In this talk, the individual contribution to diffuse gamma-ray emission from the secondary products in hadronic interactions generated by cosmic rays (CRs) is discussed, in addition to the contribution of pi0 decay. For this purpose, the Monte Carlo particle collision code DPMJET3.04 is employed to determine the multiplicity spectra of various secondary particles with gammas as the final decay state, that result from inelastic collisions between cosmic-ray protons and helium nuclei and the ISM with standard composition. An easy-to-use gamma-ray production matrix for cosmic rays with energies up to about 10 PeV is derived. This production matrix is applied to the GeV excess in diffuse galactic gamma-rays observed by EGRET. Although the non-pi0 decay components have contributed to the total emission with a different spectrum from the pi0-decay component, they are insufficient to explain the GeV excess. Finally, we test the hypothesis that the TeV-band gamma-ray emission of the shell-type SNR RX J1713.7-3946 observed with HESS is caused by shock-accelerated hadronic cosmic rays. This scenario implies a very high efficacy of particle acceleration, so the particle spectrum is expected to continuously harden toward high energies on account of cosmic-ray modification of the shock. Using the chi2 statistics we find that a continuously softening spectrum is strongly preferred, in contrast to expectations. A hardening spectrum has about 1% probability to explain the HESS data, but then only if a hard cut-off at 50-100 TeV is imposed on the particle spectrum.

We present variational schemes based on tensor networks in one and two dimensions. First, variational QMC studies based on matrix product states of one-dimensional antiferromagnetic Heisenberg and J1-J2 models with PBC is discussed. We show the matrices can be optimized not just for the ground state, but also, simultaneously, for the lowest states in several different lattice and spin symmetry sectors. Second, we will present a variational scheme of contracting a square-lattice tensor network in two dimensions, based on auxiliary tensors accomplishing successive truncations of 8-index tensors for 2x2 plaquettes into 4-index tensors. Application to the transverse Ising model is discussed.

A knot is a loop of line, which generally is “knotted”, in the 3-dimensional space. A knot invariant is an algebraic entity which is intrinsic to a knot. Mathematicians have been interested in finding knot invariants since the early 20-th century, but progress was slow and limited due to the complexity of knots. A breakthrough occurred in 1985 when Jones discovered a new invariants now known as the Jones polynomial (for which Jones was awarded the Fields medal, the “Nobel prize” in mathematics). Subsequently, it was discovered that the Jones polynomial is related to the Potts model, and that it is a special case of a host of new knot invariants that can be constructed from soluble models in statistical mechanics. This talk explores the connection of knot invariants with statistical mechanics. The talk begins with a brief review of elements of knot theory and relevant results in statistical mechanics. It is followed by a discussion on how knot invariants can be constructed by applying techniques used in solving lattice models. The talk assumes no prior knowledge of knot theory.

Although both granular gases (GG) and molecular gases (MG) are characterized by random motions of their constituents, phenomena not possible for MG, such as clustering and Maxwell's demon and granular oscillations are reported in GG. The origin of these intriguing phenomena is the dissipative collisions in GG which are coupled to the local density of the GG in a spatially extended or compartmentalized system. Systems with two or more types of grains are especially interesting because the asymmetry in the dissipative collisions between different types of grains can lead to oscillations and even more interesting dynamics. Flux models with different granular temperatures for different types of grains are employed together with nonlinear dynamics theory to understand and explore these phenomena.

A theory is presented of quantum criticality in open (coupled to reservoirs) itinerant electron magnets, with nonequilibrium drive provided by current flow across the system. Both departures from equilibrium at conventional (equilibrium) quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are treated. Nonequilibrium-induced phase transitions are found to have the same leading critical behavior as conventional thermal phase transitions. The theory is also extended to the case of a coupled bilayer system of itinerant electron magnets where coupled critical dynamics between two order parameters becomes possible.

The current observations confirm that the Universe is under accelertaing phase. Dark energy and Modified gravity are two major candidates to explain this observations. As a viable model, the modified gravity theories should be consistent with solar system test and can produce current accelerating Universe. In addition to this background evolution, modified gravity imprints some different behaviors in perturbed observables. These will give us chances to find the origin of the acceleration of the Universe.

An approach to the consistency test of dark energy models with observations will be presented. To test a dark energy model, we suggest introducing a characteristic Q(z) that in general varies with the redshift z but in that model plays the role of a constant distinct parameter. Then, by reconstructing dQ(z)/dz from observational data and comparing it with zero we can assess the consistency between data and the model under consideration. For reconstructing dQ(z)/dz from data, a parametrization of the relevant physical quantity is required. This method of the consistency test is efficient because for all models we invoke the constraint of only a single parameter space that by choice can be easily access. The general principle of our approach is not limited to dark energy. It may also be applied to the testing of various cosmological models and even the models in other fields beyond the scope of cosmology.