Casimir effect for lattice fermions

We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (M\"obius) domain-wall fermion in $1+1$ dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of $N \geq 3$, the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in M\"obius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.Comment: 8 pages, 5 figures; published versio

Casimir effect in axion electrodynamics with lattice regularizations

The Casimir effect is induced by the interplay between photon fields and boundary conditions, and in particular, photon fields modified in axion electrodynamics may lead to the sign-flipping of the Casimir energy. We propose a theoretical approach to derive the Casimir effect in axion electrodynamics. This approach is based on a lattice regularization and enables us to discuss the dependence on the lattice spacing for the Casimir energy. With this approach, the sign-flipping behavior of the Casimir energy is correctly reproduced. By taking the continuum limit of physical quantity calculated on the lattice, we can obtain the results consistent with the continuum theory. This approach can also be applied to the Casimir effect at nonzero temperature.Comment: 11 pages, 9 figure

Lattice-fermionic Casimir effect and topological insulators

The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the M\"obius domain-wall fermion formulation, in the $1+1$-, $2+1$-, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.Comment: 27 pages, 9 figures; published versio

Localization of Stem Cells in Small Intestinal Epithelium:Strategies for Identifying Small Intestinal Stem Cells

In the small intestine, stem cells are considered to exist at the bottom of the crypt. Actively proliferatingtransitional cells supplied from stem cells are differentiated into two directions upward and downward. Upwardcells are differentiated into absorbing epithelial cells, goblet cells, and endocrine cells, and downwardcells differentiated into Paneth cells. However there are some difficulties to identify the stem cells becauseof their unique characteristics. At first, stem cells occur as actual stem cells and potential stem cells, andsecond, there is diversity in stem cells. Therefore, molecules suitable for a marker of small intestinal stemcells are necessary to distinguish "true" stem cells from others. Energetically searched for in recent years,Musashi-1, type 1A bone morphogenetic protein receptor (BMPR-1A), phospho-phosphatase and tensinhomolog deleted on chromosome ten( phospho-PTEN), doublecortin and calmodulin kinase-like-1( DCAMKL1),ephrin receptors( Eph receptors), integrins, and leucine-rich repeat-containing G protein-coupled receptor5 (Lgr5) are proposed. Among them, Musashi-1 draws attention as one of a candidate marker forsmall intestinal stem cells. We here introduce our reviews about expression of Musashi-1 and Hes1 proteinsin the small intestine, and would like to overview the way to identify the small intestinal stem cells

Adaptation of Mouse Skeletal Muscle to Long-Term Microgravity in the MDS Mission

The effect of microgravity on skeletal muscles has so far been examined in rat and mice only after short-term (5–20 day) spaceflights. The mice drawer system (MDS) program, sponsored by Italian Space Agency, for the first time aimed to investigate the consequences of long-term (91 days) exposure to microgravity in mice within the International Space Station. Muscle atrophy was present indistinctly in all fiber types of the slow-twitch soleus muscle, but was only slightly greater than that observed after 20 days of spaceflight. Myosin heavy chain analysis indicated a concomitant slow-to-fast transition of soleus. In addition, spaceflight induced translocation of sarcolemmal nitric oxide synthase-1 (NOS1) into the cytosol in soleus but not in the fast-twitch extensor digitorum longus (EDL) muscle. Most of the sarcolemmal ion channel subunits were up-regulated, more in soleus than EDL, whereas Ca2+-activated K+ channels were down-regulated, consistent with the phenotype transition. Gene expression of the atrophy-related ubiquitin-ligases was up-regulated in both spaceflown soleus and EDL muscles, whereas autophagy genes were in the control range. Muscle-specific IGF-1 and interleukin-6 were down-regulated in soleus but up-regulated in EDL. Also, various stress-related genes were up-regulated in spaceflown EDL, not in soleus. Altogether, these results suggest that EDL muscle may resist to microgravity-induced atrophy by activating compensatory and protective pathways. Our study shows the extended sensitivity of antigravity soleus muscle after prolonged exposition to microgravity, suggests possible mechanisms accounting for the resistance of EDL, and individuates some molecular targets for the development of countermeasures