Exact Zero Vacuum Energy in twisted SU(N) Principal Chiral Field

We present a finite set of equations for twisted PCF model. At the special twist in the root of unity we demonstrate that the vacuum energy is exactly zero at any size L. Also in SU(2) case we numerically calculate the energy of the single particle state with zero rapidity, as a function of L.Comment: 5 pages, 3 figure

On the Marginal Cost of Road Congestion: an Evaluation Method with Application to the Paris Region

The paper analyzes the sensitivity of the marginal congestion cost on a roadway network to the level of aggregation in space, from utmost disaggregate to utmost aggregate. Simulation and aggregation are based on a static network assignment model.Marginal cost ; Road congestion ; Cost aggregation ; Congestion indicator ; Assignment model

Six-loop Konishi anomalous dimension from the Y-system

We compute the Konishi anomalous dimension perturbatively up to six loop using the finite set of functional equations derived recently by Gromov, Kazakov, Leurent and Volin. The recursive procedure can be in principle extended to higher loops, the only obstacle being the complexity of the computation.Comment: 5 pages, 1 figure, version 2 : published versio

The Theory and Practice of a Dual Criteria Assignment Model with a continuously distributed Value-of-Time

24 pagesInternational audienceA dual criteria assignment model enables an analyst to represent disaggregate trade-offs between two cost criteria in the trip-makers' route choices, e.g. time and price in the cost vs. time model in which a continuously distributed value-of-time (VOT) is assumed. This paper develops the theory and practice of dual criteria assignment. First, the economic background of the model is set out: it enables the analyst to represent various route choice behaviors, variable demand, several user classes, flow-dependent travel time and capacity constraints. Second, the mathematical framework is introduced; due to a special transformation, the model is cast into a variational inequality which under some assumptions reduces to a convex minimisation program. Third, solution algorithms are introduced and compared. Fourth, econometric tools are provided to estimate the distribution of the VOT and to evaluate the uncertainty about the predicted revenue of a toll road, arising from the uncertainty about the distribution of the VOT. It is shown that these tools ensure the practicality of a dual criteria assignment in a medium-sized application

Modelling a vehicle-sharing station as a dual waiting system: stochastic framework and stationary analysis

19 pagesA waiting system with two kinds of resources, say the vehicles and the docks in a vehicle-sharing service, is considered. Two arrival flows of customers are assumed, access customers who require a vehicle versus egress customers that bring back their vehicle and require a dock at the station. The total number of docks sets a limit capacity for the service. A stochastic, markovian, state-transition model is defined, which constitutes a bi-sided capacitated queuing system. The balance equations are stated and solved, yielding a stationary distribution under two conditions of compatibility. Indicators of service quality and system performance are defined and formulated under steady state

Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.Comment: 6 pages, CDC 2019. Website: https://eleurent.github.io/interval-prediction

Quantum spectral curve for arbitrary state/operator in AdS5_5/CFT4_4

We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system -- a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.Comment: 96 pages, 15 figures; Some mathematica examples added in v2; Published version is v

The master T-operator for the Gaudin model and the KP hierarchy

Following the approach of [arXiv:1112.3310], we construct the master T -operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. We also characterize the class of solutions to the KP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum Gaudin model and the classical Calogero-Moser system of particles.Comment: 56 pages, v2: details added in appendix C, v3: published versio