Transition state theory and the dynamics of hard disks

The dynamics of two and five disk systems confined in a square has been studied using molecular dynamics simulations and compared with the predictions of transition state theory. We determine the partition functions Z and Z^\ddagger of transition state theory using a procedure first used by Salsburg and Wood for the pressure. Our simulations show this procedure and transition state theory are in excellent agreement with the simulations. A generalization of the transition state theory to the case of a large number of disks N is made and shown to be in full agreement with simulations of disks moving in a narrow channel. The same procedure for hard spheres in three dimensions leads to the Vogel-Fulcher-Tammann formula for their alpha relaxation time.Comment: 1 new author, new simulations and figures, less speculation. Now 6 pages, 6 figures, 1 animation. Animation may be viewed at http://www.theory.physics.manchester.ac.uk/~godfrey/supplement/activated_dynamics2.htm

Bipartite quantum channels using multipartite cluster-type entangled coherent states

We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state, as well as its usefulness as a quantum channel for teleportation. We find interesting relationships among the amplitude of the coherent states constituting the CTECSs, the number of subsystems forming the logical qubits (redundancy), and the extent to which amplitude damping affects the entanglement of the channel. For instance, in the sense of sudden death of entanglement, given a fixed value of the initial coherent state amplitude, the entanglement life span is shortened if redundancy is increased.Comment: 6 pages, 3 figures, REVTeX 4.1, BibTe

First Principles Study of the Electronic and Vibrational Properties of LiNbO2

In the layered transition metal oxide LiNbO$_2$ the Nb$^{3+}$ ($4d^2$) ion is trigonal-prismatically coordinated with O ions, with the resulting crystal field leading to a single band system for low energy properties. A tight-binding representation shows that intraplanar second neighbor hopping $t_2 = 100$ meV dominates the first neighbor interaction ($t_1 = 64$ meV). The first and third neighbor couplings are strongly modified by oxygen displacements of the symmetric Raman-active vibrational mode, and electron-phonon coupling to this motion may provide the coupling mechanism for superconductivity in Li-deficient samples (where $T_c = 5$ K). We calculate all zone-center phonon modes, identify infrared (IR) and Raman active modes, and report LO-TO splitting of the IR modes. The Born effective charges for the metal ions are found to have considerable anisotropy reflecting the degree to which the ions participate in interlayer coupling and covalent bonding. Insight into the microscopic origin of the valence band density, composed of Nb $d_{z^2}$ states with some mixing of O $2p$ states, is obtained from examining Wannier functions for these bands.Comment: 12 pages, 7 figures; Updated with reviewer comments; Updated reference

FGF/heparin differentially regulates Schwann cell and olfactory ensheathing cell interactions with astrocytes: a role in astrocytosis

After injury, the CNS undergoes an astrocyte stress response characterized by reactive astrocytosis/proliferation, boundary formation, and increased glial fibrillary acidic protein (GFAP) and chondroitin sulfate proteoglycan (CSPG) expression. Previously, we showed that in vitro astrocytes exhibit this stress response when in contact with Schwann cells but not olfactory ensheathing cells (OECs). In this study, we confirm this finding in vivo by demonstrating that astrocytes mingle with OECs but not Schwann cells after injection into normal spinal cord. We show that Schwann cell-conditioned media (SCM) induces proliferation in monocultures of astrocytes and increases CSPG expression in a fibroblast growth factor receptor 1 (FGFR1)-independent manner. However, SCM added to OEC/astrocyte cocultures induces reactive astrocytosis and boundary formation, which, although sensitive to FGFR1 inhibition, was not induced by FGF2 alone. Addition of heparin to OEC/astrocyte cultures induces boundary formation, whereas heparinase or chlorate treatment of Schwann cell/astrocyte cultures reduces it, suggesting that heparan sulfate proteoglycans (HSPGs) are modulating this activity. In vivo, FGF2 and FGFR1 immunoreactivity was increased over grafted OECs and Schwann cells compared with the surrounding tissue, and HSPG immunoreactivity is increased over reactive astrocytes bordering the Schwann cell graft. These data suggest that components of the astrocyte stress response, including boundary formation, astrocyte hypertrophy, and GFAP expression, are mediated by an FGF family member, whereas proliferation and CSPG expression are not. Furthermore, after cell transplantation, HSPGs may be important for mediating the stress response in astrocytes via FGF2. Identification of factors secreted by Schwann cells that induce this negative response in astrocytes would further our ability to manipulate the inhibitory environment induced after injury to promote regeneration

Interacting Hofstadter spectrum of atoms in an artificial gauge field

Motivated by experimental advances in the synthesis of gauge potentials for ultracold atoms, we consider the superfluid phase of interacting bosons on a square lattice in the presence of a magnetic field. We show that superfluid order implies spatial symmetry breaking, and predict clear signatures of many-body effects in time-of-flight measurements. By developing a Bogoliubov expansion based on the exact Hofstadter spectrum, we find the dispersion of the quasiparticle modes within the superfluid phase, and describe the consequences for Bragg spectroscopy measurements. The theory also provides an estimate of the critical interaction strength at the transition to the Mott insulator phase.Comment: 4+ pages, 2 figures; v2: published versio

Fidelity and the communication of quantum information

We compare and contrast the error probability and fidelity as measures of the quality of the receiver's measurement strategy for a quantum communications system. The error probability is a measure of the ability to retrieve classical information and the fidelity measures the retrieval of quantum information. We present the optimal measurement strategies for maximizing the fidelity given a source that encodes information on the symmetric qubit-states

Accessible information and optimal strategies for real symmetrical quantum sources

We study the problem of optimizing the Shannon mutual information for sources of real quantum states i.e. sources for which there is a basis in which all the states have only real components. We consider in detail the sources ${\cal E}_M$ of $M$ equiprobable qubit states lying symmetrically around the great circle of real states on the Bloch sphere and give a variety of explicit optimal strategies. We also consider general real group-covariant sources for which the group acts irreducibly on the subset of all real states and prove the existence of a real group-covariant optimal strategy, extending a theorem of Davies (E. B. Davies, IEEE. Inf. Theory {\bf IT-24}, 596 (1978)). Finally we propose an optical scheme to implement our optimal strategies, enough simple to be realized with present technology.Comment: RevTeX, 16 pages, 4 eps figures with psfig, submitted to Phys. Rev. A, corrected output error of Fig. 1 in the previous versio