Real-Time Complex Langevin - A Differential Programming Perspective

In this thesis, I aim to find solutions to the NP-hard sign-problem that arises when modeling strongly correlated systems in real-time. I will use the complex Langevin (CLE) method, and address its problem of runaway trajectories and incorrect convergence using an implicit solver and a novel kernel optimization scheme, respectively. The implicit solver stabilizes the numerical solution, making the runaway solution problem a thing of the past. It also acts as a regulator, allowing for simulation along the canonical Schwinger-Keldysh contour. Additionally, our investigation shows that a kernel can act as a regulator as well, resulting in an effective change in the action and integral measure while leaving the path integral measure intact. To restore correct convergence in CLE simulations, we present a novel strategy that involves learning a kernel and utilizing functionals that encode relevant prior information, such as symmetries or Euclidean correlator data. Our approach recovers the correct convergence in the non-interacting theory on the Schwinger-Keldysh contour for any real-time extent. It achieves the correct convergence up to three times the real-time extent of the previous benchmark study for the strongly coupled quantum anharmonic oscillator. Furthermore, we investigate the stability of the CLE by calculating the Lyapunov exponents of the CLE and uncovering that the real-time CLE behaves like a chaotic dynamical system. This has consequences for obtaining a reliable gradient of a loss function that contains a real-time CLE simulation. To address this issue, we adapt the shadowing sensitivity method to a stochastic differential equation (SDE), which allows for calculating a reliable gradient of chaotic SDEs

Towards learning optimized kernels for complex Langevin

We present a novel strategy aimed at restoring correct convergence in complex Langevin simulations. The central idea is to incorporate system-specific prior knowledge into the simulations, in order to circumvent the NP-hard sign problem. In order to do so, we modify complex Langevin using kernels and propose the use of modern auto-differentiation methods to learn optimal kernel values. The optimization process is guided by functionals encoding relevant prior information, such as symmetries or Euclidean correlator data. Our approach recovers correct convergence in the non-interacting theory on the Schwinger-Keldysh contour for any real-time extent. For the strongly coupled quantum anharmonic oscillator we achieve correct convergence up to three-times the real-time extent of the previous benchmark study. An appendix sheds light on the fact that for correct convergence not only the absence of boundary terms, but in addition the correct Fokker-Plank spectrum is crucial

Kernel controlled real-time Complex Langevin simulation

This study explores the utility of a kernel in complex Langevin simulations of quantum real-time dynamics on the Schwinger-Keldysh contour. We give several examples where we use a systematic scheme to find kernels that restore correct convergence of complex Langevin. The schemes combine prior information we know about the system and the correctness of convergence of complex Langevin to construct a kernel. This allows us to simulate up to $1.5\beta$ on the real-time Schwinger-Keldysh contour with the $0+1$ dimensional anharmonic oscillator using $m=1,\lambda=24$, which was previously unattainable using the complex Langevin equation.Comment: 6 pages, 3 figures, talk given at the XVth Quark confinement and the Hadron spectrum conference, Aug. 1st - 6th, 2022, Stavanger, Norway. Date of presentation Aug. 1st 202

Kernel controlled real-time Complex Langevin simulation

This study explores the utility of a kernel in complex Langevin simulations of quantum real-time dynamics on the Schwinger-Keldysh contour. We give several examples where we use a systematic scheme to find kernels that restore correct convergence of complex Langevin. The schemes combine prior information we know about the system and the correctness of convergence of complex Langevin to construct a kernel. This allows us to simulate up to 2β on the real-time Schwinger-Keldysh contour with the 0 + 1 dimensional anharmonic oscillator using m = 1; λ = 24, which was previously unattainable using the complex Langevin equation

Enhancing detectablility of tau-sneutrino signatures using machine learning

In this thesis, the collider signatures of the scenario with a tau-sneutrino next-to-lightest supersymmetric particle (NLSP) at LHC are studied using machine learning. The parameter region of the non-universal Higgs masses model, where the tau-sneutrino is the NLSP, is studied to find a parameter point which satisfies constraints from recent experimental results. We look at the tri-lepton signature from two same sign hadronic taus and a muon. This signature have its main contribution from the slepton and sneutrino pair production channel. The aim is to enhance detectability of this signature by using a deep neural network trained on monte carlo simulated collider events. The best performing deep neural network is a multi class classifier, which is compared to other neural network architectures and a boosted decision tree. The required integrated luminosity for a 5σ significance discovery using √s=13 TeV is found to be L(5σ)= (3.4 ±0.7)⨉10³ 1/fb. We find that the multi class deep neural network performs better by a factor of 2.0 than the traditional optimized cuts

Stable solvers for real-time Complex Langevin

This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue of runaway solution moot, but they also allow us to simulate at comparatively large Langevin time steps, leading to lower computational cost. We compare different ways of regularizing the underlying path integral and estimate the errors introduced due to the finite Langevin time steps. Based on that insight, we implement benchmark (non-)thermal simulations of the quantum anharmonic oscillator on the canonical Schwinger-Keldysh contour of short real-time extent.publishedVersio

Beyond Cuts in Small Signal Scenarios -- Enhanced Sneutrino Detectability Using Machine Learning

We investigate enhancing the sensitivity of new physics searches at the LHC by machine learning in the case of background dominance and a high degree of overlap between the observables for signal and background. We use two different models, XGBoost and a deep neural network, to exploit correlations between observables and compare this approach to the traditional cut-and-count method. We consider different methods to analyze the models' output, finding that a template fit generally performs better than a simple cut. By means of a Shapley decomposition, we gain additional insight into the relationship between event kinematics and the machine learning model output. We consider a supersymmetric scenario with a metastable sneutrino as a concrete example, but the methodology can be applied to a much wider class of supersymmetric models

Distribution of Serogroups and Genotypes among Disease-Associated and Carried Isolates of Neisseria meningitidis from the Czech Republic, Greece, and Norway

The distribution of serogroups and multilocus sequence types (STs) in collections of disease-associated and carried meningococci from the period 1991 to 2000 in three European countries (the Czech Republic, Greece, and Norway) was investigated. A total of 314 patient isolates and 353 isolates from asymptomatic carriers were characterized. The frequency distributions of serogroups and clone complexes differed among countries and between disease and carrier isolate collections. Highly significant differentiation was seen at each housekeeping locus. A marked positive association of serogroup C with disease was evidenced. The ST-11 complex was strongly positively associated with disease; associations for other clone complexes were weaker. The genetic diversity of the clone complexes differed. A single ST dominated the ST-11 clone complex, while the ST-41/44 complex exhibited greater levels of diversity. These data robustly demonstrated differences in the distribution of meningococcal genotypes in disease and carrier isolates and among countries. Further, they indicated that differences in genotype diversity and pathogenicity exist between meningococcal clone complexes