Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond

We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent expansion about epsilon = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/epsilon^2 pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.Comment: 54 pages, 7 figures. v2: Added references, a few additional words about large spin limit of anomalous dimensions. v3: Expanded Sect. IV.A on multiloop ansatz; remark that form-factor prediction is now confirmed by other work; minor typos correcte

Conformal Curves in Potts Model: Numerical Calculation

We calculated numerically the fractal dimension of the boundaries of the Fortuin-Kasteleyn clusters of the $q$-state Potts model for integer and non-integer values of $q$ on the square lattice. In addition we calculated with high accuracy the fractal dimension of the boundary points of the same clusters on the square domain. Our calculation confirms that this curves can be described by SLE$_{\kappa}$.Comment: 11 Pages, 4 figure

Spin interfaces in the Ashkin-Teller model and SLE

We investigate the scaling properties of the spin interfaces in the Ashkin-Teller model. These interfaces are a very simple instance of lattice curves coexisting with a fluctuating degree of freedom, which renders the analytical determination of their exponents very difficult. One of our main findings is the construction of boundary conditions which ensure that the interface still satisfies the Markov property in this case. Then, using a novel technique based on the transfer matrix, we compute numerically the left-passage probability, and our results confirm that the spin interface is described by an SLE in the scaling limit. Moreover, at a particular point of the critical line, we describe a mapping of Ashkin-Teller model onto an integrable 19-vertex model, which, in turn, relates to an integrable dilute Brauer model.Comment: 12 pages, 6 figure

Dirac equation in the magnetic-solenoid field

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian in both above dimensions and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.Comment: 23 pages, 2 figures, LaTex fil

Modelling chemical reactions using semiconductor quantum dots

We propose using semiconductor quantum dots for a simulation of chemical reactions as electrons are redistributed among such artificial atoms. We show that it is possible to achieve various reaction regimes and obtain different reaction products by varying the speed of voltage changes applied to the gates forming quantum dots. Considering the simplest possible reaction, $H_2+H\to H+H_2$, we show how the necessary initial state can be obtained and what voltage pulses should be applied to achieve a desirable final product. Our calculations have been performed using the Pechukas gas approach, which can be extended for more complicated reactions

Observation of Heteronuclear Feshbach Resonances in a Bose-Fermi Mixture

Three magnetic-field induced heteronuclear Feshbach resonances were identified in collisions between bosonic 87Rb and fermionic 40K atoms in their absolute ground states. Strong inelastic loss from an optically trapped mixture was observed at the resonance positions of 492, 512, and 543 +/- 2 G. The magnetic-field locations of these resonances place a tight constraint on the triplet and singlet cross-species scattering lengths, yielding -281 +/- 15 Bohr and -54 +/- 12 Bohr, respectively. The width of the loss feature at 543 G is 3.7 +/- 1.5 G wide; this broad Feshbach resonance should enable experimental control of the interspecies interactions.Comment: revtex4 + 5 EPS figure