Quantum Correction in Exact Quantization Rules

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the quantum correction is an invariant, independent of the number of nodes in the wave function. In those systems, the energy levels of all the bound states can be easily calculated from the exact quantization rule and the solution for the ground state, which can be obtained by solving the Riccati equation. With this new method, we re-calculate the energy levels for the one-dimensional systems with a finite square well, with the Morse potential, with the symmetric and asymmetric Rosen-Morse potentials, and with the first and the second P\"{o}schl-Teller potentials, for the harmonic oscillators both in one dimension and in three dimensions, and for the hydrogen atom.Comment: 10 pages, no figure, Revte

Centrality, system size and energy dependences of charged-particle pseudo-rapidity distribution

Utilizing the three-fireball picture within the quark combination model, we study systematically the charged particle pseudorapidity distributions in both Au+Au and Cu+Cu collision systems as a function of collision centrality and energy, $\sqrt{s_{NN}}=$ 19.6, 62.4, 130 and 200 GeV, in full pseudorapidity range. We find that: (i)the contribution from leading particles to $dN_{ch}/d\eta$ distributions increases with the decrease of the collision centrality and energy respectively; (ii)the number of the leading particles is almost independent of the collision energy, but it does depend on the nucleon participants $N_{part}$; (iii)if Cu+Cu and Au+Au collisions at the same collision energy are selected to have the same $N_{part}$, the resulting of charged particle $dN/d\eta$ distributions are nearly identical, both in the mid-rapidity particle density and the width of the distribution. This is true for both 62.4 GeV and 200 GeV data. (iv)the limiting fragmentation phenomenon is reproduced. (iiv) we predict the total multiplicity and pseudorapidity distribution for the charged particles in Pb+Pb collisions at $\sqrt{s_{NN}}= 5.5$ TeV. Finally, we give a qualitative analysis of the $N_{ch}/$ and $dN_{ch}/d\eta/|_{\eta\approx0}$ as function of $\sqrt{s_{NN}}$ and $N_{part}$ from RHIC to LHC.Comment: 12 pages, 8 figure

A Non-equilibrium STM model for Kondo Resonance on surface

Based on a no-equilibrium STM model, we study Kondo resonance on a surface by self-consistent calculations. The shapes of tunneling spectra are dependent on the energy range of tunneling electrons. Our results show that both energy-cutoff and energy-window of tunneling electrons have significant influence on the shapes of tunneling spectra. If no energy-cutoff is used, the Kondo resonances in tunneling spectrum are peaks with the same shapes in the density of state of absorbed magnetic atoms. This is just the prediction of Tersoff theory. If we use an energy cutoff to remove high-energy lectrons, a dip structure will modulate the Kondo resonance peak in the tunneling spectrum. The real shape of Kondo peak is the mixing of the peak and dip, the so-called Fano line shape. The method of self-consistent non-equilibrium matrix Green function is discussed in details.Comment: 11 pages and 8 eps figur

Onset of unsteady horizontal convection in rectangle tank at Pr=1Pr=1

The horizontal convection within a rectangle tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of $Ra$ from steady solutions to periodic solutions, and the critical Rayleigh number $Ra_c$ is obtained as $Ra_c=5.5377\times 10^8$ for the middle plume forcing at $Pr=1$, which is much larger than the formerly obtained value. Besides, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear (shear instability) other than thermally dynamics (thermal instability). Finally, Paparella and Young's [J. Fluid Mech. 466 (2002) 205] first hypotheses about the destabilization of the flow is numerically proved, i.e. the middle plume forcing can lead to a destabilization of the flow.Comment: 4pages, 6 figures, extension of Chin. Phys. Lett. 2008, 25(6), in pres

Quantum limited particle sensing in optical tweezers

Particle sensing in optical tweezers systems provides information on the position, velocity and force of the specimen particles. The conventional quadrant detection scheme is applied ubiquitously in optical tweezers experiments to quantify these parameters. In this paper we show that quadrant detection is non-optimal for particle sensing in optical tweezers and propose an alternative optimal particle sensing scheme based on spatial homodyne detection. A formalism for particle sensing in terms of transverse spatial modes is developed and numerical simulations of the efficacy of both quadrant and spatial homodyne detection are shown. We demonstrate that an order of magnitude improvement in particle sensing sensitivity can be achieved using spatial homodyne over quadrant detection.Comment: Submitted to Biophys

