The Schultz-Mattis-Lieb fermion formulation of the two-dimensional Ising model is simplified by means of long-wavelength approximations which become exact in the critical region. The resulting continuum theory has a Hamiltonian density which is shown to be identical, to within a perfect derivative, to that of free, spinless particles satisfying the one-dimensional Dirac equation. Filling the negative-energy single-particle states of momentumq and mass gives an integral over the single-particle energies -(
2+k2)1/2. Because varies linearly with the temperature, differentiating twice gives Onsager's logarithmic singularity in the specific heat.Work supported in part by the Office of Naval Research. 相似文献
In the paper we study the problem of characterization of pluripolar hulls of a class of functions containing Blaschke products.
Mathematics Subject Classifications (2000) 32U30, 31A15, 30D50.Research partially supported by the KBN grant No. 5 P03A 033 21 and the Rectors Scholarship Fund at the Jagiellonian University. 相似文献
This work presents analytical, numerical and experimental demonstrations of light diffracted through a logarithmic spiral (LS) nanoslit, which forms a type of switchable and focus‐tunable structure. Owing to a strong dependence on the incident photon spin, the proposed LS‐nanoslit converges incoming light of opposite handedness (to that of the LS‐nanoslit) into a confined subwavelength spot, while it shapes light with similar chirality into a donut‐like intensity profile. Benefitting from the varying width of the LS‐nanoslit, different incident wavelengths interfere constructively at different positions, i.e., the focal length shifts from 7.5 μm (at λ = 632.8 nm) to 10 μm (at λ = 488 nm), which opens up new opportunities for tuning and spatially separating broadband light at the micrometer scale.
GaN layers on bulk m‐plane, , and GaN substrates were grown by metal organic vapor phase epitaxy. XRD rocking curves have a FWHM of less than 150″, indicating excellent crystalline quality. However in many cases surface morphology exhibits hillocks with a height of 1–2 µm and a lateral extension of 50–200 µm whereas a smooth surface would be desirable for optoelectronic devices. The influence of growth parameters on the surface morphology was studied. The goal was, to constrain the material redistribution, that is necessary to form large hillocks. This was achieved by lowering the adatom diffusion length by a reduction of temperature and an increased reactor pressure. In the case of the and semipolar planes a reduction of the adatom diffusion length leads to a reduction of hillock density, hillock size and a smoother surface between hillocks. However, the m‐plane surface does not react to a reduction of adatom mobility. Even at 890°C and 400 mbar rectangular pyramids cover the surface. In contrast to the other planes, the becomes instable, when the adatom diffusion length is reduced. 相似文献
This paper describes an efficient method of inducing sonochemical reactions with focussed ultrasound. A sector-vortex transducer (a phased array transducer with multiple sectors and a geometric focus) is used to produce focal ultrasound fields with spiral-shaped wavefronts. Clockwise and counter-clockwise spiral focal fields, with basically the same ultrasound power distribution but having different wavefront angles, are produced by using the same array transducer. The oxidation of the iodide ions induced from the periodic switching between such a pair of spiral focal fields is investigated at an ultrasound frequency of 750 kHz. The oxidation rate at the optimum switching period (3 ms) is about ten times higher than that at switching periods of 1 s. The optimum switching period and the sonochemical reaction rate are unchanged when the viscosity was adjusted to that of human blood. 相似文献
A simple independent-quark-model based on the Dirac equation with logarithmic potential is used to calculate several properties of octet baryons such as magnetic moment, the axial vector coupling constantgA (n) for neutronβ-decay and the charge radius of the proton. In view of the simplicity of the model, the results obtained are quite good. 相似文献
