Phase Transitions in the Early Universe

The physics of the 20th Century is governed by two pillars, Einstein's relativity principle and the quantum principle. At the beginning of the 21st Century, it becomes clear that there exist the smallest units of matter, such as electrons, neutrinos, and quarks; their behaviors are described by the Standard Model. It was believed that the temperature of the early Universe was once 300 GeV, or higher, at $10^{-11} sec$, and then going through the electroweak phase transition. But the mass phase transition happens in the purely imaginary temperature. Later on, its temperature was 150 MeV at $3.3 \times 10^{-5} sec$, and then going through the "QCD cosmological phase transition". We attempt to use the Standard Model, a completely dimensionless theory apart from the negative "ignition" term, to conclude that the EW or mass phase transition {\it does not exist}. On the front of QCD cosmological phase transition, the intriguing question about the latent heat (energy) is discussed and its role is speculated.Comment: 24 pages, 1 figur

Rattling and freezing in a 1-D transport model

We consider a heat conduction model introduced in \cite{Collet-Eckmann 2009}. This is an open system in which particles exchange momentum with a row of (fixed) scatterers. We assume simplified bath conditions throughout, and give a qualitative description of the dynamics extrapolating from the case of a single particle for which we have a fairly clear understanding. The main phenomenon discussed is {\it freezing}, or the slowing down of particles with time. As particle number is conserved, this means fewer collisions per unit time, and less contact with the baths; in other words, the conductor becomes less effective. Careful numerical documentation of freezing is provided, and a theoretical explanation is proposed. Freezing being an extremely slow process, however, the system behaves as though it is in a steady state for long durations. Quantities such as energy and fluxes are studied, and are found to have curious relationships with particle density

Variation of Entanglement Entropy in Scattering Process

In a scattering process, the final state is determined by an initial state and an S-matrix. We focus on two-particle scattering processes and consider the entanglement between these particles. For two types initial states; i.e., an unentangled state and an entangled one, we calculate perturbatively the change of entanglement entropy from the initial state to the final one. Then we show a few examples in a field theory and in quantum mechanics.Comment: 13 pages; v2: refs. adde