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Ion-Olimpiu Stamatescu

Publications and source records attributed to Ion-Olimpiu Stamatescu.

At least 37 records · Page 2Linked to original sources

Exploring the phase diagram of QCD with complex Langevin simulations

Simulations of QCD with a finite chemical potential typically lead to a severe sign problem, prohibiting any standard Monte Carlo approach. Complex Langevin simulations provide an alternative to sample path integrals with oscillating weight factors and therefore potentially enable the determination of the phase diagram of QCD. Here we present results for QCD in the limit of heavy quarks and show evidence that the phase diagram can be mapped out by direct simulation. We apply adaptive step-size scaling and adaptive gauge cooling to ensure the convergence of these simulations.

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Adaptive gauge cooling for complex Langevin dynamics

In the case of nonabelian gauge theories with a complex weight, a controlled exploration of the complexified configuration space during a complex Langevin process requires the use of SL(N,C) gauge cooling, in order to minimize the distance from SU(N). Here we show that adaptive gauge cooling can lead to an efficient implementation of this idea. First results for SU(3) Yang-Mills theory in the presence of a nonzero theta-term are presented as well.

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Complex Langevin simulation for QCD-like models

We first test the Complex Langevin method (CLE) on various simple models. We then introduce the method of Gauge Cooling to control the dynamics of the process and ensure thin distributions in the imaginary direction. We finally apply CLE with gauge cooling to a QCD-related lattice model (HQCD) and compare the results by CLE and by a refined Reweighting method (rRW). Very good agreement is found in all regions of physical interest.

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Controlling complex Langevin dynamics at finite density

At nonzero chemical potential the numerical sign problem in lattice field theory limits the use of standard algorithms based on importance sampling. Complex Langevin dynamics provides a possible solution, but it has to be applied with care. In this review, we first summarise our current understanding of the approach, combining analytical and numerical insight. In the second part we study SL(N,C) gauge cooling, which was introduced recently as a tool to control complex Langevin dynamics in nonabelian gauge theories. We present new results in Polyakov chain models and in QCD with heavy quarks and compare various adaptive cooling implementations.

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Stability of complex Langevin dynamics in effective models

The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex Langevin dynamics fails in the disordered phase in the case of the three-dimensional XY model, while it appears to work in the entire phase diagram in the case of the three-dimensional SU(3) spin model. Here we analyse this difference and argue that it is due to the presence of the nontrivial Haar measure in the SU(3) case, which has a stabilizing effect on the complexified dynamics. The freedom to modify and stabilize the complex Langevin process is discussed in some detail.

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Gauge cooling in complex Langevin for QCD with heavy quarks

We employ a new method, "gauge cooling", to stabilize complex Langevin simulations of QCD with heavy quarks. The results are checked against results obtained with reweigthing; we find agreement within the estimated errors. The method allows us to go to previously unaccessible high densities.

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Complex Langevin dynamics: criteria for correctness

The complex Langevin method is a leading candidate for solving the sign problem occurring in various physical situations, notably QCD at finite chemical potential. Its most vexing problem is `convergence to the wrong limit', where the simulation gives a well defined, but incorrect, result. Here, we first outline a formal justification of the method and identify points at which it might fail. From these we derive a condition that must be satisfied in order for correct results to be obtained. We then apply these ideas to the three-imensional SU(3) spin model at finite chemical potential and show strong indications that complex Langevin dynamics yields correct results in this theory.

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Complex Langevin: Etiology and Diagnostics of its Main Problem

The complex Langevin method is a leading candidate for solving the so-called sign problem occurring in various physical situations. Its most vexing problem is that in some cases it produces `convergence to the wrong limit'. In the first part of the paper we go through the formal justification of the method, identify points at which it may fail and identify a necessary and sufficient criterion for correctness. This criterion would, however, require checking infinitely many identities, and therefore is somewhat academic. We propose instead a truncation to the check of a few identities; this still gives a necessary criterion, but a priori it is not clear whether it remains sufficient. In the second part we carry out a detailed study of two toy models: first we identify the reasons why in some cases the method fails, second we test the efficiency of the truncated criterion and find that it works perfectly at least in the toy models studied.

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Adaptive stepsize and instabilities in complex Langevin dynamics

Stochastic quantization offers the opportunity to simulate field theories with a complex action. In some theories unstable trajectories are prevalent when a constant stepsize is employed. We construct algorithms for generating an adaptive stepsize in complex Langevin simulations and find that unstable trajectories are completely eliminated. To illustrate the generality of the approach, we apply it to the three-dimensional XY model at nonzero chemical potential and the heavy dense limit of QCD.

