Wick's theorem for q-deformed boson operators

In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated ``Feynman diagrams'' the normally ordered form of a general expression in the creation and annihilation operators can be written as a sum over all q-weighted Feynman diagrams, representing Wick's theorem in the present context.Comment: 9 page

Contact-mediated nucleation in melt emulsions investigated by rheo-nuclear magnetic resonance

Increasing the efficiency of disperse phase crystallization is of great interest for melt emulsion production as the fraction of solidified droplets determines product quality and stability. Nucleation events must appear within every single one of the μm-sized droplets for solidification. Therefore, primary crystallization requires high subcooling and is, thus, time and energy consuming. Contact-mediated nucleation is a mechanism for intensifying the crystallization process. It is defined as the successful nucleation of a subcooled liquid droplet induced by contact with an already crystallized droplet. We investigated contact-mediated nucleation under shear flow conditions up to shear rates of 457 s$^{-1}$ for a quantitative assessment of this mechanism. Rheo-nuclear magnetic resonance was successfully used for the time-resolved determination of the solids fraction of the dispersed phase of melt emulsions upon contact-mediated nucleation events. The measurements were carried out in a dedicated Taylor–Couette cell. The efficiency of contact-mediated nucleation $\lambda$$_{sec}$ decreased with increasing shear rate, whereas the effective second order kinetic constant k$_{coll, eff}$ increased approximately linearly at small shear rates and showed a linear decrease for shear rates higher than about 200 s$^{-1}$. These findings are in accordance with coalescence theory. Thus, the nucleation rate is optimal at specific flow conditions. There are limitations for successful inoculation at a low shear rate because of rare contact events and at a high shear rate due to too short contact time

Magnetic impurity coupled to interacting conduction electrons

We consider a magnetic impurity which interacts by hybridization with a system of weakly correlated electrons and determine the energy of the ground state by means of an 1/N_f expansion. The correlations among the conduction electrons are described by a Hubbard Hamiltonian and are treated to lowest order in the interaction strength. We find that their effect on the Kondo temperature, T_K, in the Kondo limit is twofold: First, the position of the impurity level is shifted due to the reduction of charge fluctuations, which reduces T_K. Secondly, the bare Kondo exchange coupling is enhanced as spin fluctuations are enlarged. In total, T_K increases. Both corrections require intermediate states beyond the standard Varma-Yafet ansatz. This shows that the Hubbard interaction does not just provide quasiparticles, which hybridize with the impurity, but also renormalizes the Kondo coupling.Comment: ReVTeX 19 pages, 3 uuenconded postscript figure

Periodic Anderson model with correlated conduction electrons

We investigate a periodic Anderson model with interacting conduction electrons which are described by a Hubbard-type interaction of strength U_c. Within dynamical mean-field theory the total Hamiltonian is mapped onto an impurity model, which is solved by an extended non-crossing approximation. We consider the particle-hole symmetric case at half-filling. Similar to the case U_c=0, the low-energy behavior of the conduction electrons at high temperatures is essentially unaffected by the f-electrons and for small U_c a quasiparticle peak corresponding to the Hubbard model evolves first. These quasiparticles screen the f-moments when the temperature is reduced further, and the system turns into an insulator with a tiny gap and flat bands. The formation of the quasiparticle peak is impeded by increasing either U_c or the c-f hybridization. Nevertheless almost dispersionless bands emerge at low temperature with an increased gap, even in the case of initially insulating host electrons. The size of the gap in the one-particle spectral density at low temperatures provides an estimate for the low-energy scale and increases as U_c increases.Comment: 11 pages RevTeX with 13 ps figures, accepted by PR

Magnetic Impurity in a Metal with Correlated Conduction Electrons: An Infinite Dimensions Approach

