Method for Finding the Exact Effective Hamiltonian of Time‐Driven Quantum Systems

Time‐driven quantum systems are important in many different fields of physics as cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator or the effective Hamiltonian. Finding these operators usually requires very complex calculations that often involve some approximations. To perform this task, a systematic scheme that can be cast in the form of a symbolic computational algorithm is presented. It is suitable for periodic and non‐periodic potentials and, for convoluted systems, can also be adapted to yield numerical solutions. The method exploits the structure of the associated Lie group and a decomposition of the evolution operator on each group generator. To illustrate the use of the method, five examples are provided: harmonic oscillator with time‐dependent frequency (Paul trap), modulated optical lattice, time‐driven quantum oscillator, a step‐wise driving of a free particle, and the non‐periodic Caldirola‐Kanai Hamiltonian. To the extent of the authors' knowledge, whereas the exact form of Paul trap's evolution operator is well known, its effective Hamiltonian was until now unknown. The remaining four examples accurately reproduce previous results.     

Weakly driven anomalous diffusion in non-ergodic regime: an analytical solution

We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic fluctuations with a given distribution ψ(τ) of residence times in each velocity state. We obtain analytical solutions for the diffusion process in a generic external potential and for a generic statistics of residence times, including the non-ergodic regime in which the mean residence time diverges. We show that these analytical solutions are in agreement with numerical simulations.     

Graphene functionalisation with a conjugated poly(fluorene) by click coupling: striking electronic properties in solution

Graphene flakes covalently modified with a conjugated polymer, poly[(9,9-dihexylfluorene)-co-alt-(9,9-bis-(6-azidohexyl)fluorene)] (PFA), were efficiently synthesised by a Cu-catalysed Huisgen 1,3-dipolar cycloaddition between alkyne-modified graphene and an azide-functionalised polymer. Two approaches for the modification of graphene with alkyne groups were investigated (coupling with a diazonium salt generated in situ or an amidation reaction) and the optimum conditions determined. The success of the click-coupling approach was confirmed by FTIR, (1)H?NMR, Raman, and X-ray photoelectron spectroscopy (XPS). The absorption and emission spectra of the click product show a strong solvent dependency.     

Mechanistic insight on the catecholase activity of dinuclear copper complexes with distant metal centers

The catecholase activity of two dinuclear Cu(II) complexes with distant metal centers is discussed together with solid state and solution studies. The crystal structure for one of them, [Cu(2)(diep)(H(2)O)(4)](ClO(4))(4)·2H(2)O, is described, showing the two copper ions are 7.457 ? apart and in a square pyramidal coordination. Both complexes display a weak antiferromagnetic coupling in the solid state that is manifest in the dimer EPR spectra obtained in frozen solution. The pH-potentiometric speciation performed in 1:1 MeOH-H(2)O allowed the assignment of hydrolyzed copper species as those catalytically active in the oxidation of 3,5-di-tert-butylcatechol (DTBC). The kinetic measurements led us to propose behavior consistent with Michaelis-Menten plus a linear dependence of the initial rate on [DTBC]. This can be associated with the presence of more than one catalytically active species, which is consistent with the evidence of several differently hydrolyzed species shown in the predominance diagrams. Product characterization studies led to establishing the formation of hydrogen peroxide during the catalytic cycle, while semiquinone and superoxide radicals were detected by EPR spectroscopy, supporting one-electron transference at each of the copper centers.     

Majorana modes in time-reversal invariant s-wave topological superconductors

We present a time-reversal invariant s-wave superconductor supporting Majorana edge modes. The multiband character of the model together with spin-orbit coupling are key to realizing such a topological superconductor. We characterize the topological phase diagram by using a partial Chern number sum, and show that the latter is physically related to the parity of the fermion number of the time-reversal invariant modes. By taking the self-consistency constraint on the s-wave pairing gap into account, we also establish the possibility of a direct topological superconductor-to-topological insulator quantum phase transition.     

Improved methods for thermal rearrangement of alicyclic α-hydroxyimines to α-aminoketones: synthesis of ketamine analogues as antisepsis candidates

Ketamine is an analgesic/anesthetic drug, which, in combination with other drugs, has been used as anesthetic for over 40 years. Ketamine induces its analgesic activities by blocking the N-methyl-D-aspartate (NMDA) receptor in the central nervous system (CNS). We have reported that low doses of ketamine administrated to patients before incision significantly reduced post-operative inflammation as reflected by reduced interleukin-6 (IL-6) sera-levels. Our data demonstrated in a rat model of Gram-negative bacterial-sepsis that if we inject a low dose of ketamine following bacterial inoculation we reduce mortality from approximately 75% to 25%. Similar to what we have observed in operated patients, the levels of TNF-α and IL-6 in ketamine-treated rats were significantly lower than in septic animals not treated with ketamine. On the base of these results, we have designed and synthesized series of new analogues of ketamine applying a thermal rearrangement of alicyclic α-hydroxyimines to a-aminoketones in parallel arrays. One of the analogues (compound 6e) displayed high activity in down-regulating the levels of IL-6 and TNF-α in vivo as compared to ketamine.     

Room Temperature Synthesis and Size Control of HKUST‐1

We report the synthesis of HKUST‐1 (Cu₃(btc)₂; btc=benzene‐1,3,5‐tricarboxylate) and its growth kinetics by dynamic light scattering completely at room temperature without prior nucleation‐induction steps. Upon an increase in concentration of the starting solutions, the generation of a pure phase requires adjustment of the H₂O/EtOH ratio. The presence of DMF is important to avoid competitive side phases. Replacement of DMF by a minimal amount of diethylamine resulted in the instantaneous formation of pure HKUST‐1 upon mixing at room temperature. Additionally, the synthesis parameters strongly influence the final crystallite size and porous properties.