Massive Hyper-Kahler Sigma Models and BPS Domain Walls

With the non-Abelian Hyper-Kahler quotient by U(M) and SU(M) gauge groups, we give the massive Hyper-Kahler sigma models that are not toric in the N=1 superfield formalism. The U(M) quotient gives N!/[M! (N-M)!] (N is a number of flavors) discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua. We derive BPS domain wall solution in the case of N=2 and M=1 in the U(M) quotient model.Comment: 16 pages, 1 figure, contribution to the Proceedings of the International Conference on "Symmetry Methods in Physics (SYM-PHYS10)" held at Yerevan, Armenia, 13-19 Aug. 200

Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities

We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal potentials related to the weights in the above mentioned inequalities.Comment: 16 page

Field evolution of the magnetic structures in Er2_2Ti2_2O7_7 through the critical point

We have measured neutron diffraction patterns in a single crystal sample of the pyrochlore compound Er$_2$Ti$_2$O$_7$ in the antiferromagnetic phase (T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the [110] direction. We determine all the characteristics of the magnetic structure throughout the quantum critical point at $H_c$=2\,T. As a main result, all Er moments align along the field at $H_c$ and their values reach a minimum. Using a four-sublattice self-consistent calculation, we show that the evolution of the magnetic structure and the value of the critical field are rather well reproduced using the same anisotropic exchange tensor as that accounting for the local paramagnetic susceptibility. In contrast, an isotropic exchange tensor does not match the moment variations through the critical point. The model also accounts semi-quantitatively for other experimental data previously measured, such as the field dependence of the heat capacity, energy of the dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure

Matrix representation of the time operator

In quantum mechanics the time operator $\Theta$ satisfies the commutation relation $[\Theta,H]=i$, and thus it may be thought of as being canonically conjugate to the Hamiltonian $H$. The time operator associated with a given Hamiltonian $H$ is not unique because one can replace $\Theta$ by $\Theta+ \Theta_{\rm hom}$, where $\Theta_{\rm hom}$ satisfies the homogeneous condition $[\Theta_{\rm hom},H]=0$. To study this nonuniqueness the matrix elements of $\Theta$ for the harmonic-oscillator Hamiltonian are calculated in the eigenstate basis. This calculation requires the summation of divergent series, and the summation is accomplished by using zeta-summation techniques. It is shown that by including appropriate homogeneous contributions, the matrix elements of $\Theta$ simplify dramatically. However, it is still not clear whether there is an optimally simple representation of the time operator.Comment: 13 pages, 3 figure

On the Spectral Analysis of Quantum Electrodynamics with Spatial Cutoffs. I

In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground state for sufficiently small values of coupling constants. The spectral scattering theory is studied as well and it is shown that asymptotic fields exist and the spectral gap is closed

Amplitude dependence of image quality in atomically-resolved bimodal atomic microscopy

In bimodal FM-AFM, two flexural modes are excited simultaneously. The total vertical oscillation deflection range of the tip is the sum of the peak-to-peak amplitudes of both flexural modes (sum amplitude). We show atomically resolved images of KBr(100) in ambient conditions in bimodal AFM that display a strong correlation between image quality and sum amplitude. When the sum amplitude becomes larger than about 200 pm, the signal-to-noise ratio (SNR) is drastically decreased. We propose this is caused by the temporary presence of one or more water layers in the tip-sample gap. These water layers screen the short range interaction and must be displaced with each oscillation cycle. Further decreasing the sum amplitude, however, causes a decrease in SNR. Therefore, the highest SNR in ambient conditions is achieved when the sum amplitude is slightly less than the thickness of the primary hydration layer.Comment: 3000 words, 3 Figures, 3 supplimentary figure

Femtosecond laser nanostructuring of transparent materials: from bulk to fiber lasers

Progress in high power ultra-short pulse lasers has opened new frontiers in the physics of light-matter interactions and laser material processing. Recently there has been considerable interest in the application of femtosecond lasers to writing inside transparent materials and in particular to fabrication of three-dimensional microstructures

Channel Capacity Enhancement by Pattern Controlled Handset Antenna

This paper presents a radiation pattern controlled antenna for handset terminals to reduce the correlation coefficient between antennas and enhance the channel capacity in MIMO applications. A pair of small inverted-F shaped antennas combined by a phase shifter provides a single port with controlled pattern. To enhance the channel capacity, the phase difference for the IFA array is optimized using the evaluation parameter of reception level, correlation coefficient and mean effective gain of the proposed array geometry. The channel capacity enhancement is verified by assuming Croneker scattering under Nakagami-Rice propagation model