3/25/2023 0 Comments Boson x isnt sized correctly![]() ![]() + Conformally invariant systems and AdS/CFT. + Topological effects in field theory and cosmology. + Theory and applications of relativity and its possible limitations. + Algorithmic research and Computational methods for physics of and beyond the Standard Model. + High energy particles in astrophysics and cosmology. + Models and phenomenology of dark matter, the mysterious component of the universe, that has so far been detected only by its gravitational effects. Some specific research accomplishments include + Theories of the electroweak interactions, the forces that give rise to many forms of radioactive decay + Physics of the recently discovered Higgs boson. The results reported here apply to physics beyond the so-called Standard Model of particle physics physics of high energy collisions such as those observed at the Large Hadron Collider theoretical and mathematical tools and frameworks for describing the laws of more » nature at short distances cosmology and astrophysics and analytic and computational methods to solve theories of short distance physics. These theoretical developments apply to experiments in laboratories such as CERN, the facility that operates the Large Hadron Collider outside Geneva, as well as to cosmological investigations done using telescopes and satellites. This award supported a broadly based research effort in theoretical particle physics, including research aimed at uncovering the laws of nature at short (subatomic) and long (cosmological) distances. In order to solve the equation for clusters of interest it is necessary to make a number of approximations and use numerical methods. The analytic solution is only known for a two particle problem. The dimensionality of the Schroedinger equation is determined by the number of particles (nuclei and electrons) in the cluster. The wave function gives all information about the quantum state of the cluster and can be used to calculate different physical and chemical properties, such as photoelectron, X-ray, NMR, EPR spectra, dipole moment, polarizability etc. The other solutions correspond to excited states. ![]() The lowest energy solution (wave function) corresponds to the ground state of the cluster. The solution of the Schroedinger equation is a set of eigenvectors (wave functions) and their eigenvalues (energies). ![]() This equation represents a multidimensional eigenvalue problem. If one is not interested in dynamics of clusters it is enough to solve the stationary (time-independent) Schroedinger equation (HΦ=EΦ). However, to predict their accurate geometries and other physical and chemical properties it is necessary to solve a Schroedinger equation. Some qualitative information about the geometries of such clusters can be obtained with classical empirical methods, for example geometry optimization using an empirical Lennard-Jones potential. ![]() The atomic clusters studied in this work contain from a few atoms to tens of atoms. In addition to accurate results for specific clusters, such methods can be used for benchmarking of different empirical and semiempirical approaches. On the other hand, because of significant advances in quantum chemical methods and computer capabilities, it is now possible to do high quality ab-initio calculations not only on systems of few atoms but on clusters of practical interest as well. However, more » since empirical and semiempirical methods rely on simple models with many parameters, it is often difficult to estimate the quantitative and even qualitative accuracy of the results. These methods allow one to study large and small dusters using the same approximations. Most of the theoretical approaches have been based on empirical or semiempirical methods. The theoretical methods are frequently used to help in interpretation of complex experimental data. However, the interpretation of the results is often difficult. In recent years significant advances in experimental techniques allow one to synthesize and study atomic clusters of specified sizes. Another example is a potential application of atomic clusters in microelectronics, where their band gaps can be adjusted by simply changing cluster sizes. One example is the catalytic activity of clusters of specific sizes in different chemical reactions. Because physical and chemical properties of clusters can be adjusted simply by changing the cluster's size, different applications of atomic clusters were proposed. However, recently it has become clear that many properties of atomic clusters can change drastically with the size of the clusters. For a long time it was thought that physical and chemical properties of atomic dusters monotonically change with increasing size of the cluster from a single atom to a condensed matter system. Atomic clusters are unique objects, which occupy an intermediate position between atoms and condensed matter systems. ![]()
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