulated) have a set of solutions $S$ that can be decompose in two subsets $S_{+\text{}}$ and $S_{-}$ of time asymmetric solutions. Choosing one of these two sets, as the arena to formulate the theory, time asymmetry is established. The aim of these lectures is to explain, in the simplest- self-contained, unbiased, and, honest way, the main characteristics of both schools and to point out the advantages and disadvantages of both formalism, in such a way that, the polemic between the schools, turns out to be explicit and organized in the mind of the reader (who will be considered the supreme judge to give the final verdict). 064 Some cosmological features of the theory will be also considered, mainly the problem of the low entropy initial state of the universe
A very simplified model of the Universe is considered in order to propose an alternative approach to the irreversible evolution of the Universe at very early times. The entropy generation at the quantum stage can be thought as a consequence of an instability of the system. Then particle creation arises from this instability.
The importance of the global nature of the arrow of time is shown. Classical Reichenbach diagram and quantum Bohm-Reichenbach diagram, for the universe are introduced. They are used to show the increase of entropy in closed systems, the global nature of the quantum measurement, and the relation among the different arrows of time.
Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution that is used to study the time evolution of the reduced density operator. It is derived in a closed form, in the one-particle sector of the model. The irreversible behavior of the Brownian particle is described by a reduced density matrix.
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical one in a higher dimension. The instability results from the inverted oscillator structure which appears in the Hamiltonian. We show that the `proper time' unitary evolution splits into two semigroups. The semigroup associated with decaying Gamov vectors is related to the Feynman boundary conditions for the Green functions and the semigroup associated with growing Gamov vectors is related to the Dyson boundary conditions.