Kac's isospectrality question revisited in neutrino billiards.

"Can one hear the shape of a drum?" Kac raised this famous question in 1966, referring to the possibility of the existence of nonisometric planar domains with identical Dirichlet eigenvalue spectra of the Laplacian. Pairs of nonisometric isospectral billiards were eventually found by employing the transplantation method which was deduced from Sunada's theorem. Our main focus is the question to what extent isospectrality of nonrelativistic quantum billiards is present in the corresponding relativistic case, i.e., for massless spin-1/2 particles governed by the Dirac equation and confined to a domain of corresponding shape by imposing boundary conditions on the wave function components. We consider those for neutrino billiards [Berry and Mondragon, Proc. R. Soc. London A 412, 53 (1987)2053-916910.1098/rspa.1987.0080] and demonstrate that the transplantation method fails and thus isospectrality is lost when changing from the nonrelativistic to the relativistic case. To confirm this we compute the eigenvalues of pairs of neutrino billiards with the shapes of various billiards which are known to be isospectral in the nonrelativistic limit. Furthermore, we investigate their spectral properties, in particular, to find out whether not only their eigenvalues but also the fluctuations in their spectra and their length spectra differ.

Relativistic quantum chaos-An emergent interdisciplinary field.

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera.

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting-henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Diallyl trisulfide suppresses tumor growth through the attenuation of Nrf2/Akt and activation of p38/JNK and potentiates cisplatin efficacy in gastric cancer treatment.

Diallyl trisulfide (DATS), a garlic organosulfide, has shown excellent chemopreventive potential. Cisplatin (DDP) is widely used to treat solid malignant tumors, but causing serious side effects. In the current study, we attempted to elucidate the chemopreventive mechanisms of DATS in human gastric cancer BGC-823 cells in vitro, and to investigate whether DATS could enhance the anti-tumor efficacy of DDP and improve quality of life in BGC-823 xenograft mice in vivo. Treatment with DATS (25-400 µmol/L) dose-dependently inhibited the viability of BGC-823 cells in vitro with an IC50 of 115.2±4.3 µmol/L after 24 h drug exposure. DATS (50-200 µmol/L) induced cell cycle arrest at G2/M phase in BGC-823 cells, which correlated with significant accumulation of cyclin A2 and B1. DATS also induced BGC-823 cell apoptosis, which was accompanied by the modulation of Bcl-2 family members and caspase cascade activation. In BGC-823 xenograft mice, administration of DATS (20-40 mg·kg-1·d-1, ip) dose-dependently inhibited tumor growth and markedly reduced the number of Ki-67 positive cells in tumors. Interestingly, combined administration of DATS (30 mg·kg-1·d-1, ip) with DDP (5 mg/kg, every 5 d, ip) exhibited enhanced anti-tumor activity with fewer side effects. We showed that treatment of BGC-823 cells with DATS in vitro and in vivo significantly activated kinases such as p38 and JNK/MAPK and attenuated the Nrf2/Akt pathway. This study provides evidence that DATS exerts anticancer effects and enhances the antitumor efficacy of DDP, making it a novel candidate for adjuvant therapy for gastric cancer.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards.

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.