We consider the Hubbard model with a magnetic Anderson impurity coupled to a lattice site. In the case of infinite dimensions, one-particle correlations of the impurity electron are described by the effective Hamiltonian of the two-impurity system. One of the impurities interacts with a bath of free electrons and represents the Hubbard lattice, and the other is coupled to the first impurity by the bare hybridization interaction. A study of the effective two-impurity Hamiltonian in the frame of the 1/N expansion and for the case of a weak conduction-electron interaction (small U) reveals an enhancement of the usual exponential Kondo scale. However, an intermediate interaction (U/D = 1 - 3), treated by the variational principle, leads to the loss of the exponential scale. The Kondo temperature T_K of the effective two-impurity system is calculated as a function of the hybridization parameter and it is shown that T_K decreases with an increase of U. The non-Fermi-liquid character of the Kondo effect in the intermediate regime at the half filling is discussed.Comment: 12 pages with 8 PS figures, RevTe

The Wallbot: A Low-cost Robot for Green Wall Inspection

The benefits of urban green infrastructure, such as attenuating the urban heat island effect and improving air quality, are widely accepted. Regardless, the uptake of green walls (i.e. vertical gardens) is low due to the high costs relating to maintenance and OH&S. These barriers to adoption may be mitigated by using robotics to inspect and maintain green walls. In this work we present the Wallbot, a robotic system to inspect, monitor and aid in the maintenance of green walls. In its current form the system comprises of affordable off-the-shelf components to keep the system cost low. Preliminary development of the system, results of initial tests and findings are presented. The system offers the chance to reduce OH&S issues and maintenance costs associated with green walls

The Green Wallbot

The need and demand for robotic technology to increase the uptake of green walls and facades whilst reducing OHS and maintenance costs is clear. The benefits of urban green infrastructure are widely accepted and include urban heat island attenuation, increased bio diversity, reduced carbon emission, biophilia effects, provision of spaces for social interaction, attenuation of rainwater flooding and improved air quality. With climate change and increasing temperatures a stark reality, resilience and liveability as well as sustainability are greatly enhanced through the adoption of Green Infrastructure (GI). Wallbot, a robotic installation to inspect, monitor and maintain green walls offers the chance to reduce OHS issues and maintenance costs associated with green walls

Interaction of a Magnetic Impurity with Strongly Correlated Conduction Electrons

We consider a magnetic impurity which interacts by hybridization with a system of strongly correlated conduction electrons. The latter are described by a Hubbard Hamiltonian. By means of a canconical transformation the charge degrees of freedom of the magnetic impurity are eliminated. The resulting effective Hamiltonian $H_{\rm eff}$ is investigated and various limiting cases are considered. If the Hubbard interaction $U$ between the conduction electrons is neglected $H_{\rm eff}$ reduces to a form obtained by the Schrieffer-Wolff transformation, which is essentially the Kondo Hamiltonian. If $U$ is large and the correlations are strong $H_{\rm eff}$ is changed. One modification concerns the coefficient of the dominant exchange coupling of the magnetic impurity with the nearest lattice site. When the system is hole doped, there is also an antiferromagnetic coupling to the nearest neighbors of that site involving additionally a hole. Furthermore, it is found that the magnetic impurity attracts a hole. In the case of electron doping, double occupancies are repelled by the impurity. In contrast to the hole-doped case, we find no magnetic coupling which additionally involves a doubly occupied site.Comment: 16 pages, Revtex 3.

The boson-fermion model with on-site Coulomb repulsion between fermions

The boson-fermion model, describing a mixture of itinerant electrons hybridizing with tightly bound electron pairs represented as hard-core bosons, is here generalized with the inclusion of a term describing on-site Coulomb repulsion between fermions with opposite spins. Within the general framework of the Dynamical Mean-Field Theory, it is shown that around the symmetric limit of the model this interaction strongly competes with the local boson-fermion exchange mechanism, smoothly driving the system from a pseudogap phase with poor conducting properties to a metallic regime characterized by a substantial reduction of the fermionic density. On the other hand, if one starts from correlated fermions described in terms of the one-band Hubbard model, the introduction in the half-filled insulating phase of a coupling with hard-core bosons leads to the disappearance of the correlation gap, with a consequent smooth crossover to a metallic state.Comment: 7 pages, 6 included figures, to appear in Phys. Rev.