One-dimensional interacting anyon gas: Low-energy properties and haldane exclusion statistics

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.

Energy as an entanglement witness for quantum many-body systems

We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.

Integration of sulphate reduction, autotrophic denitrification and nitrification to achieve low-cost excess sludge minimisation for Hong Kong sewage

An integrated anaerobic-aerobic treatment system of sulphate-laden wastewater was proposed here to achieve low sludge production, low energy consumption and effective sulphide control. Before integrating the whole system, the feasibility of autotrophic denitrification utilising dissolved sulphide produced during anaerobic treatment of sulphate rich wastewater was studied here. An upflow anaerobic sludge blanket reactor was operated to treat sulphate-rich synthetic wastewater (TOC = 100 mg/L and sulphate = 500 mg/L) and its effluent with dissolved sulphide and external nitrate solution were fed into an anoxic biofilter. The anaerobic reactor was able to remove 77-85% of TOC at HRT of 3 h and produce 70-90 mg S/L sulphide in dissolved form for the subsequent denitrification. The performance of anoxic reactor was stable, and the anoxic reactor could remove 30 mg N/L nitrate at HRT of 2 h through autotrophic denitrification. Furthermore, sulphur balance for the anoxic filter showed that more than 90% of the removed sulphide was actually oxidised into sulphate, thereby there was no accumulation of sulphur particles in the filter bed. The net sludge productions were approximately 0.15 to 0.18 g VSS/g COD in the anaerobic reactor and 0.22 to 0.31 g VSS/g NO3--N in the anoxic reactor. The findings in this study will be helpful in developing the integrated treatment system to achieve low-cost excess sludge minimisation.