Research / Annual reports / Main research results of the Institute for Condensed Matter Physics of NAS of Ukraine in 2015

# Main research results of the Institute for Condensed Matter Physics of NAS of Ukraine in 2015

**а) Main fundamental results**

A single particle confined in a Penning trap (electron, proton, ionized atom) is a suitable system for high-precision measurements of fundamental particle properties. Charged particle is confined by a superposition of static magnetic and electric fields. A strong magnetic field (3-5 T) confines the particle radially and a quadruple electrostatic field provides axial confinement. For the first time, the dynamics of a single charge in the Penning trap in the relativistic framework without approximations is analyzed. Quasi-relativistic models where the terms v2/c2 are taken into account while v4/c4 and higher powers are neglected have been studied before. As the restoring quadruple potential has the axial symmetry, the dynamics of the system can be reduced to two degrees of freedom. Analysis of Poincare sections demonstrates coexistence of regular and chaotic dynamics, namely periodic, quasiperiodic, and chaotic orbits. Because the periodic orbits an apparatus analogical to Penning trap can be used to measure fundamental properties of high-energy particles, in particular extragalactic ultra-high energy cosmic rays (Yaremko Yu., Chaos v.25, 053102, 2015).

Important feature of the proteins dissolved in the water-electrolyte solutions is their abilities to aggregate. A key step in developing biotech drugs is to formulate proteins so that they do not aggregate. This is because good shelf-life requires long-term solution stability, and because patient compliance requires liquids having low viscosity. The importance of such formulations comes from the fact that the world market for protein biologicals is about the same size as for smartphones. Protein aggregation in the cell plays a key role in protein condensation diseases, such as Alzheimer’s, Parkinson’s, Huntington’s, and others. However, currently the mechanisms of protein aggregation is poorly understood. For the investigation of the mechanisms of these processes we develop a theoretical model for reversible protein–protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, Strength of the site-site attraction depends on the nature of the salt in the system. With few parameters and with knowledge of the cloud-point temperatures as a function of added salt, the model gives good predictions for properties including the liquid–liquid coexistence curves, the second virial coefficients, and others for lysozyme and gamma-crystallin. (Kastelic, M.; Kalyuzhnyi, Y.V.; Hribar-Lee, B.; Dill K.A., Vlachy V. "Protein aggregation in salt solutions" PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 112 Issue: 21 Pages: 6766-6770 (2015)).

The study of the critical behavior of interacting particles located on the nodes of complex networks has a number of interesting applications ranging from sociophysics to nanophysics. We have applied the method of complex zeros analysis for the partition function of the Ising model on an annealed scale-free network with the node degree distribution power-law decay . For the Ising model on lattices the Lee-Yang theorem holds: all zeros in complex magnetic field plane are purely imaginary. We have shown that the theorem fails on complex networks for a certain region of λ (for the so-called “fat-tail” distributions). This differs from the case of regular lattices where the theorem holds for any values of dimensionality. It has been found recently that imaginary zeros are associated with times of quantum coherence of spin systems. That is why physical interpretation of Lee-Yang zeros is important not only for the understanding the critical behavior at a fundamental level but also it points their experimental observation.( M. Krasnytska, B. Berche, Yu. Holovatch, and R. Kenna, Eur. Phys. Lett. 111 (2015) 60009).

We have studied a possibility of the dynamic purification of an open quantum system due to its interaction with an environment. Using the dephasing model for a simple spin-boson system, it is shown that the thermal bath can influence the system behaviour at the initial stage of its evolution in different ways. For instance, at the nonselective measurements of the special type the purity enhancement is possible, which is very important for the quantum registers design. We have also investigated peculiarities of the nonselective measurements on the overcomplete basis of the state vectors. It is found that in contrast to the von Neumann-Lüders projection scheme, at the certain measurement settings there appears a possibility for the additional temperature – induced purification of the q-bit, which had been prepared initially in the most mixed state. The obtained results may have practical application in the theory of quantum measurements and control (Ignatyuk Vasyl).

The exactly solvable spin-1/2 Ising-Heisenberg diamond chain with geometric frustration is generalized to a purely quantum diamond chain by adding a small XY part to the Ising interactions. Applying the many-body perturbation theory the effective Hamiltonian is obtained describing the low-temperature behavior of the purely quantum model in the vicinity of the critical field, at which the ground state of the Ising-Heisenberg chain changes from the ferrimagnetic to fully magnetized state. Performing exact-diagonalization and density-matrix-renormalization-group numerical calculations, we investigate high-field behavior of the magnetization at low temperatures and low-temperature behavior of the specific heat at high fields for the initial and effective models. It is shown that the XY part added gives rise to the spin-liquid phase with continuously varying magnetization, which is located between the ferrimagnetic 1/3-plateau phase and the fully magnetized phase. The elaborated approach can be applied to investigations of quantum generalizations of other hybrid systems similar to the considered Ising-Heisenberg model (Krupnitska O., Lisnyj B., Derzhko O.).

Influence of intercalation on the electronic band structure of the layered nanohybrid compound of the GaSe-type with a stage ordering, formed by packets with the small number of layers, is studied within the modified version of the periodic Anderson model. Such compounds are widely used for powerful secondary cells and supercapacitors. Density of electron states (electron DOS) and electron contribution into quantum capacity of the system are calculated and analyzed for the case of neutral impurities with the local level broadening (of the Lorentzian-type) due to electron correlations. The situations are considered, when intercalated particles form an additional band like the narrow impurity band (being far enough from the main band) or the more extended band hybridized with the main one (at their overlapping). The anomalous behaviour of the electron components of capacity in the region of the DOS singularities (appearing due to stage ordering and hybridization effects) is revealed and studied. Changes in the total DOS and the quantum capacity because of impurity level broadening and increase of the intercalant concentration are investigated (Velychko O.V., Stasyuk I.V.).

**b) Main applied results**

The analytical methods for the synthesis of color image by traditional technologies and by new technology ICaS-ColorPrint (two color + black paint) for multicolor printing were developed. The efficiency of the new technology, which provides high quality of color reproduction, optimal technological conditions of color printing and achieving significant savings (50%) of color paints was demonstrated. New methods of digital processing of color images to quantify the maximum blending of color and black paints in dark areas of the print and gamma correction (addition and subtraction) of colored paints at stage of prepress forms were developed.The new version of the computer program «ICaS - Color Synthesis 2.0» was developed and submitted for state registration (Shovhenyuk M.V).