Computational Soundness Results for Stateful Applied pi Calculus

In recent years, many researches have been done to establish symbolic models of stateful protocols. Two works among them, the SAPIC tool and StatVerif tool, provide a high-level specification language and an automated analysis. Their language, the stateful applied \pi-calculus, is extended from the applied \pi-calculus by defining explicit state constructs. Symbolic abstractions of cryptography used in it make the analysis amenable to automation. However, this might overlook the attacks based on the algebraic properties of the cryptographic algorithms. In our paper, we establish the computational soundness results for stateful applied \pi-calculus used in SAPIC tool and StatVerif tool. In our approach, we build our results on the CoSP framework. For SAPIC, we embed the non-monotonic protocol states into the CoSP protocols, and prove that the resulting CoSP protocols are efficient. Through the embedding, we provide the computational soundness result for SAPIC (by Theorem 1). For StatVerif, we encode the StatVerif process into a subset of SAPIC process, and obtain the computational soundness result for StatVerif (by Theorem 2). Our encoding shows the differences between the semantics of the two languages. Our work inherits the modularity of CoSP, which allows for easily extending the proofs to specific cryptographic primitives. Thus we establish a computationally sound automated verification result for the input languages of SAPIC and StatVerif that use public-key encryption and signatures (by Theorem 3).Comment: to appear in POST 201

Non-standard interactions and the CP phase measurements in neutrino oscillations at low energies

We study the effects of non-standard interactions (NSI) and the genuine CP phase $\delta_D$ in neutrino oscillations at low, E_\nu \lesssim 1\,\mbox{GeV}, and very low, E_\nu \lesssim 0.1\,\mbox{GeV}, energies. For experimental setup with baseline and neutrino energy tuned to the first 1-3 oscillation maximum, we develop a simple analytic formalism to show the effects of NSI. The vacuum mimicking and its violation as well as the use of the separation basis play a central role in our formalism. The NSI corrections that affect the CP phase measurement mainly come from the violation of vacuum mimicking as well as from the corrections to the 1-3 mixing angle and mass-squared difference. We find that the total NSI correction to the $\nu_\mu - \nu_e$ probability $P_{\mu e}$ can reach $20\% - 30\%$ ($1 \sigma$) at T2(H)K. Correspondingly, the correction to the CP phase can be as large as $50^\circ$ and hence significantly deteriorates the CP sensitivity at T2(H)K. The proposed TNT2K experiment, a combination of T2(H)K and the short baseline experiment $\mu$Kam that uses the Super-K/Hyper-K detector at Kamioka to measure the oscillation of the antineutrinos from muon decay at rest ($\mu$DAR), can substantially reduce the degeneracy between NSI and the genuine CP phase $\delta_D$ to provide high CP sensitivity. The NSI correction to $P_{\mu e}$ is only $2\%$ ($1 \sigma$) for $\mu$DAR neutrinos.Comment: The signs of the CP phases in analytic expressions are changed while the conclusions are unchange

Harnack Inequalities for Stochastic (Functional) Differential Equations with Non-Lipschitzian Coefficients

By using coupling arguments, Harnack type inequalities are established for a class of stochastic (functional) differential equations with multiplicative noises and non-Lipschitzian coefficients. To construct the required couplings, two results on existence and uniqueness of solutions on an open domain are presented.Comment: 22 page

Hyperscaling violating black hole solutions and Magneto-thermoelectric DC conductivities in holography

We derive new black hole solutions in Einstein-Maxwell-Axion-Dilaton theory with a hyperscaling violation exponent. We then examine the corresponding anomalous transport exhibited by cuprate strange metals in the normal phase of high-temperature superconductors via gauge/gravity duality. Linear temperature dependence resistivity and quadratic temperature dependence inverse Hall angle can be achieved. In the high temperature regime, the heat conductivity and Hall Lorenz ratio are proportional to the temperature. The Nernst signal first increases as temperature goes up but it then decreases with increasing temperature in the high temperature regime.Comment: 10 pages, two figures, major revision, published versio

