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.

scholarly journals Instability in the molecular dynamics step of a hybrid Monte Carlo algorithm in dynamical fermion lattice QCD simulations

2000 ◽  
Vol 62 (11) ◽  
Author(s):  
Bálint Joó ◽  
Brian Pendleton ◽  
Anthony D. Kennedy ◽  
Alan C. Irving ◽  
James C. Sexton ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Lattice Qcd ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo

scholarly journals Tuning the hybrid Monte Carlo algorithm using molecular dynamics forces’ variances

2019 ◽  
Vol 234 ◽  
pp. 179-187 ◽  
Author(s):  
A. Bussone ◽  
M. Della Morte ◽  
V. Drach ◽  
C. Pica
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo

scholarly journals ACCEPTANCES AND AUTOCORRELATIONS IN THE HYBRID MONTE CARLO ALGORITHM

1992 ◽  
Vol 03 (01) ◽  
pp. 43-52 ◽  
Author(s):  
SOURENDU GUPTA
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Quark Mass ◽  
Monte Carlo Algorithm ◽  
Xy Model ◽  
Acceptance Probability ◽  
Hybrid Monte Carlo ◽  
Lattice Size

The acceptance probability in Hybrid Monte Carlo simulations of QCD, in particular, its dependence on the lattice size, quark mass and the coupling, is discussed. Results on the tuning of parameters required in order to achieve low autocorrelations in the 2-d XY model are presented. In both phases of this model, the dynamical critical exponent is close to 2 for runs with trajectory lengths between 1 and 3 molecular dynamics units.

scholarly journals Extremal correlators and random matrix theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Alba Grassi ◽  
Zohar Komargodski ◽  
Luigi Tizzano
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Matrix Model ◽  
Effective Field Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Effective Field ◽  
Random Matrix Model ◽  
Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

scholarly journals Testing a Fourier-accelerated hybrid Monte Carlo algorithm

2002 ◽  
Vol 528 (3-4) ◽  
pp. 301-305 ◽  
Author(s):  
Simon Catterall ◽  
Sergey Karamov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo

scholarly journals COMPARISON OF UPDATE ALGORITHMS FOR PURE GAUGE SU(3)

1988 ◽  
Vol 03 (14) ◽  
pp. 1367-1378 ◽  
Author(s):  
RAJAN GUPTA ◽  
GREGORY W. KILCUP ◽  
APOORVA PATEL ◽  
STEPHEN R. SHARPE ◽  
PHILIPPE DE FORCRAND
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo ◽  
Pure Gauge

We show that the overrelaxed algorithm of Creutz and of Brown and Woch is the optimal local update algorithm for simulation of pure gauge SU(3). Our comparison criterion includes computer efficiency and decorrelation times. We also investigate the rate of decorrelation for the Hybrid Monte Carlo algorithm.

scholarly journals Asymptotics of the partition function of a random matrix model

2005 ◽  
Vol 55 (6) ◽  
pp. 1943-2000 ◽  
Author(s):  
Pavel M. Bleher ◽  
Alexander Its
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Random Matrix ◽  
Random Matrix Model

scholarly journals Computational Prediction of Heteromeric Protein Complex Disassembly Order with Hybrid Monte Carlo/Molecular Dynamics Simulation

2022 ◽  
Author(s):  
Ikuo Kurisaki ◽  
Shigenori Tanaka
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Protein Complex ◽  
Protein Complexes ◽  
Structural Bioinformatics ◽  
Dynamics Simulation ◽  
Tryptophan Synthase ◽  
Selection Scheme ◽  
Hybrid Monte Carlo ◽  
Multimeric Protein

The physicochemical entity of biological phenomenon in the cell is a network of biochemical reactions and the activity of such a network is regulated by multimeric protein complexes. Mass spectroscopy (MS) experiments and multimeric protein docking simulations based on structural bioinformatics techniques have revealed the molecular-level stoichiometry and static configuration of subcomplexes in their bound forms, then revealing the subcomplex populations and formation orders. Meanwhile, these methodologies are not designed to straightforwardly examine temporal dynamics of multimeric protein assembly and disassembly, essential physicochemical properties to understand functional expression mechanisms of proteins in the biological environment. To address the problem, we had developed an atomistic simulation in the framework of the hybrid Monte Carlo/Molecular Dynamics (hMC/MD) method and succeeded in observing disassembly of homomeric pentamer of the serum amyloid P component protein in experimentally consistent order. In this study, we improved the hMC/MD method to examine disassembly processes of the tryptophan synthase tetramer, a paradigmatic heteromeric protein complex in MS studies. We employed the likelihood-based selection scheme to determine a dissociation-prone subunit pair at each hMC/MD simulation cycle and achieved highly reliable predictions of the disassembly orders with the success rate over 0.9 without a priori knowledge of the MS experiments and structural bioinformatics simulations. We similarly succeeded in reliable predictions for the other three tetrameric protein complexes. These achievements indicate the potential availability of our hMC/MD approach as the general purpose methodology to obtain microscopic and physicochemical insights into multimeric protein complex formation.

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