Evidence for a Quantum Hall Insulator in an InGaAs/InP Heterostructure

We study the quantum critical behavior of the plateau-insulator (PI) transition in a low mobility InGaAs/InP heterostructure. By reversing the direction of the magnetic field (B) we find an averaged Hall resistance \rho_xy which remains quantized at the plateau value h/e^2 throughout the PI transition. We extract a critical exponent \kappa'= 0.57 +/- 0.02 for the PI transition which is slightly different from (and possibly more accurate than) the established value 0.42 +/- 0.04 as previously obtained from the plateau-plateau (PP) transitions.Comment: 3pages, 2 figures; submitted to EP2DS-14 conference proceeding

Parameterizing Majorana Neutrino Couplings in the Higgs Sector

Nonzero masses for the active neutrinos - regardless of their nature or origin - arise only after electroweak symmetry breaking. We discuss the parameterization of neutrino couplings to a Higgs sector consisting of one SU(2)_L scalar doublet and one SU(2)_L scalar triplet, and allow for right-handed neutrinos whose Majorana mass parameters arise from the vacuum expectation value of a Standard Model scalar singlet. If the neutrinos are Majorana fermions, all Yukawa couplings can be expressed as functions of the neutrino mass eigenvalues and a subset of the elements of the neutrino mixing matrix. In the mass basis, the Yukawa couplings are, in general, not diagonal. This is to be contrasted to the case of charged-fermions or Dirac neutrinos, where couplings to the Higgs-boson are diagonal in the mass basis and proportional only to the fermion masses. Nonetheless, all physically distinguishable parameters can be reached if all neutrino masses are constrained to be positive, all mixing angles constrained to lie in the first quadrant (theta in [0,pi/2]), and all Majorana phases to lie in the first two quadrants (phi in [0,pi]), as long as all Dirac phases vary within the entire unit circle (delta in [0,2pi}). We discuss several concrete examples and comment on the Casas-Ibarra parameterization for the neutrino Yukawa couplings in the case of the type-I Seesaw Lagrangian.Comment: 13 pages, 2 eps figure

Mandate-driven networking eco-system : a paradigm shift in end-to-end communications

The wireless industry is driven by key stakeholders that follow a holistic approach of "one-system-fits-all" that leads to moving network functionality of meeting stringent End-to-End (E2E) communication requirements towards the core and cloud infrastructures. This trend is limiting smaller and new players for bringing in new and novel solutions. For meeting these E2E requirements, tenants and end-users need to be active players for bringing their needs and innovations. Driving E2E communication not only in terms of quality of service (QoS) but also overall carbon footprint and spectrum efficiency from one specific community may lead to undesirable simplifications and a higher level of abstraction of other network segments may lead to sub-optimal operations. Based on this, the paper presents a paradigm shift that will enlarge the role of wireless innovation at academia, Small and Medium-sized Enterprises (SME)'s, industries and start-ups while taking into account decentralized mandate-driven intelligence in E2E communications

Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker

The quantum geometry in the momentum space of semiconductors and insulators, described by the quantum metric of the valence band Bloch state, has been an intriguing issue owing to its connection to various material properties. Because the Brillouin zone is periodic, the integration of quantum metric over momentum space represents an average distance between neighboring Bloch states, of which we call the fidelity number. We show that this number can further be expressed in real space as a fidelity marker, which is a local quantity that can be calculated directly from diagonalizing the lattice Hamiltonian. A linear response theory is further introduced to generalize the fidelity number and marker to finite temperature, and moreover demonstrates that they can be measured from the global and local optical absorption power against linearly polarized light. In particular, the fidelity number spectral function in 2D systems can be easily measured from the opacity of the material. Based on the divergence of quantum metric, a nonlocal fidelity marker is further introduced and postulated as a universal indicator of any quantum phase transitions provided the crystalline momentum remains a good quantum number, and it may be interpreted as a Wannier state correlation function. The ubiquity of these concepts is demonstrated for a variety of topological insulators and topological phase transitions in different dimensions.Comment: 11 pages, 5 figure