Linear and quadratic in temperature resistivity from holography

We present a new black hole solution in the asymptotic Lifshitz spacetime with a hyperscaling violating factor. A novel computational method is introduced to compute the DC thermoelectric conductivities analytically. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario.Comment: 1+26 pages, 2 figures, major revision; perturbation of the auxiliary field considered; a new method was developed to compute the dc conductivities; published in JHE

Some Spectral Properties and Characterizations of Connected Odd-bipartite Uniform Hypergraphs

A $k$-uniform hypergraph $G=(V,E)$ is called odd-bipartite ([5]), if $k$ is even and there exists some proper subset $V_1$ of $V$ such that each edge of $G$ contains odd number of vertices in $V_1$. Odd-bipartite hypergraphs are generalizations of the ordinary bipartite graphs. We study the spectral properties of the connected odd-bipartite hypergraphs. We prove that the Laplacian H-spectrum and signless Laplacian H-spectrum of a connected $k$-uniform hypergraph $G$ are equal if and only if $k$ is even and $G$ is odd-bipartite. We further give several spectral characterizations of the connected odd-bipartite hypergraphs. We also give a characterization for a connected $k$-uniform hypergraph whose Laplacian spectral radius and signless Laplacian spectral radius are equal, thus provide an answer to a question raised in [9]. By showing that the Cartesian product $G\Box H$ of two odd-bipartite $k$-uniform hypergraphs is still odd-bipartite, we determine that the Laplacian spectral radius of $G\Box H$ is the sum of the Laplacian spectral radii of $G$ and $H$, when $G$ and $H$ are both connected odd-bipartite.Comment: 16 page

First law of black hole mechanics in variable background fields

It is well known that in general theories of gravity with the diffeomorphism symmetry, the black hole entropy is a Noether charge. But what will happen if the symmetry is explicitly broken? By investigating the covariant first law of black hole mechanics with background fields, we show that the Noether entropy is still applicable due to the local nature of the black hole entropy. Moreover, motivated by the proposal that the cosmological constant behaves as a thermodynamic variable, we allow the non-dynamical background fields to be varied. To illustrate this general formalism, we study a generic static black brane in the massive gravity. Using the first law and the scaling argument, we obtain two Smarr formulas. We show that both of them can be retrieved without relying on the first law, hence providing a self-consistent check of the theory.Comment: 15 pages, presentation improved, clarifications and references adde

Holographic RG flow of thermo-electric transports with momentum dissipation

We construct the holographic renormalization group (RG) flow of thermo-electric conductivities when the translational symmetry is broken. The RG flow is probed by the intrinsic observers hovering on the sliding radial membranes. We obtain the RG flow by solving a matrix-form Riccati equation. The RG flow provides a high-efficient numerical method to calculate the thermo-electric conductivities of strongly coupled systems with momentum dissipation. As an illustration, we recover the AC thermo-electric conductivities in the Einstein-Maxwell-axion model. Moreover, in several homogeneous and isotropic holographic models which dissipate the momentum and have the finite density, it is found that the RG flow of a particular combination of DC thermo-electric conductivities does not run. As a result, the DC thermal conductivity on the boundary field theory can be derived analytically, without using the conserved thermal current.Comment: 27 pages, 6 figures, typo corrected, a ref adde

Brane worlds in critical gravity

Recently, Lu and Pope proposed critical gravities in [Phys. Rev. Lett. 106, 181302 (2011)]. In this paper we construct analytic brane solutions in critical gravity with matter. The Gibbons-Hawking surface term and junction condition are investigated, and the thin and thick brane solutions are obtained. All these branes are embedded in five-dimensional anti-de Sitter spacetimes. Our solutions are stable against scalar perturbations, and the zero modes of scalar perturbations cannot be localized on the branes.Comment: 8 pages, no figures, investigation of Gibbons-Hawking surface term and junction condition added, revised version to be published in Phys. Rev.

Collective diffusion and quantum chaos in holography

We define a particular combination of charge and heat currents that is decoupled with the heat current. This `heat-decoupled' (HD) current can be transported by diffusion at long distances, when some thermo-electric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z=2. In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.Comment: v4: 26 pages, 1 figure, major revisio