Position measurements in the de Broglie–Bohm interpretation of quantum mechanics

The de Broglie–Bohm interpretation of quantum mechanics assigns positions and trajectories to particles. We analyze the validity of a formula for the velocities of Bohmian particles which makes the analysis of these trajectories particularly simple. We apply it to particle detectors of four different types and show that the detectors of three of these types lead to “surrealistic trajectories”, i.e., leave a trace where the Bohmian particle was not present.     

Synthesis of “living” chains of polyvinylpyridine and their application to the construction of homo- and hybrid polymer with complex architecture

Experimental conditions ensuring the formation of living poly(2- and 4-vinyl pyridine) chains in the vinyl pyridine - allyl derivatives of chromium, molybdenum and tungsten systems are described. Variation of the reagents nature, polarity of the solvent permits to obtain polymers differing in their structural and molecular parameters. Synthesized polymers contain block and graft sequences, as well as macrocyclic fragments. Living chains under consideration were applied for polymerization of different monomers. Hybrid polymers obtained by this way were studied in detail by the same methods as the homopolymers.     

Tensor rank bounds and explicit QTT representations for the inverses of circulant matrices

In this paper, we are concerned with the inversion of circulant matrices and their quantized tensor-train (QTT) structure. In particular, we show that the inverse of a complex circulant matrix $A$, generated by the first column of the form ${(a_0,\dots ,a_{m-1},0,\dots ,0,a_{-n},\dots ,a_{-1})}^{\top }$ admits a QTT representation with the QTT ranks bounded by $(m+n)$. Under certain assumptions on the entries of $A$, we also derive an explicit QTT representation of $A^{-1}$. The latter can be used, for instance, to overcome stability issues arising when numerically solving differential equations with periodic boundary conditions in the QTT format.