A. V. Zolotaryuk

A zero-thickness limit of multilayer structures: a resonant-tunnelling δ′-potential

A zero-thickness limit for two-terminal and three-terminal devices from the quantum electronics domain is analysed. The study is focused on heterostructures composed of a single barrier with, adjacent, one or two prewells. The point interactions obtained in this limit are shown to be described by a family of resonant diagonal matrices that connect the two-sided boundary conditions at the device origin, which are a subclass of the whole four-parameter family of point interactions. Transmission through such a device is absent almost everywhere, except at a few points, whose number and position can be controlled by a gate voltage applied externally to the barrier subsystem. It is remarkable that the existence of resonances in the zero-thickness limit occurs only if a squeezing sequence is constructed in a -like way. In this case, the -limit describes adequately the resonant behaviour of a barrier–well heterostructure with realistic parameters. Simple analytical expressions obtained for resonance sets are supported by direct numerical calculations of the transmission being in agreement with the results of experiments on semiconductor devices. The zero-thickness -like limiting procedure can be used in the design of nanodevices or contacting quantum wires.

Ratchet Device with Broken Friction Symmetry

An experimental setup (gadget) has been made for demonstration of a ratchet mechanism induced by broken symmetry of a dependence of dry friction on external forcing. This gadget converts longitudinal oscillating or fluctuating motion into a unidirectional rotation, the direction of which is in accordance with given theoretical arguments. Despite the setup being three dimensional, the ratchet rotary motion is proved to be described by one simple dynamic equation. This kind of motion is a result of the interplay of friction and inertia.

From the FPU Chain to Biomolecular Dynamics

The molecular dynamics simulations originally performed by Fermi, Pasta, and Ulam for an isolated one-dimensional chain with cubic anharmonicity had led afterwards to the discovery of stable coherent structures called “solitons”. Any study of the stability of solitons on such a one-dimensional lattice with respect to transverse motions of chain atoms or molecules requires introduction of a secondary structure realized for biological macromolecules in the form of a helix. In the simplest case of intermolecular interactions with spherical symmetry, the straightforward generalization of the Fermi-Pasta-Ulam chain to higher dimensions gives rise to the helical structure: zigzag in two dimensions and α-helix in three dimensions. The planar zigzag structure is provided by the first-and second-neighbor intermolecular bonds, whereas the helical structure in three dimensions requires for its stabilization, at least, three types of interactions. The coupled nonlinear field equations that describe longitudinal and transverse displacements of molecules in the helix backbone are studied. In particular, stable non-topological two- and three-component soliton solutions in two and three dimensions, respectively, are shown to exist. These solutions describe supersonic pulses of longitudinal compression propagating together with localized transverse thickening (“bulging”) and torsional stretching (twisting). Other, more specific, types of solitons are investigated in two dimensions for the zigzag backbone.

Soliton and ratchet motions in helices

A.V.Zolotaryuk 1,2 , P.L.Christiansen 2 , B.Nordén 3 , A.V.Savin 2,4 1 Bogolyubov Institute for Theoretical Physics, 252143 Kyiv, Ukraine 2 Department of Mathematical Modelling, Technical University of Denmark, DK-2800 Lyngby, Denmark 3 Department of Physical Chemistry, Chalmers University of Technology, S-412 96 Gothenburg, Sweden 4 State Institute for Problems of Physics and Technology, 119034 Moscow, The Russian Federation

Lattice stretching bistability and dynamic heterogeneity

A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearest-neighbor interaction of a Morse-like potential (required to have a saturation branch) and a harmonic second-neighbor coupling. Under an external stretching applied to the chain ends, the intersite Morse-like potential results in the appearance of a double-well potential within each chain monomer, whereas the interaction between the second neighbors provides a homogeneous bistable (degenerate) ground state, at least within a certain part of the chain. As a result, different conformational changes occur in the chain under the external forcing. The transition regions between these conformations are described as topological solitons. With a strong second-neighbor interaction, the solitons describe the transition between the bistable ground states. However, the key point of the model is the appearance of a heterogenous structure, when the second-neighbor coupling is sufficiently weak. In this case, a part of the chain has short bonds with a single-well potential, whereas the complementary part admits strongly stretched bonds with a double-well potential. This case allows us to explain the existence of a plateau in the force-extension diagram for DNA and α-helix protein. Finally, the soliton dynamics are studied in detail.