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  • 1
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    One-species Vlasov-Poisson-Landau system for soft potentials in ℝ3 (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-08
    Description: We consider the global classical solution near a global Maxwellian to the one-species Vlasov-Poisson-Landau system in the whole space R x 3 . It is shown that our global solvability result is obtained under the weaker smallness condition on the initial perturbation than that of Duan et al. , [preprint arXiv:1112.3261 (2011)] and Lei et al. , [Kinet. Relat. Models 7 (3), 551–590 (2014)].
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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  • 2
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    The kite integral to all orders in terms of elliptic polylogarithms (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-07
    Description: We show that the Laurent series of the two-loop kite integral in D = 4 − 2ε space-time dimensions can be expressed in each order of the series expansion in terms of elliptic generalisations of (multiple) polylogarithms. Using differential equations, we present an iterative method to compute any desired order. As an example, we give the first three orders explicitly.
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    Electronic ISSN: 1089-7658
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  • 3
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    All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-06
    Description: We give a complete, self-contained, and mathematically rigorous proof that Euclidean Yang-Mills theories are perturbatively renormalisable, in the sense that all correlation functions of arbitrary composite local operators fulfill suitable Ward identities. Our proof treats rigorously both all ultraviolet and infrared problems of the theory and provides, in the end, detailed analytical bounds on the correlation functions of an arbitrary number of composite local operators. These bounds are formulated in terms of certain weighted spanning trees extending between the insertion points of these operators. Our proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, combined with estimation techniques based on tree structures. Compared with previous mathematical treatments of massless theories without local gauge invariance [R. Guida and Ch. Kopper, e-print arXiv:1103.5692 and J. Holland, S. Hollands, and Ch. Kopper, Commun. Math. Phys. 342 , 385 (2016)], our constructions require several technical advances; in particular, we need to fully control the BRST invariance of our correlation functions.
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    Electronic ISSN: 1089-7658
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  • 4
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    Definition of the Riesz derivative and its application to space fractional quantum mechanics (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-06
    Description: We investigate and compare different representations of the Riesz derivative, which plays an important role in anomalous diffusion and space fractional quantum mechanics. In particular, we show that a certain representation of the Riesz derivative, R x α , that is generally given as also valid for α = 1, behaves no differently than the other definition given in terms of its Fourier transform. In the light of this, we discuss the α → 1 limit of the space fractional quantum mechanics and its consistency.
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    Electronic ISSN: 1089-7658
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  • 5
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    Non-Markovian quantum feedback networks I: Quantum transmission lines, lossless bounded real property and limit Markovian channels (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-06
    Description: The purpose of this paper is to set out the problems of modeling quantum communication and signal processing where the communication between systems is via a non-Markovian channel. This is a general feature of quantum transmission lines. Our ultimate objective is to extend the network rules that have been developed for Markovian models. To this end we recall the Hamiltonian description of such non-Markov models of transmission lines and their quantization. These have occurred in the context of non-equilibrium thermodynamics, but our interest is in the transmission lines as carriers of information rather than heat baths. We show that there is an analytic scattering matrix associated with these models and that stability may be formulated in terms of the lossless bounded real property. Noting that the input and output fields do not separately satisfy a non-self-demolition principle, we discuss the rigorous limit in which such models appear Markov and so amenable to standard approaches of quantum filtering and control.
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    Electronic ISSN: 1089-7658
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  • 6
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    Isotropic wave turbulence with simplified kernels: Existence, uniqueness, and mean-field limit for a class of instantaneous coagulation-fragmentation processes (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-06
    Description: The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at most linear. We also consider finite stochastic particle systems undergoing instantaneous coagulation-fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit).
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  • 7
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    Dynamical quantum tomography (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-06
    Description: We consider quantum state tomography with measurement procedures of the following type: First, we subject the quantum state we aim to identify to a known time evolution for a desired period of time. Afterwards we perform a measurement with a fixed measurement setup. This procedure can then be repeated for other periods of time, the measurement setup however remains unaltered. Given an n -dimensional system with suitable unitary dynamics, we show that any two states can be discriminated by performing a measurement with a setup that has n outcomes at n + 1 points in time. Furthermore, we consider scenarios where prior information restricts the set of states to a subset of lower dimensionality. Given an n -dimensional system with suitable unitary dynamics and a semi-algebraic subset R of its state space, we show that any two states of the subset can be discriminated by performing a measurement with a setup that has n outcomes at l steps of the time evolution if ( n − 1 ) l ≥ 2 dim R . In addition, by going beyond unitary dynamics, we show that one can in fact reduce to a setup with the minimal number of two outcomes.
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  • 8
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    AdS-Carroll branes (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-01
    Description: Coset methods are used to determine the action of a co-dimension one brane (domain wall) embedded in (d + 1)-dimensional AdS space in the Carroll limit in which the speed of light goes to zero. The action is invariant under the non-linearly realized symmetries of the AdS-Carroll spacetime. The Nambu-Goldstone field exhibits a static spatial distribution for the brane with a time varying momentum density related to the brane’s spatial shape as well as the AdS-C geometry. The AdS-C vector field dual theory is obtained.
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  • 9
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    Quantum Hurwitz numbers and Macdonald polynomials (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-01
    Description: Parametric families in the center Z ( C [ S n ]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ -functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of S n generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.
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  • 10
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    Integrable multi-component generalization of a modified short pulse equation (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-12-01
    Description: We propose a multi-component generalization of the modified short pulse (SP) equation which was derived recently as a reduction of Feng’s two-component SP equation. Above all, we address the two-component system in depth. We obtain the Lax pair, an infinite number of conservation laws and multisoliton solutions for the system, demonstrating its integrability. Subsequently, we show that the two-component system exhibits cusp solitons and breathers for which the detailed analysis is performed. Specifically, we explore the interaction process of two cusp solitons and derive the formula for the phase shift. While cusp solitons are singular solutions, smooth breather solutions are shown to exist, provided that the parameters characterizing the solutions satisfy certain conditions. Last, we discuss the relation between the proposed system and existing two-component SP equations.
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