Integrability of a t-J model with impurities

A t-J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2/1)Comment: 14 page

Waste-to-fuel opportunities for British quick service restaurants: A case study

The fast food supply chain is facing increasing operating costs due to volatile food and energy prices. Based on a case study of a major fast food logistics operator, this paper quantifies the potential for fuel generation from the waste generated by quick-service restaurants in Britain. Several fuel pathways and supply chains were mapped to understand the carbon intensity of the various waste-to-fuel opportunities, the number of heavy goods vehicles that might be powered and the key factors that could help companies make better informed decisions related to fuel generation from waste. The research suggested that depending on the scenarios considered, between 13.9 and 17.2 million GJ of energy could be obtained from fuels made from the waste arisings of British quick service restaurants and their distribution centres (DCs), representing between 4.4 and 5.8% of the national energy consumption from heavy goods vehicles (HGVs) and well-to-wheel (WTW) greenhouse gases (GHG) savings of between 652 and 898 thousand tonnes of CO2 equivalent annually. Used cooking oil and burger fat arising from British quick-service restaurants could generate enough energy to power up to 3891 HGVs with FAME diesel (B100), 1622 with HVO diesel (B100) or 1943 with biomethane annually. The paper and card generated by these same establishments could also power an additional 4623 biomethane vehicles, wood pallets could power an additional 73 bioethanol trucks and plastics could also power 341 vehicles running with synthetic diesel. The results showed that collections of separate waste fractions by logistics operators could make a relevant contribution towards the decarbonisation of the supply chain while reducing disposal fees and fuel costs. The carbon emissions resulting from this approach depend greatly on the footprint of the collection and transportation systems used to move waste from the restaurants to the processing plants and return the converted fuel back to the distribution centres where the vehicles are refuelled. Logistics firms are in a privileged position to manage these flows as they can use empty back-haul trips to collect and consolidate waste in distribution centres

Reactive dynamics on fractal sets: anomalous fluctuations and memory effects

We study the effect of fractal initial conditions in closed reactive systems in the cases of both mobile and immobile reactants. For the reaction $A+A\to A$, in the absence of diffusion, the mean number of particles $A$ is shown to decay exponentially to a steady state which depends on the details of the initial conditions. The nature of this dependence is demonstrated both analytically and numerically. In contrast, when diffusion is incorporated, it is shown that the mean number of particles $$ decays asymptotically as $t^{-d_f/2}$, the memory of the initial conditions being now carried by the dynamical power law exponent. The latter is fully determined by the fractal dimension $d_f$ of the initial conditions.Comment: 7 pages, 2 figures, uses epl.cl

Exact Solution of a Electron System Combining Two Different t-J Models

A new strongly correlated electron model is presented. This is formed by two types of sites: one where double occupancy is forbidden, as in the t-J model, and the other where double occupancy is allowed but vacancy is not allowed, as an inverse t-J model. The Hamiltonian shows nearest and next-to-nearest neighbour interactions and it is solved by means of a modified algebraic nested Bethe Ansatz. The number of sites where vacancy is not allowed, may be treated as a new parameter if the model is looked at as a t-J model with impurities. The ground and excited states are described in the thermodynamic limit.Comment: Some corrections and references added. To be published in J. Phys.

Integrable su(3) spin chain combining different representations

The general expression for the local matrix $t(\theta)$ of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing $t(\theta)$ from the fundamental representation and imposing the fulfillment of the Yang-Baxter equation. Then, a non-homogeneous spin chain combining different representations of su(3) is solved by developing a method inspired in the nested Bethe ansatz. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations. A conjecture about the solution of a chain with the site states in different representations of su(n) is presented. The thermodynamic limit of the ground state is calculated.Comment: PlainTex harvmac, 30 pages, 7 figures, to appear in Journal of Physics

Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing

Achieving efficient terahertz (THz) generation using compact turn-key sources operating at room temperature and modest power levels represents one of the critical challeges that must be overcome to realize truly practical applications based on THz. Up to now, the most efficient approaches to THz generation at room temperature -- relying mainly on optical rectification schemes -- require intricate phase-matching set-ups and powerful lasers. Here we show how the unique light-confining properties of triply-resonant photonic resonators can be tailored to enable dramatic enhancements of the conversion efficiency of THz generation via nonlinear frequency down-conversion processes. We predict that this approach can be used to reduce up to three orders of magnitude the pump powers required to reach quantum-limited conversion efficiency of THz generation in nonlinear optical material systems. Furthermore, we propose a realistic design readily accesible experimentally, both for fabrication and demonstration of optimal THz conversion efficiency at sub-W power levels

Opportunities for hydrogen and fuel cell technologies to contribute to clean growth in the UK

Hydrogen is important because it is one of three key zero-carbon vectors for decarbonising economies in the future, along with electricity and hot water. The UK Government’s Clean Growth Strategy and the UK Committee on Climate Change have identified hydrogen as the most cost-effective option for decarbonising several parts of the UK energy system. Fuel cells convert fuels, including hydrogen, to electricity and heat. Fuel cells are important because they can generate electricity at higher efficiencies than most internal combustion engines, and with no emissions. For road transport, this means that they have a higher fuel economy than cars powered by engines