Phonon Squeezing in a Superconducting Molecular Transistor

Josephson transport through a single molecule or carbon nanotube is considered in the presence of a local vibrational mode coupled to the electronic charge. The ground-state solution is obtained exactly in the limit of a large superconducting gap, and is extended to the general case by variational analysis. Coherent charge fluctuations are entangled with non-classical phonon states. The Josephson current induces squeezing of the phonon mode, which is controlled by the superconducting phase difference and by the junction asymmetry. Optical probes of non-classical phonon states are briefly discussed

Impact of noise and damage on collective dynamics of scale-free neuronal networks

We study the role of scale-free structure and noise in collective dynamics of neuronal networks. For this purpose, we simulate and study analytically a cortical circuit model with stochastic neurons. We compare collective neuronal activity of networks with different topologies: classical random graphs and scale-free networks. We show that, in scale-free networks with divergent second moment of degree distribution, an influence of noise on neuronal activity is strongly enhanced in comparison with networks with a finite second moment. A very small noise level can stimulate spontaneous activity of a finite fraction of neurons and sustained network oscillations. We demonstrate tolerance of collective dynamics of the scale-free networks to random damage in a broad range of the number of randomly removed excitatory and inhibitory neurons. A random removal of neurons leads to gradual decrease of frequency of network oscillations similar to the slowing-down of the alpha rhythm in Alzheimer's disease. However, the networks are vulnerable to targeted attacks. A removal of a few excitatory or inhibitory hubs can impair sustained network oscillations.Comment: 12 pages, 10 figure

Phase diagram of the one dimensional anisotropic Kondo-necklace model

The one dimensional anisotropic Kondo-necklace model has been studied by several methods. It is shown that a mean field approach fails to gain the correct phase diagram for the Ising type anisotropy. We then applied the spin wave theory which is justified for the anisotropic case. We have derived the phase diagram between the antiferromagnetic long range order and the Kondo singlet phases. We have found that the exchange interaction (J) between the itinerant spins and local ones enhances the quantum fluctuations around the classical long range antiferromagnetic order and finally destroy the ordered phase at the critical value, J_c. Moreover, our results show that the onset of anisotropy in the XY term of the itinerant interactions develops the antiferromagnetic order for J<J_c. This is in agreement with the qualitative feature which we expect from the symmetry of the anisotropic XY interaction. We have justified our results by the numerical Lanczos method where the structure factor at the antiferromagnetic wave vector diverges as the size of system goes to infinity.Comment: 9 pages and 9 eps figure

Hall resistance in the hopping regime, a "Hall Insulator"?

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always {\it diverges} exponentially as the temperature tends to zero. But when the Hall resistivity is derived from the averaged conductivity, the resulting temperature dependence is sensitive to the disorder configuration. Then the Hall resistivity may approach a constant value as $T\to 0$. This is the Hall insulating behavior. It is argued that for strictly dc conditions, the transport quantity that should be averaged is the resistivity.Comment: Late

Observation of the Holstein shift in high TcT_c superconductors with thermal modulation reflectometry

We use the experimental technique of thermal modulation reflectometry to study the relatively small temperature dependence of the optical conductivity of superconductors. Due to a large cancellation of systematic errors, this technique is shown to a be very sensitive probe of small changes in reflectivity. We analyze thermal modulation reflection spectra of single crystals and epitaxially grown thin films of YBa$_2$Cu$_3$O$_{7-\delta}$ and obtain the ${\alpha_tr}^2F(\omega)$ function in the normal state, as well as the superconductivity induced changes in reflectivity. We present detailed model calculations, based on the Eliashberg-Migdal extension of the BCS model, which show good qualitative and quantitative agreement with the experimental spectra. VSGD.93.12.thComment: 6 pages, figures on request. Revtex, version 2, Materials Science Center Internal Report Number VSGD.93.12.t

Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model

We present polaron effective masses and selected polaron band structures of the Holstein molecular crystal model in 1-D as computed by the Global-Local variational method over a wide range of parameters. These results are augmented and supported by leading orders of both weak- and strong-coupling perturbation theory. The description of the polaron effective mass and polaron band distortion that emerges from this work is comprehensive, spanning weak, intermediate, and strong electron-phonon coupling, and non-adiabatic, weakly adiabatic, and strongly adiabatic regimes. Using the effective mass as the primary criterion, the self-trapping transition is precisely defined and located. Using related band-shape criteria at the Brillouin zone edge, the onset of band narrowing is also precisely defined and located. These two lines divide the polaron parameter space into three regimes of distinct polaron structure, essentially constituting a polaron phase diagram. Though the self-trapping transition is thusly shown to be a broad and smooth phenomenon at finite parameter values, consistency with notion of self-trapping as a critical phenomenon in the adiabatic limit is demonstrated. Generalizations to higher dimensions are considered, and resolutions of apparent conflicts with well-known expectations of adiabatic theory are suggested.Comment: 28 pages, 15 figure

Entanglement between atomic condensates in an optical lattice: effects of interaction range

We study the area-dependent entropy and two-site entanglement for two state Bose-Einstein condensates in a 2D optical lattice. We consider the case where the array of two component condensates behave like an ensemble of spin-half particles with the interaction to its nearest neighbors and next nearest neighbors. We show how the Hamiltonian of their Bose-Einstein condensate lattice with nearest-neighbor and next-nearest-neighbor interactions can be mapped into a harmonic lattice. We use this to determine the entropy and entanglement content of the lattice.Comment: 5 pages, 3 figures, title change

Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment

The exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.Comment: 9 pages (two-coulumn), 6 figures. To appear in Phys. Rev.

Jacobson generators of the quantum superalgebra Uq[sl(n+1∣m)]U_q[sl(n+1|m)] and Fock representations

As an alternative to Chevalley generators, we introduce Jacobson generators for the quantum superalgebra $U_q[sl(n+1|m)]$. The expressions of all Cartan-Weyl elements of $U_q[sl(n+1|m)]$ in terms of these Jacobson generators become very simple. We determine and prove certain triple relations between the Jacobson generators, necessary for a complete set of supercommutation relations between the Cartan-Weyl elements. Fock representations are defined, and a substantial part of this paper is devoted to the computation of the action of Jacobson generators on basis vectors of these Fock spaces. It is also determined when these Fock representations are unitary. Finally, Dyson and Holstein-Primakoff realizations are given, not only for the Jacobson generators, but for all Cartan-Weyl elements of $U_q[sl(n+1|m)]$.Comment: 27 pages, LaTeX; to be published in J. Math. Phy

Pion and Kaon Polarizabilities and Radiative Transitions

CERN COMPASS plans measurements of gamma-pi and gamma-K interactions using 50-280 GeV pion (kaon) beams and a virtual photon target. Pion (kaon) polarizabilities and radiative transitions will be measured via Primakoff effect reactions such as pi+gamma->pi'+gamma and pi+gamma->meson. The former can test a precise prediction of chiral symmetry; the latter for pi+gamma->a1(1260) is important for understanding the polarizability. The radiative transition of a pion to a low mass two-pion system, pi+gamma->pi+pi0, can also be studied to measure the chiral anomaly amplitude F(3pi) (characterizing gamma->3pi), arising from the effective Chiral Lagrangian. We review here the motivation for the above physics program. We describe the beam, target, detector, and trigger requirements for these experiments. We also describe FNAL SELEX attempts to study related physics via the interaction of 600 GeV pions with target electrons. Data analysis in progress aims to identify the reactions pi+e->pi'+e'+pi0 related to the chiral anomaly, and pi+e->pi'+e'+gamma related to pion polarizabilities.Comment: 16 pages, 6 figures, Latex Springer-Verlag style Tel Aviv U. Preprint TAUP-2469-97, Contribution to the Workshop on Chiral Dynamics Theory and Experiment, U. of Mainz, Sept. 1-5, 1997, to be published in Springer-Verlag, Eds. A. Bernstein, Th. Walcher, 199