The finite remainder function for planar, color-ordered, maximally helicity violating scattering processes in N=4 super Yang-Mills theory possesses a non-vanishing multi-Regge limit that depends on the choice of a Mandelstam region. We analyze the combined multi-Regge collinear limit in all Mandelstam regions through an analytic continuation of the Wilson loop OPE. At leading order, the former is determined by the gluon excitation of the Gubser-Klebanov-Polyakov string. We illustrate the general procedure at the example of the heptagon remainder function at two loops. In this case, the continuation of the leading order terms in the Wilson loop OPE suffices to determine the two-loop multi-Regge heptagon functions in all Mandelstam regions from their symbols. The expressions we obtain are fully consistent with recent results by Del Duca et al.

In this paper, we derive a generalized second fluctuation-dissipation theorem (FDT) for stochastic dynamical systems in the steady state. The established theory is built upon the Mori-type generalized Langevin equation for stochastic dynamical systems and only uses the properties of the Kolmogorov operator. The new second FDT expresses the memory kernel of the generalized Langevin equation as the correlation function of the fluctuation force plus an additional term. In particular, we show that for nonequilibrium states such as heat transport between two thermostats with different temperatures, the classical second FDT is valid even when the exact form of the steady state distribution is unknown. The obtained theoretical results enable us to construct a data-driven nanoscale fluctuating heat conduction model based on the second FDT. We numerically verify that the new model of heat transfer yields better predictions than the Green-Kubo formula for systems far from the equilibrium.

We briefly recall the procedure for computing the Ward Identities in the presence of a regulator which violates the symmetry being considered. We compute the first non-trivial correction to the supersymmetry Ward Identity of the Wess-Zumino model in the presence of background supergravity using dimensional regularisation. We find that the result can be removed using a finite local counter term and so there is no supersymmetry anomaly.

Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for $q$-state CA. It is based on the vector representation of $q$-state CA, that is, the $q$-states are assigned to the standard basis vectors of the $q$-dimensional real space and the local rule can be expressed by a tuple of $q$ polynomials. Then, the $q$-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the $q$-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.

Instantaneous non-local quantum computation requires multiple parties to jointly perform a quantum operation, using pre-shared entanglement and a single round of simultaneous communication. We study this task for its close connection to position-based quantum cryptography, but it also has natural applications in the context of foundations of quantum physics and in distributed computing. The best known general construction for instantaneous non-local quantum computation requires a pre-shared state which is exponentially large in the number of qubits involved in the operation, while efficient constructions are known for very specific cases only. We partially close this gap by presenting new schemes for efficient instantaneous non-local computation of several classes of quantum circuits, using the Clifford+T gate set. Our main result is a protocol which uses entanglement exponential in the T-depth of a quantum circuit, able to perform non-local computation of quantum circuits with a (poly-)logarithmic number of layers of T gates with quasi-polynomial entanglement. Our proofs combine ideas from blind and delegated quantum computation with the garden-hose model, a combinatorial model of communication complexity which was recently introduced as a tool for studying certain schemes for quantum position verification. As an application of our results, we also present an efficient attack on a recently-proposed scheme for position verification by Chakraborty and Leverrier.

Gamma Ray Burst and Soft Gamma Repeaters are neither standard candle nor isotropic explosions. Our model explain them as strong blazing of a light-house, spinning and precessing gamma jet. Such jets at maximal output (as GRBs in Supernova like sources at cosmic edges) or at late lower power stages (SGRs in nearer planetary nebulae in galactic halo) may blaze the observer by extreme beaming $(Ω< 10^{-8})$ and apparent huge luminosity. \keywords{GRB, Jet, Inverse Compton, SGR}

Gamma Ray Bursts as recent GRB990123 and GRB990510 are observed to occur in cosmic volumes with a corresponding output reaching, for isotropic explosions, energies as large as two solar masses annihilation. These energies are underestimated because of the neglected role of comparable ejected neutrinos bursts. These extreme power cannot be explained with any standard spherically symmetric Fireball model. A too heavy black hole or Star would be unable to coexist with the shortest millisecond time structure of Gamma ray Burst. Beaming of the gamma radiation may overcome the energy puzzle. However any mild explosive beam $(Ω> 10^{-2})$ should not solve the jet containment at those disruptive energies. Only extreme beaming $(Ω< 10^{-8})$, by a slow decaying, but long-lived precessing jet, it may coexist with characteristic Supernova energies, apparent GRBs output, statistics as well as their connection with older and nearer SGRs relics.

Tau Air-showers are the best trace of rarest Ultra High Energy neutrinos UHE $ν_τ$, $\barν_τ$ and $\barν_e$ at PeV and higher energy. $τ$ Air-showers may generate billion times amplified signals by their secondaries . Horizontal amplified $τ$ air-showers by $ν_τ N$ and UHE $\barν_{e} e$ at PeV emerging from mountain chain might be the most power-full imprint. Upward UHE $ν_τ N$ interaction on Earth crust at horizontal edge and from below, their consequent UHE $τ$ air-showers beaming toward high mountains should flash $γ$,$μ$,X and optical detectors on the top. Upward $τ$ air-shower may hit nearby satellite flashing them by short, hard, diluted $γ-$burst at the edge of Gamma Ray Observatory BATSE threshold. We identify these events with recent (1994) discovered upward Terrestrial Gamma Flashes (TGF) and we probed their UHE $τ$ - UHE $ν_τ$ origin. From these TGF data approximated UHE $ν_τ$ flux and $Δm_{ν_μν_τ}$ sever lower bound are derived. Partial TGF Galactic signature is also manifest within known 47 TGF events clustered within three degrees from the Galactic plane at ${\simeq 2\cdot 10^{-3}}$probability. Well known $X-γ-\mathrm{TeV}$ active galactic and extragalactic sources have found probable counterpart in TGF arrival directions. Detection of elusive UHE $ν_τ$ seem finally achieved.