The phonon theory of liquid thermodynamics

Heat capacity of matter is considered to be its most important property because it holds information about system's degrees of freedom as well as the regime in which the system operates, classical or quantum. Heat capacity is well understood in gases and solids but not in the third state of matter, liquids, and is not discussed in physics textbooks as a result. The perceived difficulty is that interactions in a liquid are both strong and system-specific, implying that the energy strongly depends on the liquid type and that, therefore, liquid energy can not be calculated in general form. Here, we develop a phonon theory of liquids where this problem is avoided. The theory covers both classical and quantum regimes. We demonstrate good agreement of calculated and experimental heat capacity of 21 liquids, including noble, metallic, molecular and hydrogen-bonded network liquids in a wide range of temperature and pressure.Comment: 7 pages, 4 figure

Liquid heat capacity in the approach from the solid state: anharmonic theory

Calculating liquid energy and heat capacity in general form is an open problem in condensed matter physics. We develop a recent approach to liquids from the solid state by accounting for the contribution of anharmonicity and thermal expansion to liquid energy and heat capacity. We subsequently compare theoretical predictions to the experiments results of 5 commonly discussed liquids, and find a good agreement with no free fitting parameters. We discuss and compare the proposed theory to previous approaches.Comment: 8 pages, 6 figure

Heat capacity at the glass transition

A fundamental problem of glass transition is to explain the jump of heat capacity at the glass transition temperature $T_g$ without asserting the existence of a distinct solid glass phase. This problem is also common to other disordered systems, including spin glasses. We propose that if $T_g$ is defined as the temperature at which the liquid stops relaxing at the experimental time scale, the jump of heat capacity at $T_g$ follows as a necessary consequence due to the change of system's elastic, vibrational and thermal properties. In this picture, we discuss time-dependent effects of glass transition, and identify three distinct regimes of relaxation. Our approach explains widely observed logarithmic increase of $T_g$ with the quench rate and the correlation of heat capacity jump with liquid fragility

Crystal-like high frequency phonons in the amorphous phases of solid water

The high frequency dynamics of low- (LDA) and high-density amorphous-ice (HDA) and of cubic ice (I_c) has been measured by inelastic X-ray Scattering (IXS) in the 1-15 nm^{-1} momentum transfer (Q) range. Sharp phonon-like excitations are observed, and the longitudinal acoustic branch is identified up to Q = 8nm^{-1} in LDA and I_c and up to 5nm^{-1} in HDA. The narrow width of these excitations is in sharp contrast with the broad features observed in all amorphous systems studied so far. The "crystal-like" behavior of amorphous ices, therefore, implies a considerable reduction in the number of decay channels available to sound-like excitations which is assimilated to low local disorder.Comment: 4 pages, 3 figure

Energy landscape, two-level systems and entropy barriers in Lennard-Jones clusters

We develop an efficient numerical algorithm for the identification of a large number of saddle points of the potential energy function of Lennard- Jones clusters. Knowledge of the saddle points allows us to find many thousand adjacent minima of clusters containing up to 80 argon atoms and to locate many pairs of minima with the right characteristics to form two-level systems (TLS). The true TLS are singled out by calculating the ground-state tunneling splitting. The entropic contribution to all barriers is evaluated and discussed.Comment: 4 pages, RevTex, 2 PostScript figure

Sparse random matrices and vibrational spectra of amorphous solids

A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n independent non-zero elements in each row. The average values =0 and dispersion =V^2 for all non-zero elements. The density of vibrational states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle law with radius independent of N. We argue that for n^2 << N this model can be used to describe the interaction of atoms in amorphous solids. The level statistics of matrix M is well described by the Wigner surmise and corresponds to repulsion of eigenfrequencies. The participation ratio for the major part of vibrational modes in three dimensional system is about 0.2 - 0.3 and independent of N. Together with term repulsion it indicates clearly to the delocalization of vibrational excitations. We show that these vibrations spread in space by means of diffusion. In this respect they are similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous silicon. Our results are in a qualitative and sometimes in a quantitative agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure

THE ROLE OF THE BUDGETING SYSTEM IN MERGERS AND ACQUISITIONS

The article considers the role of the budgeting system in mergers and absorption at all stages of their implementation – the search for the target company and preparation for the transaction, the process of conducting and concluding the transaction, the integration of the initiator company and the target company in the post-transaction period and describes the options for the build budget models during the integration period. The article suggests models of interaction of budgeting systems using project budgets in mergers and absorption in general, as well as in the implementation of vertical integration of companies that are parties to the transaction. It shows the role of project budgets in relationship between budget model of initiation company and target company. The advantages and disadvantages of the considered models have been highlighted

ESG Investment Profitability in Developed and Emerging Markets with Regard to the Time Horizon

The development of the ESG (Environmental, social, and governance) concept has led to the rapid spread of financial instruments for investing in sustainable development on all continents. The purpose of the article is to study the attractiveness of sustainable investing in the developed and emerging markets of America, Europe and Asia, in particular, to conduct a comparative analysis of the returns of market indices based on ESG criteria and those of indices that do not take them into account. Particular attention is paid to the duration of the investment period: the authors studied profitability on time intervals from one to five years. The object of the study is stock indices. The subject of the study is profitability of ESG-oriented and ESG-neutral indices. A comparative analysis of 28 market indices, 15 of which were formed with ESG indicators in the period from 2013 to 2022 led to the conclusion that it is advisable to invest in ESG index funds in both developed and emerging markets, since in more than 50% of cases, the return of ESG indices is higher than that of non-ESG indices. Investments in ESG indices over a longer time horizon tend to have higher returns on invested capital than traditional investments in non-sustainable indices. Analysis of European stock market returns has shown insufficient efficiency of ESG investments and requires additional analysis of the factors that have influenced this. A promising direction for further research is also the analysis of the mutual influence of stock markets of developed and developing countries on financial ESG instruments and indices. The applied value of the study lies in the possibility of using the results of the analysis in the reorientation of Russian investors in the face of sanctions pressure on stock markets in the Asia-Pacific region