Supersymmetric Extension of the Snyder Algebra

We obtain a minimal supersymmetric extension of the Snyder algebra and study its representations. The construction differs from the general approach given in Hatsuda and Siegel ({\tt hep-th/0311002}), and does not utilize super-de Sitter groups. The spectra of the position operators are discrete, implying a lattice description of space, and the lattice is compatible with supersymmetry transformations.Comment: 14 page

Spectrum of the Vortex Bound States of the Dirac and Schrodinger Hamiltonian in the presence of Superconducting Gaps

We investigate the vortex bound states both Schrodinger and Dirac Hamiltonian with the s-wave superconducting pairing gap by solving the mean-field Bogoliubov-de-Gennes equations. The exact vortex bound states spectrum is numerically determined by the integration method, and also accompanied by the quasi-classical analysis. It is found that the bound state energies is proportional to the vortex angular momentum when the chemical potential is large enough. By applying the external magnetic field, the vortex bound state energies of the Dirac Hamiltonian are almost unchanged; whereas the energy shift of the Schrodinger Hamiltonian is proportional to the magnetic field. These qualitative differences may serve as an indirect evidence of the existence of Majorana fermions in which the zero mode exists in the case of the Dirac Hamiltonian only.Comment: 8 pages, 9 figure

Dephasing and Measurement Efficiency via a Quantum Dot Detector

We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.Comment: 7 pages, 3 figure

Observation of Spin-Orbit Berry's Phase in Magnetoresistance of a Two-Dimensional Hole Anti-dot System

We report observation of spin-orbit Berry's phase in the Aharonov-Bohm (AB) type oscillation of weak field magnetoresistance in an anti-dot lattice (ADL) of a two-dimensional hole system. An AB-type oscillation is superposed on the commensurability peak, and the main peak in the Fourier transform is clearly split up due to variation in Berry's phase originating from the spin-orbit interaction. A simulation considering Berry's phase and the phase arising from the spin-orbit shift in the momentum space shows qualitative agreement with the experiment.Comment: 13 pages, 5 figure

Tests of the Standard Model Using Muon Polarization Asymmetries in Kaon Decays

We have examined the physics and the experimental feasibility of studying various kaon decay processes in which the polarization of a muon in the final state is measured. Valuable information on CP violation, the quark mixing (CKM) matrix, and new physics can be obtained from such measurements. We have considered muon polarization in K_L to mu+ mu- and K to pi mu+ mu- decays. Although the effects are small, or difficult to measure because of the small branching ratios involved, these studies could provide clean measurements of the CKM parameters. The experimental difficulty appears comparable to the observation of K to pi nu barnu. New sources of physics, involving non-standard CP violation, could produce effects observable in these measurements. Limits from new results on the neutron and electron electric dipole moment, and epsilon-prime over epsilon in neutral kaon decays, do not eliminate certain models that could contribute to the signal. A detailed examination of muon polarization out of the decay plane in KMU3 and radiative KMU2 decays also appears to be of interest. With current kaon beams and detector techniques, it is possible to measure the T-violating polarization for KMU3 with uncertainties approaching 0.0001. This level of sensitivity would provide an interesting probe of new physics.Comment: 24 pages, 3 figures, To be published in the International Journal of Modern Physics

Dynamic correlations in symmetric electron-electron and electron-hole bilayers

The ground-state behavior of the symmetric electron-electron and electron-hole bilayers is studied by including dynamic correlation effects within the quantum version of Singwi, Tosi, Land, and Sjolander (qSTLS) theory. The static pair-correlation functions, the local-field correction factors, and the ground-state energy are calculated over a wide range of carrier density and layer spacing. The possibility of a phase transition into a density-modulated ground state is also investigated. Results for both the electron-electron and electron-hole bilayers are compared with those of recent diffusion Monte Carlo (DMC) simulation studies. We find that the qSTLS results differ markedly from those of the conventional STLS approach and compare in the overall more favorably with the DMC predictions. An important result is that the qSTLS theory signals a phase transition from the liquid to the coupled Wigner crystal ground state, in both the electron-electron and electron-hole bilayers, below a critical density and in the close proximity of layers (d <~ r_sa_0^*), in qualitative agreement with the findings of the DMC simulations.Comment: 13 pages, 11 figures, 2 table

Interaction-Induced Enhancement of Spin-Orbit Coupling in Two-Dimensional Electronic System

We study theoretically the renormalization of the spin-orbit coupling constant of two-dimensional electrons by electron-electron interactions. We demonstrate that, similarly to the $g$ factor, the renormalization corresponds to the enhancement, although the magnitude of the enhancement is weaker than that for the $g$ factor. For high electron concentrations (small interaction parameter $r_s$) the enhancement factor is evaluated analytically within the static random phase approximation. For large $r_s\sim 10$ we use an approximate expression for effective electron-electron interaction, which takes into account the local field factor, and calculate the enhancement numerically. We also study the interplay between the interaction-enhanced Zeeman splitting and interaction-enhanced spin-orbit coupling.Comment: 18 pages, 2 figures, REVTe

Meson-meson Scattering in QCD-like Theories

We discuss meson-meson scattering at next-to-next-to-leading order in the chiral expansion for QCD-like theories with general $n$ degenerate flavours for the cases with a complex, real and pseudo-real representation. I.e. with global symmetry and breaking pattern $SU(n)_L\times SU(n)_R\to SU(n)_V$, $SU(2n)\to SO(2n)$ and $SU(2n)\to Sp(2n)$. We obtain fully analytical expressions for all these cases. We discuss the general structure of the amplitude and the structure of the possible intermediate channels for all three cases. We derive the expressions for the lowest partial wave scattering length in each channel and present some representative numerical results. We also show various relations between the different cases in the limit of large $n$.Comment: 61 page

Condensed Matter Theory of Dipolar Quantum Gases

Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: weakly interacting Bose gases, weakly interacting Fermi gases, multilayer systems, strongly interacting dipolar gases and dipolar gases in 1D and quasi-1D geometries. Within each of these topics, purely dipolar effects and connections with experimental realizations are emphasized.Comment: Review article; submitted 09/06/2011. 158 pages, 52 figures. This document is the unedited author's version of a Submitted Work that was subsequently accepted for publication in Chemical Reviews, copyright American Chemical Society after peer review. To access the final edited and published work, a link will be provided soo

Kappa-Minkowski spacetime, Kappa-Poincar\'{e} Hopf algebra and realizations

We unify kappa-Minkowki spacetime and Lorentz algebra in unique Lie algebra. Introducing commutative momenta, a family of kappa-deformed Heisenberg algebras and kappa-deformed Poincare algebras are defined. They are specified by the matrix depending on momenta. We construct all such matrices. Realizations and star product are defined and analyzed in general and specially, their relation to coproduct of momenta is pointed out. Hopf algebra of the Poincare algebra, related to the covariant realization, is presented in unified covariant form. Left-right dual realizations and dual algebra are introduced and considered. The generalized involution and the star inner product are analyzed and their properties are discussed. Partial integration and deformed trace property are obtained in general. The translation invariance of the star product is pointed out. Finally, perturbative approach up to the first order in $a$ is presented in Appendix.Comment: references added, typos corrected, acceped in J. Phys.