Deformed supersymmetric quantum mechanics with spin variables

We quantize the one-particle model of the ${\rm SU}(2|1)$ supersymmetric multi-particle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the mass-dimension deformation parameter $m$ and ${\rm SU}(2)$ spin $q \in \big( \mathbb{Z}_{>0}\,$, $1/2 + \mathbb{Z}_{\geqslant 0}\big)\,$. It is found that the states at the fixed energy level form irreducible multiplets of the supergroup ${\rm SU}(2|1)\,$. Also, the hidden superconformal symmetry ${\rm OSp}(4|2)$ of the model is revealed in the classical and quantum cases. We calculate the ${\rm OSp}(4|2)$ Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed $q$ are unified into an irreducible ${\rm OSp}(4|2)$ multiplet.Comment: 19 pages, 2 figures; v3: comments and new reference added, typos corrected, published versio

Deformed N= 8{\cal N}{=}\,8 mechanics of (8,8,0){\bf(8,8,0)} multiplets

We construct new models of `curved' SU$(4|1)$ supersymmetric mechanics based on two versions of the off-shell multiplet ${\bf(8,8,0)}$ which are `mirror' to each other. The worldline realizations of the supergroup SU$(4|1)$ are treated as a deformation of flat ${\cal N}{=}\,8$, $d\,{=}\,1$ supersymmetry. Using SU$(4|1)$ chiral superfields, we derive invariant actions for the first-type ${\bf(8,8,0)}$ multiplet, which parametrizes special K\"ahler manifolds. Since we are not aware of a manifestly SU$(4|1)$ covariant superfield formalism for the second-type ${\bf(8,8,0)}$ multiplet, we perform a general construction of SU$(4|1)$ invariant actions for both multiplet types in terms of SU$(2|1)$ superfields. An important class of such actions enjoys superconformal OSp$(8|2)$ invariance. We also build off-shell actions for the SU$(4|1)$ multiplets ${\bf(6,8,2)}$ and ${\bf(7,8,1)}$ through appropriate substitutions for the component fields in the ${\bf(8,8,0)}$ actions. The ${\bf(6,8,2)}$ actions are shown to respect superconformal SU$(4|1,1)$ invariance.Comment: 1+34 pages; v2: section 3 revised, typos corrected, 5 additional references, clarifying comments and acknowledgment added, matches published versio

Non-linear (3, 4, 1) multiplet of N=4{\cal N} = 4, d=1d = 1 supersymmetry as a semi-dynamical spin multiplet

We consider a new type of ${\cal N}=4$, $d=1$ semi-dynamical multiplet based on the non-linear version of the mirror multiplet ${\bf (3, 4, 1)}$, with the triplet of bosonic physical fields parametrizing a three-dimensional sphere $S^3$ of the radius $R$. The limit $R\to\infty$ amounts to the contraction $S^3\to\mathbb{R}^3$ and leads to the linear mirror multiplet ${\bf (3, 4, 1)}$. Spin degrees of freedom described by a Wess-Zumino action specify a two-dimensional surface embedded in the sphere $S^3$. A pair of the examples considered correspond to the round and squashed ``fuzzy'' 2-spheres. We couple the squashed 2-sphere model to the dynamical mirror multiplet ${\bf (2, 4, 2)}$. A notable feature of this coupling is the dependence of the squashing parameter on the bosonic fields $z, \bar z$ of the chiral multiplet.Comment: 1+17 page

SU(2|2) supersymmetric mechanics

We introduce a new kind of non-relativistic N = 8 supersymmetric mechanics, associated with worldline realizations of the supergroup SU(2|2) treated as a deformation of flat N = 8, d=1 supersymmetry. Various worldline SU(2|2) superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed. For the off-shell SU(2|2) multiplets (3,8,5), (4,8,4) and (5,8,3), we construct and analyze the most general superfield and component actions. Common features are mass oscillator-type terms proportional to the deformation parameter and a trigonometric realization of the superconformal group OSp(4∗|4) in the conformal cases. For the simplest (5,8,3) model the quantization is performed. © 2016, The Author(s)

Influence of antimony on structure and physical properties of molten tin

Structure of liquid Sb-Sn alloys were studied by means of viscosity measurements and X-ray diffraction. Structural factors and pair correlation functions were analysed and interpreted using the random atomic distribution model. The features of temperature dependence of the viscosity coeff cient were analysed taking into account X-ray diff raction patterns. The results allow us to conclude that Sb atoms substitute for Sn atoms, forming a typical atomic solution, which reveals chemical and topological short-range order. Moreover, certain atoms form Sb- and Sn-based SbnSnm associates and self-associates.peer-reviewe