Color-Kinematics Duality for QCD Amplitudes

We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n-3)!(2k-2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD.Comment: 33 pages + refs, 7 figures, 4 tables; v3 minor corrections, journal versio

Pure Gravities via Color-Kinematics Duality for Fundamental Matter

We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.Comment: 48 pages + refs, 15 figures, 3 tables; v2 minor corrections, journal versio

Cavity QED in superconducting circuits: susceptibility at elevated temperatures

We study the properties of superconducting electrical circuits, realizing cavity QED. In particular we explore the limit of strong coupling, low dissipation, and elevated temperatures relevant for current and future experiments. We concentrate on the cavity susceptibility as it can be directly experimentally addressed, i.e., as the impedance or the reflection coefficient of the cavity. To this end we investigate the dissipative Jaynes-Cummings model in the strong coupling regime at high temperatures. The dynamics is investigated within the Bloch-Redfield formalism. At low temperatures, when only the few lowest levels are occupied the susceptibility can be presented as a sum of contributions from independent level-to-level transitions. This corresponds to the secular (random phase) approximation in the Bloch-Redfield formalism. At temperatures comparable to and higher than the oscillator frequency, many transitions become important and a multiple-peak structure appears. We show that in this regime the secular approximation breaks down, as soon as the peaks start to overlap. In other words, the susceptibility is no longer a sum of contributions from independent transitions. We treat the dynamics of the system numerically by exact diagonalization of the Hamiltonian of the qubit plus up to 200 states of the oscillator. We compare the results obtained with and without the secular approximation and find a qualitative discrepancy already at moderate temperatures.Comment: 7 pages, 6 figure

Janossy Densities of Coupled Random Matrices

We explicitly calculate Janossy densities for a special class of finite determinantal point processes with several types of particles introduced by Pr\"ahofer and Spohn and, in the full generality, by Johansson in connection with the analysis of polynuclear growth models. The results of our paper generalize the theorem we proved earlier with Borodin about the Janossy densities in biorthogonal ensembles. In particular, our results can be applied to coupled random matrices.Comment: We revised the introduction and added a couple of new reference

Swarm Bug Algorithms for Path Generation in Unknown Environments

In this paper, we consider the problem of a swarm traveling between two points as fast as possible in an unknown environment cluttered with obstacles. Potential applications include search-and-rescue operations where damaged environments are typical. We present swarm generalizations, called SwarmCom, SwarmBug1, and SwarmBug2, of the classical path generation algorithms Com, Bug1, and Bug2. These algorithms were developed for unknown environments and require low computational power and memory storage, thereby freeing up resources for other tasks. We show the upper bound of the worst-case travel time for the first agent in the swarm to reach the target point for SwarmBug1. For SwarmBug2, we show that the algorithm underperforms in terms of worst-case travel time compared to SwarmBug1. For SwarmCom, we show that there exists a trivial scene for which the algorithm will not halt, and it thus has no performance guarantees. Moreover, by comparing the upper bound of the travel time for SwarmBug1 with a universal lower bound for any path generation algorithm, it is shown that in the limit when the number of agents in the swarm approaches infinity, no other algorithm has strictly better worst-case performance than SwarmBug1 and the universal lower bound is tight.Comment: Accepted for IEEE Conference on Decision and Control, Dec. 13-15, 2023, Singapor

Large-Scale Multi-Fleet Platoon Coordination: A Dynamic Programming Approach

Truck platooning is a promising technology that enables trucks to travel in formations with small inter-vehicle distances for improved aerodynamics and fuel economy. The real-world transportation system includes a vast number of trucks owned by different fleet owners, for example, carriers. To fully exploit the benefits of platooning, efficient dispatching strategies that facilitate the platoon formations across fleets are required. This paper presents a distributed framework for addressing multi-fleet platoon coordination in large transportation networks, where each truck has a fixed route and aims to maximize its own fleet's platooning profit by scheduling its waiting times at hubs. The waiting time scheduling problem of individual trucks is formulated as a distributed optimal control problem with continuous decision space and a reward function that takes non-zero values only at discrete points. By suitably discretizing the decision and state spaces, we show that the problem can be solved exactly by dynamic programming, without loss of optimality. Finally, a realistic simulation study is conducted over the Swedish road network with $5,000$ trucks to evaluate the profit and efficiency of the approach. The simulation study shows that, compared to single-fleet platooning, multi-fleet platooning provided by our method achieves around $15$ times higher monetary profit and increases the CO$_2$ emission reductions from $0.4\%$ to $5.5\%$. In addition, it shows that the developed approach can be carried out in real-time and thus is suitable for platoon coordination in large transportation systems.Comment: IEEE Transactions on Intelligent Transportation Systems, accepte

Random Words, Toeplitz Determinants and Integrable Systems. I

It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles subject to an overall constraint that the eigenvalues lie in a hyperplane.Comment: 15 pages, no figure

Hub-Based Platoon Formation: Optimal Release Policies and Approximate Solutions

This paper studies the optimal hub-based platoon formation at hubs along a highway under decentralized, distributed, and centralized policies. Hubs are locations along highways where trucks can wait for other trucks to form platoons. A coordinator at each hub decides the departure time of trucks, and the released trucks from the hub will form platoons. The problem is cast as an optimization problem where the objective is to maximize the platooning reward. We first show that the optimal release policy in the decentralized case, where the hubs do not exchange information, is to release all trucks at the hub when the number of trucks exceeds a threshold computed by dynamic programming. We develop efficient approximate release policies for the dependent arrival case using this result. To study the value of information exchange among hubs on platoon formation, we next study the distributed and centralized platoon formation policies which require information exchange among hubs. To this end, we develop receding horizon solutions for the distributed and centralized platoon formation at hubs using the dynamic programming technique. Finally, we perform a simulation study over three hubs in northern Sweden. The profits of the decentralized policies are shown to be approximately 3.5% lower than the distributed policy and 8% lower than the centralized release policy. This observation suggests that decentralized policies are prominent solutions for hub-based platooning as they do not require information exchange among hubs and can achieve a similar performance compared with distributed and centralized policies.Comment: Accepted for T-ITS 202