Renormalization Group Study of the Electron-phonon Interaction in the High Tc Cuprates

We generalize the numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$. After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.Comment: 4 pages, 3 figures, references added, added more details about others' previous studie

A Method of Areas for Manipulating the Entanglement Properties of One Copy of a Two-Particle Pure State

We consider the problem of how to manipulate the entanglement properties of a general two-particle pure state, shared between Alice and Bob, by using only local operations at each end and classical communication between Alice and Bob. A method is developed in which this type of problem is found to be equivalent to a problem involving the cutting and pasting of certain shapes along with a certain colouring problem. We consider two problems. Firstly we find the most general way of manipulating the state to obtain maximally entangled states. After such a manipulation the entangled state |11>+|22>+....|mm> is obtained with probability p_m. We obtain an expression for the optimal average entanglement. Also, some results of Lo and Popescu pertaining to this problem are given simple geometric proofs. Secondly, we consider how to manipulate one two particle entangled pure state to another with certainty. We derive Nielsen's theorem (which states the necessary and sufficient condition for this to be possible) using the method of areas.Comment: 29 pages, 9 figures. Section 2.4 clarified. Error in second colouring theorem (section 3.2) corrected. Some other minor change

Determinations of |V_ub| and |V_cb| from measurements of B -> X_u,c\ell\nu differential decay rates

Methods are described in the framework of light-cone expansion which allow one to determine the Cabibbo-Kobayashi-Maskawa matrix elements |V_ub| and |V_cb| from measurements of the differential decay rates as a function of the scaling variables in the inclusive semileptonic decays of B mesons. By these model-independent methods the dominant hadronic uncertainties can be avoided and the B -> X_u\ell\nu decay can be very efficiently differentiated from the B -> X_c\ell\nu decay, which may lead to precise determinations of |V_ub| and |V_cb|.Comment: 11 pages, 2 figures, version as published in Mod. Phys. Lett. A, more discussion, references added, title chang

Binding between endohedral Na atoms in Si clathrate I; a first principles study

We investigate the binding nature of the endohedral sodium atoms with the ensity functional theory methods, presuming that the clathrate I consists of a sheaf of one-dimensional connections of Na@Si$_{24}$ cages interleaved in three perpendicular directions. Each sodium atom loses 30% of the 3s$^1$ charge to the frame, forming an ionic bond with the cage atoms; the rest of the electron contributes to the covalent bond between the nearest Na atoms. The presumption is proved to be valid; the configuration of the two Na atoms in the nearest Si$_{24}$ cages is more stable by 0.189 eV than that in the Si$_{20}$ and Si$_{24}$ cages. The energy of the beads of the two distorted Na atoms is more stable by 0.104 eV than that of the two infinitely separated Na atoms. The covalent bond explains both the preferential occupancies in the Si$_{24}$ cages and the low anisotropic displacement parameters of the endohedral atoms in the Si$_{24}$ cages in the [100] directions of the clathrate I.Comment: First page: Affiliation added to PDF and PS versio

Turbulence and turbulent mixing in natural fluids

Turbulence and turbulent mixing in natural fluids begins with big bang turbulence powered by spinning combustible combinations of Planck particles and Planck antiparticles. Particle prograde accretions on a spinning pair releases 42% of the particle rest mass energy to produce more fuel for turbulent combustion. Negative viscous stresses and negative turbulence stresses work against gravity, extracting mass-energy and space-time from the vacuum. Turbulence mixes cooling temperatures until strong-force viscous stresses freeze out turbulent mixing patterns as the first fossil turbulence. Cosmic microwave background temperature anisotropies show big bang turbulence fossils along with fossils of weak plasma turbulence triggered as plasma photon-viscous forces permit gravitational fragmentation on supercluster to galaxy mass scales. Turbulent morphologies and viscous-turbulent lengths appear as linear gas-proto-galaxy-clusters in the Hubble ultra-deep-field at z~7. Proto-galaxies fragment into Jeans-mass-clumps of primordial-gas-planets at decoupling: the dark matter of galaxies. Shortly after the plasma to gas transition, planet-mergers produce stars that explode on overfeeding to fertilize and distribute the first life.Comment: 23 pages 12 figures, Turbulent Mixing and Beyond 2009 International Center for Theoretical Physics conference, Trieste, Italy. Revision according to Referee comments. Accepted for Physica Scripta Topical Issue to be published in 201

Fault tolerant quantum key distribution protocol with collective random unitary noise

We propose an easy implementable prepare-and-measure protocol for robust quantum key distribution with photon polarization. The protocol is fault tolerant against collective random unitary channel noise. The protocol does not need any collective quantum measurement or quantum memory. A security proof and a specific linear optical realization using spontaneous parametric down conversion are given.Comment: Accepted by PRA as a Rapid Communicatio

Eavesdropping without quantum memory

In quantum cryptography the optimal eavesdropping strategy requires that the eavesdropper uses quantum memories in order to optimize her information. What happens if the eavesdropper has no quantum memory? It is shown that the best strategy is actually to adopt the simple intercept/resend strategy.Comment: 9 pages LaTeX, 3 figure