Noncommutative gravity, a `no strings attached' quantum-classical duality, and the cosmological constant puzzle

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the `weakly quantum, strongly gravitational' dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the `strongly quantum, weakly gravitational' dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.Comment: 7 pages. Second Prize in Gravity Research Foundation Essay Competition, 2008. Two paragraphs added to original essay to enhance clarity. To appear in Gen. Rel. Gra

Spin-wave excitation spectra and spectral weights in square lattice antiferromagnets

Using a recently developed method for calculating series expansions of the excitation spectra of quantum lattice models, we obtain the spin-wave spectra for square lattice, $S=1/2$ Heisenberg-Ising antiferromagnets. The calculated spin-wave spectrum for the Heisenberg model is close to but noticeably different from a uniformly renormalized classical (large-$S$) spectrum with the renormalization for the spin-wave velocity of approximately $1.18$. The relative weights of the single-magnon and multi-magnon contributions to neutron scattering spectra are obtained for wavevectors throughout the Brillouin zone.Comment: Two postscript figures, 4 two-column page

Type-I superconductivity in noncentrosymmetric superconductor AuBe

The noncentrosymmetric superconductor AuBe have been investigated using the magnetization, resistivity, specific heat, and muon-spin relaxation/rotation measurements. AuBe crystallizes in the cubic FeSi-type B20 structure with superconducting transition temperature observed at $T_{c}$ = 3.2 $\pm$ 0.1 K. The low-temperature specific heat data, $C_{el}$(T), indicate a weakly-coupled fully gapped BCS superconductivity with an isotropic energy gap 2$\Delta(0)/k_{B}T_{c}$ = 3.76, which is close to the BCS value of 3.52. Interestingly, type-I superconductivity is inferred from the $\mu$SR measurements, which is in contrast with the earlier reports of type-II superconductivity in AuBe. The Ginzburg-Landau parameter is $\kappa_{GL}$ = 0.4 $<$ 1/$\sqrt{2}$. The transverse-field $\mu$SR data transformed in the maximum entropy spectra depicting the internal magnetic field probability distribution, P(H), also confirms the absence of the mixed state in AuBe. The thermodynamic critical field, $H_{c}$, calculated to be around 259 Oe. The zero-field $\mu$SR results indicate that time-reversal symmetry is preserved and supports a spin-singlet pairing in the superconducting ground state.Comment: 9 pages, 9 figure