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The Complex Langevin method: When can it be trusted?

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.

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Lattice Landau gauge with stochastic quantisation

We calculate Landau gauge ghost and gluon propagators in pure SU(2) lattice gauge theory in two, three and four dimensions. The gauge fixing method we use, sc. stochastic quantisation, serves as a viable alternative approach to standard gauge fixing algorithms. We also investigate the spectrum of the Faddeev-Popov operator. At insufficiently accurate gauge fixing, we find evidence that stochastic quantisation samples configurations close to the Gribov horizon. Standard gauge fixing does so only at specific parameters; otherwise, there is a clear difference. However, this difference disappears if the gauge is fixed to sufficient accuracy. In this case, we confirm previous lattice results for the gluon and ghost propagator in two, three and four dimensions.

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Scalar Field Theory with a Non-Standard Potential

We study the phase structure of a 4D complex scalar field theory with a potential V(Phi) = | Lambda^3 / Phi - Lambda Phi |^2 at zero and at finite temperature. The model is analyzed by mean field and Monte Carlo methods. At zero temperature the theory falls in the universality class of the 4D Ising model when varying Lambda. The situation is less clear-cut for variations w.r.t. Lambda at large temperatures and variations w.r.t. temperature at a given value of Lambda. We observe temperature independence of the mass of the first excitation.

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Stochastic quantization at nonzero chemical potential

Lattice QCD at finite chemical potential is difficult due to the sign problem. We use stochastic quantization and complex Langevin dynamics to study this issue. First results for QCD in the hopping expansion are encouraging. U(1) and SU(3) one link models are used to gain further insight into why the method appears to be successful.

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Stochastic quantization at finite chemical potential

A nonperturbative lattice study of QCD at finite chemical potential is complicated due to the complex fermion determinant and the sign problem. Here we apply the method of stochastic quantization and complex Langevin dynamics to this problem. We present results for U(1) and SU(3) one link models and QCD at finite chemical potential using the hopping expansion. The phase of the determinant is studied in detail. Even in the region where the sign problem is severe, we find excellent agreement between the Langevin results and exact expressions, if available. We give a partial understanding of this in terms of classical flow diagrams and eigenvalues of the Fokker-Planck equation.

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Learning with incomplete information - and the mathematical structure behind it

Learning and the ability to learn are important factors in development and evolutionary processes [1]. Depending on the level, the complexity of learning can strongly vary. While associative learning can explain simple learning behaviour [1,2] much more sophisticated strategies seem to be involved in complex learning tasks. This is particularly evident in machine learning theory [3] (reinforcement learning [4], statistical learning [5]), but it equally shows up in trying to model natural learning behaviour [2]. A general setting for modelling learning processes in which statistical aspects are relevant is provided by the neural network (NN) paradigm. This is in particular of interest for natural, learning by experience situations. NN learning models can incorporate elementary learning mechanisms based on neuro-physiological analogies, such as the Hebb rule, and lead to quantitative results concerning the dynamics of the learning process [6]. The Hebb rule, however, cannot be directly applied in all cases, and in particular for realistic problems, such as "delayed reinforcement" [4,6], the sophistication of the algorithms rapidly increases. We want to present here a model which can cope with such non trivial tasks, while still being elementary and based only on procedures which one may think of as natural, without any appeal to higher strategies [7]. We can show the capability of this model to provide good learning in many, very different settings [7,8,9]. It may help therefore understanding some basic features of learning.

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The high density region of QCD in a large mass and chemical potential model

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion. The model still acknowledges the sign problem peculiar to non-zero chemical potential, but it permits the development of refined algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model, including the most explicit form of the resumed expansion, and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density.

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Contribution of disconnected diagrams to the hyperfine splitting of charmonium

We discuss the contribution of OZI-suppressed diagrams to the hyperfine splitting of charmonium in lattice QCD. We study valence quark mass regions from strange to charm quark masses. No contribution of the disconnected diagram is seen in the vector meson channel. In the pseudo-scalar channel and for valence quark masses around the strange quark, the disconnected contribution induces a considerable increase of the meson mass. This contribution quickly decreases as the quark mass increases. For charmonium the effect is very small although a decrease of the pseudoscalar mass induced by the disconnected contribution cannot be ruled out.

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