The g.s. of heavy and superheavy hydrogen isotopes, namely ^{4-7 }H, are successfully examined by applying the Isomorphic Shell Model. Properties examined are binding energies and effective radii. The novelty of the present work is that, due to the small number of nucleons involved and the subsequently large deformation, an internal collective rotation appears which is inseparable from the usual internal motion even in the ground states of these nuclei, i.e., for such nuclei the adiabatic approximation is not valid. This extra degree of freedom leads to a reduction of binding energies, an increase of effective radii, and an increase of level widths.

Abstract:
The Bogoliubov theory is extended to a Bose-Einstein condensation with internal degrees of freedom, realized recently in $^{23}$Na gases where several hyperfine states are simultaneously cooled optically. Starting with a Hamiltonian constructed from general gauge and spin rotation symmetry principles fundamental equations for condensate are derived. The ground state where time reversal symmetry is broken in some case and low-lying collective modes, e.g. spin and density wave modes, are discussed. Novel vortex as a topological defect can be created experimentally.

Abstract:
This work deals with the effects of an anharmonic trap on an interacting two-boson system in one dimension. Our primary focus is on the role of the induced coupling between the center of mass and the relative motion as both anharmonicity and the (repulsive) interaction strength are varied. The ground state reveals a strong localization in the relative coordinate, counteracting the tendency to fragment for stronger repulsion. To explore the quantum dynamics, we study the system's response upon (i) exciting the harmonic ground state by continuously switching on an additional anharmonicity, and (ii) displacing the center of mass, this way triggering collective oscillations. The interplay between collective and internal dynamics materializes in the collapse of oscillations, which are explained in terms of few-mode models.

Abstract:
In the approximation B3LYP/cc-pVTZ, the geometry of a methanol molecule surrounded by eight argon atoms has been optimized. By the independent rotation of the methyl and the hydroxyl groups at the fixed position of the C-O bond relative to the argon atoms there was obtained the two-dimensional grid of values of the internal-overall rotation energy. Despite the fact that, initially the energy was calculated for 65 points in the square , the presence of period for methyl group rotation has allowed to increase the number of points up to 195. The analytical approximation for internal rotation energy was found. Two dimensional Schr dinger equation for internal rotation – overall rotation of rotator with fixed axis was solved, energy levels, wave functions and transition probabilities were found. According to the results of these computations, degeneracy of the Е-type states is relieved with increase in splitting of the ground torsional state.

Abstract:
Lithium is an excellent tracer of mixing in stars as it is destroyed (by nuclear reactions) at a temperature around $\sim 2.5\times 10^6$ K. The lithium destruction zone is typically located in the radiative region of a star. If the radiative regions are stable, the observed surface value of lithium should remain constant with time. However, comparison of the meteoritic and photospheric Li abundances in the Sun indicate that the surface abundance of Li in the Sun has been depleted by more than two orders of magnitude. This is not predicted by solar models and is a long standing problem. Observations of Li in open clusters indicate that Li depletion is occurring on the main sequence. Furthermore, there is now compelling observational evidence that a spread of lithium abundances is present in nearly identical stars. This suggests that some transport process is occurring in stellar radiative regions. Helioseismic inversions support this conclusion, for they suggest that standard solar models need to be modified below the base of the convection zone. There are a number of possible theoretical explanations for this transport process. The relation between Li abundances, rotation rates and the presence of a tidally locked companion along with the observed internal rotation in the Sun indicate that the mixing is most likely induced by rotation. The current status of non-standard (particularly rotational) stellar models which attempt to account for the lithium observations are reviewed.

Abstract:
The relaxation time of several ferrocene derivatives was measured, and the internal rotation was discussed. For almost all the derivatives, the degree of the internal rotation was constant in spite of the different molecular weights. However, for (triphenylmethyl)ferrocene, the rotation of the unsubstituted ring would be slower due to the bulkiness of the substituent. Furthermore, the derivatives that have a hydroxyl- or acetyl group on the substituent were also discussed. Their rotation would be influenced by the location of these substituents.

Abstract:
We investigate collective phenomena with rotationally driven spinners of concave shape. Each spinner experiences a constant internal torque in either a clockwise or counterclockwise direction. Although the spinners are modeled as hard, otherwise non-interacting rigid bodies, we find that their active motion induces an effective interaction that favors rotation in the same direction. With increasing density and activity, phase separation occurs via spinodal decomposition, as well as self-organization into rotating crystals. We observe the emergence of cooperative, super-diffusive motion along interfaces, which can transport inactive test particles. Our results demonstrate novel phase behavior of actively rotated particles that is not possible with linear propulsion or in non-driven, equilibrium systems of identical hard particles.

Abstract:
We present and investigate a new class of quantum channels, what we call `universal collective rotation channels', that includes the well-known class of collective rotation channels as a special case. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this C*-algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We prove that there is an abundance of noiseless subsystems for every channel in this class and that Young tableaux combinatorics can be used to explicitly compute these subsystems.

Abstract:
We have examined the influence of rotation on the potential energy and the transport coefficients of the collective motion (friction and mass coefficients). For axially symmetric deformation of nucleus Th-224 we have found that at excitations corresponding to temperatures T > 1 MeV the shell correction to the liquid drop energy practically does not depend on the angular rotation. The friction and mass coefficients obtained within the linear response theory for the same nucleus at temperatures larger than T=2 MeV are rather stable with respect to rotation provided that the contributions from spurious states arising due to the violation of rotation symmetry are removed. At smaller excitations both friction and mass parameters corresponding to the elongation mode are growing functions of rotational frequency.

Abstract:
The latitudinal distributions of the yearly mean rotation rates measured respectively by Suzuki in 1998 and 2012 and Pulkkinen $\&$ Tuominen in 1998 are utilized to investigate internal-cycle variation of solar differential rotation. The rotation rate at the solar Equator seems to decrease since cycle 10 onwards. The coefficient $B$ of solar differential rotation, which represents the latitudinal gradient of rotation, is found smaller in the several years after the minimum of a solar cycle than in the several years after the maximum time of the cycle, and it peaks several years after the maximum time of the solar cycle. The internal-cycle variation of the solar rotation rates looks similar in profile to that of the coefficient $B$. A new explanation is proposed to address such a solar-cycle related variation of the solar rotation rates. Weak magnetic fields may more effectively reflect differentiation at low latitudes with high rotation rates than at high latitudes with low rotation rates, and strong magnetic fields may more effectively repress differentiation at relatively low latitudes than at high latitudes. The internal-cycle variation is inferred to the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity to differentiation.