Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons

Due to their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G_2-structures and admit the G_2-instanton equations, which are natural BPS equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons-type functional. We consider the Chern-Simons flow between different G_2-instantons on Aloff-Wallach spaces, which is equivalent to Spin(7)-instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C^3 x R^2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape.Comment: 1+17 pages, 1 figur

Supermembrane limit of Yang-Mills theory

We consider Yang-Mills theory with $N{=}1$ super translation group in eleven auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\Sigma_3\times S^1$, where $\Sigma_3$ is a three-dimensional Lorentzian manifold and $S^1$ is a circle. We show that in the infrared limit, when the metric on $S^1$ is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term reduces to the action of an M2-brane.Comment: 1+6 page

Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transition with control fields

We show that atoms from wide velocity interval can be concurrently involved in Doppler-free two-photon resonant far from frequency degenerate four-wave mixing with the aid of auxiliary electromagnetic field. This gives rise to substantial enhancement of the output radiation generated in optically thick medium. Numerical illustrations addressed to typical experimental conditions are given.Comment: LaTeX2e, hyperref, 7 pages, 5 figures, to appear in PRA 1 august 200

Transformation of amorphous carbon clusters to fullerenes

Transformation of amorphous carbon clusters into fullerenes under high temperature is studied using molecular dynamics simulations at microsecond times. Based on the analysis of both structure and energy of the system, it is found that fullerene formation occurs in two stages. Firstly, fast transformation of the initial amorphous structure into a hollow sp$^2$ shell with a few chains attached occurs with a considerable decrease of the potential energy and the number of atoms belonging to chains and to the amorphous domain. Then, insertion of remaining carbon chains into the sp$^2$ network takes place at the same time with the fullerene shell formation. Two types of defects remaining after the formation of the fullerene shell are revealed: 7-membered rings and single one-coordinated atoms. One of the fullerene structures obtained contains no defects at all, which demonstrates that defect-free carbon cages can be occasionally formed from amorphous precursors directly without defect healing. No structural changes are observed after the fullerene formation, suggesting that defect healing is a slow process in comparison with the fullerene shell formation. The schemes of the revealed reactions of chain atoms insertion into the fullerene shell just before its completion are presented. The results of the performed simulations are summarized within the paradigm of fullerene formation due to selforganization of the carbon system.Comment: 35 pages, 9 figure

Formation of nickel-carbon heterofullerenes under electron irradiation

arXiv.-- et al.A way to produce new metal-carbon nanoobjects by transformation of a graphene flake with an attached transition metal cluster under electron irradiation is proposed. The transformation process is investigated by molecular dynamics simulations by the example of a graphene flake with a nickel cluster. The parameters of the nickel-carbon potential (I. V. Lebedeva et al., J. Phys. Chem. C, 2012, 116, 6572) are modified to improve the description of the balance between the fullerene elastic energy and graphene edge energies in this process. The metal-carbon nanoobjects formed are found to range from heterofullerenes with a metal patch to particles consisting of closed fullerene and metal clusters linked by chemical bonds. The atomic-scale transformation mechanism is revealed by the local structure analysis. The average time of formation of nanoobjects and their lifetime under electron irradiation are estimated for the experimental conditions of high-resolution transmission electron microscopy (HRTEM). The sequence of images of nanostructure evolution with time during its observation by HRTEM is also modelled. Furthermore, the possibility of batch production of studied metal-carbon nanoobjects and solids based on these nanoobjects is discussed.AS, IL, AK and AP acknowledges Russian Foundation of Basic Research (14-02-00739-a). AP acknowledges Samsung Global Research Outreach Program. IL acknowledges support from the Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme (Grant Agreement PIIF-GA-2012-326435 RespSpatDisp), Grupos Consolidados del Gobierno Vasco (IT-578-13) and the computational time on the Supercomputing Center of Lomonosov Moscow State University and the Multipurpose Computing Complex NRC “Kurchatov Institute.” EB acknowledges EPSRC Career Acceleration Fellowship, New Directions for EPSRC Research Leaders Award (EP/G005060), and ERC Starting Grant for financial support.Peer Reviewe

New Perturbation Theory for Nonstationary Anharmonic Oscillator

The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency in external field is used. Based on some intrinsic properties of unperturbed wave function the variational-iterational method is proposed, that make it possible to correct both the amplitude and the phase of wave function. As an application the first order correction are proposed both for wave function and S-matrix elements for asymmetric perturbation potential of type $V(x,\tau)=\alpha (\tau)x^3+\beta (\tau)x^4.$ The transition amplitude ''ground state - ground state'' $W_{00}(\lambda ;\rho)$ is analyzed in detail depending on perturbation parameter $\lambda$ (including strong coupling region $$ $\sim 1$) and one-dimensional refraction coefficient $\rho$.Comment: LaTeX, 13 page

String theories as the adiabatic limit of Yang-Mills theory

We consider Yang-Mills theory with a matrix gauge group $G$ on a direct product manifold $M=\Sigma_2\times H^2$, where $\Sigma_2$ is a two-dimensional Lorentzian manifold and $H^2$ is a two-dimensional open disc with the boundary $S^1=\partial H^2$. The Euler-Lagrange equations for the metric on $\Sigma_2$ yield constraint equations for the Yang-Mills energy-momentum tensor. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills equations plus constraints on the energy-momentum tensor become the equations describing strings with a worldsheet $\Sigma_2$ moving in the based loop group $\Omega G=C^\infty (S^1, G)/G$, where $S^1$ is the boundary of $H^2$. By choosing $G=R^{d-1, 1}$ and putting to zero all parameters in $\Omega R^{d-1, 1}$ besides $R^{d-1, 1}$, we get a string moving in $R^{d-1, 1}$. In arXiv:1506.02175 it was described how one can obtain the Green-Schwarz superstring action from Yang-Mills theory on $\Sigma_2\times H^2$ while $H^2$ shrinks to a point. Here we also consider Yang-Mills theory on a three-dimensional manifold $\Sigma_2\times S^1$ and show that in the limit when the radius of $S^1$ tends to zero, the Yang-Mills action functional supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring action.Comment: 11 pages, v3: clarifying remarks added, new section on embedding of the Green-Schwarz superstring into d=3 Yang-Mills theory include