Scientific Series

In the de Broglie-Bohm pilot-wave theory, an ensemble of fermions is not only described by a spinor,  but also by a distribution of position beables. If the distribution of positions is different from the one predicted by the Born rule, the ensemble is said to be in quantum non-equilibrium. Such ensembles, which can lead to an experimental discrimination between the pilot-wave theory and standard quantum mechanics, are thought to quickly relax to quantum equilibrium in most cases.   In this talk, I will look at the Majorana equation from the point of view of the pilot-wave theory and I will show that it predicts peculiar trajectories for the beables; they have to move luminally at all times and they usually undergo complex helical trajectories to give the illusion that their motion is subluminal. The nature of the Majorana trajectory suggests that relaxation to quantum equilibrium could only be partial and that quantum non-equilibrium could still survive at length scales below the Compton wavelength.  I investigate this claim, thanks to some numerical simulations of the temporal evolution of non-equilibrium distributions,  for three-dimensional confined systems governed by the Dirac and Majorana equations.

Models with right-handed currents have recently attracted attention because of their potential ability to solve the discrepancy in various determinations of |V_{ub}|. We consider a minimal setup with an SU(2)_L x SU(2)_R x U(1)_{B-L} gauge symmetry, for which we perform a simultaneous analysis of the most important constraints from electroweak precision observables, particle anti-particle mixing and the B -> X_{s,d} gamma decays. The main goals of our analysis are the determination of allowed parameter space for the new right-handed mixing matrix and the possible solution of various anomalies in the current flavor data.

One of the biggest challenges in physics is to develop accurate and efficient methods that can solve many currently intractable problems in correlated quantum or statistical systems. Tensor-network model/state is drawing more and more attention since it captures the feature of the area law and is absent from the sign problem. The evaluation of the expectation value of the observables can be reduced to the contraction of a tensor-network, which can be done by means of renormalization group method, and this is exactly what tensor renormalization group (TRG) method has done. In the light of comparison between numerical renormalization group (NRG) and density matrix renormalization group(DMRG), having considered the renormalization effect of the environment, second renormalization group (SRG) method has been proposed to improve the performance of TRG. Although TRG and SRG have achieved great success in 2D lattice, application to 3D is not easy. The talk will give a review of TRG and SRG, and talk about the HOTRG, i.e., TRG based on the higher-order singular value decomposition, and its SRG version, HOSRG. They can be easily applied to 3D lattice with relatively low memory and computation cost. The well-known 3D Ising model on simple cubic lattice has been tested. As far as our group know, HOSRG have achieved by far the most accurate renormalization group results for the 3D Ising model. Some analysis and possible applications will be also discussed.

Instantons and W-bosons in 5d N=2 Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of U(1) instantons for any instanton number. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally propose that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.

The axion provides a solution to the strong CP problem and is a cold dark matter candidate.  I'll briefly review the limits on the axion from particle physics, stellar evolution and cosmology.  The various constraints suggest that the axion mass is in the micro-eV to milli-eV range.  In this window, axions contribute significantly to the energy density of the universe in the form of cold dark matter.  It was recently found that dark matter axions thermalize and form a Bose-Einstein condensate (BEC).  As a result, it may be possible to distinguish axions from other forms of dark matter, such as weakly interacting massive particles (WIMPs), on observational grounds.  Axions accreting onto a galactic halo fall in with net overall rotation because almost all go to the lowest energy available state for given angular momentum.  In contrast, WIMPs accrete onto galactic halos with an irrotational velocity field.  The inner caustics are different in the two cases.  I'll argue that the dark matter is axions because there is observational evidence for the type of inner caustic produced by, and only by, an axion BEC.

I will discuss a wide class of models which realise a bounce in a spatially flat Friedmann universe in standard General Relativity. The key ingredient is a noncanonical, minimally coupled scalar field
belonging to the class of theories with Kinetic Gravity Braiding/Galileon-like self-couplings. In these models, the universe smoothly volves from contraction to expansion, suffering neither from ghosts
nor gradient instabilities around the turning point. The end-point of he evolution can be a standard radiation-domination era or an nflationary phase.
The talk is based on arXiv:1109.1047v2 [hep-th], JCAP11(2011)021.