Comparing classical and quantum equilibration.

By using a physically relevant and theory independent definition of measurement-based equilibration, we show quantitatively that equilibration is easier for quantum systems than for classical systems, in the situation where the initial state of the system is completely known (a pure state). This shows that quantum equilibration is a fundamental aspect of many quantum systems, while classical equilibration relies on experimental ignorance. When the state is not completely known (a mixed state), this framework also shows that quantum equilibration requires weaker conditions.

Rapid spatial equilibration of a particle in a box.

We study the equilibration behavior of a quantum particle in a one-dimensional box, with respect to a coarse-grained position measurement (whether it lies in a certain spatial window or not). We show that equilibration in this context indeed takes place and does so very rapidly, in a time comparable to the time for the initial wave packet to reach the edges of the box. We also show that, for this situation, the equilibration behavior is relatively insensitive to the precise choice of position measurements or initial condition.

Quantum systems equilibrate rapidly for most observables.

Considering any Hamiltonian, any initial state, and measurements with a small number of possible outcomes compared to the dimension, we show that most measurements are already equilibrated. To investigate nontrivial equilibration, we therefore consider a restricted set of measurements. When the initial state is spread over many energy levels, and we consider the set of observables for which this state is an eigenstate, most observables are initially out of equilibrium yet equilibrate rapidly.

Importance of the structure of vancomycin binding pocket in designing compounds active against vancomycin-resistant enterococci (VRE).

16-Membered meta, para-cyclophanes mimicking the vancomycin binding pocket (D-O-E ring) are designed and synthesized. The structural features of these biaryl ether containing macrocycles are: a) the deletion of the carboxyl group of vancomycin's central amino acid (amino acid D); b) the elongation of the N-terminal; c) the presence of lipidated aminoglucose at the D-ring. Cycloetherification by way of an intramolecular nucleophilic aromatic substitution reaction (S(N)Ar) is used as a key step for the construction of the macrocycle.

Design and synthesis of simple macrocycles active against vancomycin-resistant enterococci (VRE).

16-membered meta,para-cyclophanes mimicking the vancomycin binding pocket (D-O-E ring) were designed and synthesized. The structural key features of these biaryl ether containing macrocycles are (1) the presence of beta-amino-alpha-hydroxy acid or alpha,beta-diamino acid as the C-terminal component of the cyclopeptide and (2) the presence of a hydrophobic chain or lipidated aminoglucose at the appropriate position. Cycloetherification by an intramolecular nucleophilic aromatic substitution reaction (S(N)Ar) is used as the key step for the construction of the macrocycle.