Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Extended Coherent-state Approach

We propose a general extended coherent state approach to the qubit (or fermion) and multi-mode boson coupling systems. The application to the spin-boson model with the discretization of a bosonic bath with arbitrary continuous spectral density is described in detail, and very accurate solutions can be obtained. The quantum phase transition in the nontrivial sub-Ohmic case can be located by the fidelity and the order-parameter critical exponents for the bath exponents $s<1/2$ can be correctly given by the fidelity susceptibility, demonstrating the strength of the approach.Comment: 4 pages, 3 figure

Quantum phase transitions in coupled two-level atoms in a single-mode cavity

The dipole-coupled two-level atoms(qubits) in a single-mode resonant cavity is studied by extended bosonic coherent states. The numerically exact solution is presented. For finite systems, the first-order quantum phase transitions occur at the strong interatomic interaction. Similar to the original Dicke model, this system exhibits a second-order quantum phase transition from the normal to the superradiant phases. Finite-size scaling for several observables, such as the average fidelity susceptibility, the order parameter, and concurrence are performed for different interatomic interactions. The obtained scaling exponents suggest that interatomic interactions do not change the universality class.Comment: 13 pages, 5 figure

Recent Advances in Electrocatalytic Applications of Ionic Liquids

Ionic liquids have emerged as an environmentally friendly alternative to the volatile organic solvents. Being designer solvents, they can be modulated to suit the reaction conditions, therefore earning the name “task-specific ionic liquids.” Though primarily used as solvents, they are now finding applications in various fields such as catalysis, electrochemistry, spectroscopy, and material science to mention a few. The goal of this chapter is focused on the electrocatalytic applications of ionic liquids, which can be used as catalysts and catalytic supports in electrochemistry. Their scope has marched beyond academic research laboratories to industries where their practical applications have been leading to various sustainable technologies. Flexibility to modulate properties by changing design endows freedom to a chemist to design an ionic liquid according to one’s own requirement. To conclude, it can be said that the field of ionic liquid electrocatalysis holds enormous possibilities to be explored

Accurate numerical solution to the finite-size Dicke model

By using extended bosonic coherent states, a new technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in literature. Finite-size scaling for several observables, such as the ground-state energy, Berry phase, and concurrence are analyzed. The existing discrepancy for the scaling exponent of the concurrence is reconciled.Comment: 4 pages, 5 figures. Phys. Rev. A (in press, a Rapid Communication

Novel and high efficient cycloaddition of CO2 with epoxides to cyclic carbonates over reusable mesoporous KIT-6 supported imidazolium lactate catalyst

ABSTRACT. A series of mesoporous KIT-6 supported ionic liquids were prepared and tested as effective and practical catalysts for the synthesis of cyclic carbonates by the cycloaddition of CO2 with epoxides. The effects of type of catalysts, catalyst amount, CO2 pressure, reaction temperature and catalyst stability have also been investigated in detail, the catalyst KIT-6@ILCH3CH(OH)COO(0.6) exhibited excellent activity in good to excellent yields, may be attributed to the synergetic effect between hydroxyl groups and lactate anion of the ionic liquid. In addition, the supported catalyst can be easily recovered and reused for six times still with satisfactory catalytic activity. Moreover, a general synergetic catalytic mechanism for the reaction was proposed. This work introduces a new and highly efficient pathway to explore the supported ionic liquids for the chemical fixation of carbon dioxide. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; KEY WORDS: Mesoporous KIT-6, Ionic liquid, High efficient, Carbon dioxide, Cyclic carbonates, Recyclable catalyst &nbsp; Bull. Chem. Soc. Ethiop. 2022, 36(2), 433-450.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; DOI: https://dx.doi.org/10.4314/bcse.v36i2.16&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp