scholarly journals Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

2022 ◽  
Author(s):  
Ding Jia
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Quantum Gravity ◽  
Path Integrals ◽  
Gradient Flow ◽  
Classical Solutions ◽  
Integration Contour ◽  
Sign Problem ◽  
Flow Algorithm ◽  
Bonnet Theorem

Abstract Evaluating gravitational path integrals in the Lorentzian has been a long-standing challenge due to the numerical sign problem. We show that this challenge can be overcome in simplicial quantum gravity. By deforming the integration contour into the complex, the sign fluctuations can be suppressed, for instance using the holomorphic gradient flow algorithm. Working through simple models, we show that this algorithm enables efficient Monte Carlo simulations for Lorentzian simplicial quantum gravity. In order to allow complex deformations of the integration contour, we provide a manifestly holomorphic formula for Lorentzian simplicial gravity. This leads to a complex version of simplicial gravity that generalizes the Euclidean and Lorentzian cases. Outside the context of numerical computation, complex simplicial gravity is also relevant to studies of singularity resolving processes with complex semi-classical solutions. Along the way, we prove a complex version of the Gauss-Bonnet theorem, which may be of independent interest.

scholarly journals Worldvolume approach to the tempered Lefschetz thimble method

2021 ◽  
Author(s):  
Masafumi Fukuma ◽  
Nobuyuki Matsumoto
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Matrix Model ◽  
Random Matrix ◽  
Gradient Flow ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo ◽  
Random Matrix Model ◽  
Sign Problem ◽  
Multimodal Problems

Abstract As a solution towards the numerical sign problem, we propose a novel Hybrid Monte Carlo algorithm, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow (“the worldvolume of an integration surface”). This is an extension of the tempered Lefschetz thimble method (TLTM), and solves the sign and multimodal problems simultaneously as the original TLTM does. Furthermore, in this new algorithm, one no longer needs to compute the Jacobian of the gradient flow in generating a configuration, and only needs to evaluate its phase upon measurement. To demonstrate that this algorithm works correctly, we apply the algorithm to a chiral random matrix model, for which the complex Langevin method is known not to work.

Numerical Methods for the Kinetic Theory of Fluids

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Numerical Methods ◽  
Kinetic Theory ◽  
Computational Efficiency ◽  
Lattice Boltzmann ◽  
Direct Simulation Monte Carlo ◽  
Particle Methods ◽  
Direct Simulation ◽  
Simulation Monte Carlo

This chapter provides a bird’s eye view of the main numerical particle methods used in the kinetic theory of fluids, the main purpose being of locating Lattice Boltzmann in the broader context of computational kinetic theory. The leading numerical methods for dense and rarified fluids are Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC), respectively. These methods date of the mid 50s and 60s, respectively, and, ever since, they have undergone a series of impressive developments and refinements which have turned them in major tools of investigation, discovery and design. However, they are both very demanding on computational grounds, which motivates a ceaseless demand for new and improved variants aimed at enhancing their computational efficiency without losing physical fidelity and vice versa, enhance their physical fidelity without compromising computational viability.

scholarly journals Quantum channels in quantum gravity

2014 ◽  
Vol 23 (12) ◽  
pp. 1442009 ◽  
Author(s):  
Mukund Rangamani ◽  
Massimilliano Rota
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Quantum Gravity ◽  
Path Integrals ◽  
Quantum Channels ◽  
Hole Formation ◽  
Integral Formalism ◽  
Final State ◽  
State Boundary ◽  
Gauge Gravity

The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this proposal can be embedded in the gauge/gravity context by invoking a path integral formalism inspired by the Schwinger–Keldysh like thermo-field double construction in the dual field theory. This allows us to realize the gravitational quantum channels for information retrieval to specific deformations of the field theory path integrals and opens up new connections between geometry and information theory.

TACKLING THE SIGN PROBLEM

1994 ◽  
Vol 05 (02) ◽  
pp. 275-277
Author(s):  
T D Kieu ◽  
C J Griffin
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
New Approach ◽  
Statistical Errors ◽  
Sign Problem ◽  
Complex Valued ◽  
1D Complex

To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. The 1D complex-coupling Ising model is employed as an illustration.

Solitons propagation dynamics in a saturable PT-symmetric fractional medium

2021 ◽  
Author(s):  
Davood Hajitaghi Tehrani ◽  
Mehdi Solaimani ◽  
Mahboubeh Ghalandari ◽  
Bahman Babayar Razlighi
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Physical Properties ◽  
Maximum Intensity ◽  
Step Method ◽  
Saturation Parameter ◽  
Potential Depth ◽  
Fractional System ◽  
Nonlinear Fractional Schrödinger Equation ◽  
Good Agreement

Abstract In the current research, the propagation of solitons in a saturable PT-symmetric fractional system is studied by solving nonlinear fractional Schrödinger equation. Three numerical methods are employed for this purpose, namely Monte Carlo based Euler-Lagrange variational schema, split-step method, and extrapolation approach. The results show good agreement and accuracy. The effect of different parameters such as potential depth, Levy indices, and saturation parameter, on the physical properties of the systems such as maximum intensity and soliton width oscillations are considered.

Novel use of the Monte-Carlo methods to visualize singularity configurations in serial manipulators

2021 ◽  
Vol 15 (2) ◽  
pp. 7948-7963
Author(s):  
Mohamed Aboelnasr ◽  
Hussein M Bahaa ◽  
Ossama Mokhiamar
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Curve Fitting ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Graphical Methods ◽  
Kinematic Singularity ◽  
Serial Manipulators ◽  
Serial Robots ◽  
Contour Plots

This paper analyses the problem of the kinematic singularity of 6 DOF serial robots by extending the use of Monte-Carlo numerical methods to visualize singularity configurations. To achieve this goal, first, forward kinematics and D-H parameters have been derived for the manipulator. Second, the derived equations are used to generate and visualize a workspace that gives a good intuition of the motion shape of the manipulator. Third, the Jacobian matrix is computed using graphical methods, aiming to locate positions that cause singularity. Finally, the data obtained are processed in order to visualize the singularity and to design a trajectory free of singularity. MATLAB robotics toolbox, Symbolic toolbox, and curve fitting toolbox are the MATLAB toolboxes used in the calculations. The results of the surface and contour plots of the determinate of the Jacobian matrix behavior lead to design a manipulator’s trajectory free of singularity and show the parameters that affect the manipulator’s singularity and its behavior in the workspace.

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