scholarly journals Optimisation of complex integration contours at higher order

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Francis Bursa ◽  
Michael Kroyter
Keyword(s):  
Chemical Potential ◽  
Substantial Reduction ◽  
Space Time ◽  
Phase Factor ◽  
Lattice Size ◽  
Sign Problem ◽  
Complex Integration ◽  
Practical Tool ◽  
Contour Deformation ◽  
The Mean

Abstract We continue our study of contour deformation as a practical tool for dealing with the sign problem using the d-dimensional Bose gas with non-zero chemical potential as a toy model. We derive explicit expressions for contours up to the second order with respect to a natural small parameter and generalise these contours to an ansatz for which the evaluation of the Jacobian is fast (O(1)). We examine the behaviour of the various proposed contours as a function of space-time dimensionality, the chemical potential, and lattice size and geometry and use the mean phase factor as a measure of the severity of the sign problem. In turns out that this method leads to a substantial reduction of the sign problem and that it becomes more efficient as space-time dimensionality is increased. Correlations among contributions to Im 〈S〉 play a key role in determining the mean phase factor and we examine these correlations in detail.

scholarly journals Complex Langevin calculations in QCD at finite density

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Yuta Ito ◽  
Hideo Matsufuru ◽  
Yusuke Namekawa ◽  
Jun Nishimura ◽  
Shinji Shimasaki ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Expansion Method ◽  
Finite Density ◽  
Fermi Sphere ◽  
Expectation Value ◽  
Sign Problem ◽  
Zero Momentum ◽  
Effective Theories ◽  
Severe Sign

Abstract We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with β = 5.7 and four-flavor staggered fermions with degenerate quark mass ma = 0.01 and nonzero quark chemical potential μ. We confirm that a sufficient condition for correct convergence is satisfied for μ/T = 5.2 − 7.2 on a 83 × 16 lattice and μ/T = 1.6 − 9.6 on a 163 × 32 lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to μ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) × 4 (flavor) × 2 (spin) = 24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

scholarly journals Sign problem via imaginary chemical potential

2007 ◽  
Vol 75 (11) ◽  
Author(s):  
K. Splittorff ◽  
B. Svetitsky
Keyword(s):  
Chemical Potential ◽  
Sign Problem

Modification of charge density wave fluctuations by charge perturbations

2002 ◽  
Vol 12 (9) ◽  
pp. 77-78
Author(s):  
S. N. Artemenko
Keyword(s):  
Electric Field ◽  
Linear Response ◽  
Chemical Potential ◽  
Density Wave ◽  
Mean Field ◽  
Phase Fluctuations ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
The Mean ◽  
Field Transition

Spectral density of fluctuations of the CDW phase are calculated taking into account electric field induced by phase fluctuations. The approach based upon the fluctuation-dissipation theorem (FDT) combined with equations of linear response of the CDW conductor is used. Fluctuating electric field is found to suppress fluctuations of the phase, while fluctuations of the electric potential are sizeable. This suggests that transition from the CDW to the normal state (which is usually observed well below the mean-field transition temperature) may he provoked by fluctuations of the chemical potential, rather than by destruction of the CDW coherence between conducting chains due to phase fluctuations.

Noncommutative scalar field in de Sitter space–time and pair creation process

2021 ◽  
Vol 36 (02) ◽  
pp. 2150011
Author(s):  
Nabil Mehdaoui ◽  
Lamine Khodja ◽  
Salah Haouat
Keyword(s):  
Scalar Field ◽  
Chemical Potential ◽  
De Sitter Space ◽  
Space Time ◽  
Pair Creation ◽  
De Sitter ◽  
Creation Process ◽  
Scalar Particles ◽  
Constant Electromagnetic Field

In this work, we address the process of pair creation of scalar particles in [Formula: see text] de Sitter space–time in presence of a constant electromagnetic field by applying the noncommutativity on the scalar field up to first-order in [Formula: see text]. We calculate the density of particles created in the vacuum by the mean of the Bogoliubov transformations. In contrast to a previous result, we show that noncommutativity contributes to the pair creation process. We find that the noncommutativity plays the same role of chemical potential and gives an important interest for studies at high energies.

scholarly journals Locating the critical end point using the linear sigma model coupled to quarks.

2018 ◽  
Vol 172 ◽  
pp. 02003
Author(s):  
Alejandro Ayala ◽  
J. A. Flores ◽  
L. A. Hernández ◽  
S. Hernández-Ortiz
Keyword(s):  
Sigma Model ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Baryon Density ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
End Point ◽  
The Mean

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.

scholarly journals Lefschetz-thimble path integral for solving the mean-field sign problem

2016 ◽  
Author(s):  
Yuya Tanizaki ◽  
Hiromichi Nishimura ◽  
Kouji Kashiwa
Keyword(s):  
Path Integral ◽  
Mean Field ◽  
Sign Problem ◽  
The Mean

On the non-existence of consistent estimates in Galton-Watson processes

1982 ◽  
Vol 19 (4) ◽  
pp. 842-846 ◽  
Author(s):  
Richard Lockhart
Keyword(s):  
Offspring Distribution ◽  
Lattice Size ◽  
Single Realization ◽  
The Mean ◽  
Watson Process ◽  
Mean Variance

Estimation of the offspring distribution from a single realization of a supercritical Galton-Watson process is studied. It is shown that, based on population totals, a parameter of the offspring distribution cannot be estimated unless it is determined by the mean, variance, lattice size and lattice offset of the offspring distribution.

scholarly journals DISORDER INDUCED BCS-BEC CROSSOVER

2012 ◽  
Vol 11 ◽  
pp. 120-126 ◽  
Author(s):  
AYAN KHAN
Keyword(s):  
Order Parameter ◽  
Chemical Potential ◽  
Random Potential ◽  
Mean Field ◽  
Superconducting Order Parameter ◽  
Interesting Issue ◽  
Coupled Equations ◽  
Weak Regime ◽  
The Mean ◽  
Superconducting Fluctuations

Of late, the study of BCS-BEC crossover in the presence of weak random impurity is an interesting issue. In this proceedings we study the effect of this disorder which is included through the Nozières and Smith-Rink theory of superconducting fluctuations. In the weak regime, the random potential leaves an effect on the superconducting order parameter but it spares the chemical potential. Here we present the exact behavior of the mean field quantities as a function of the disorder by self-consistently solving the coupled equations.

Increased teniposide clearance with concomitant anticonvulsant therapy.

1992 ◽  
Vol 10 (2) ◽  
pp. 311-315 ◽  
Author(s):  
D K Baker ◽  
M V Relling ◽  
C H Pui ◽  
M L Christensen ◽  
W E Evans ◽  
...  
Keyword(s):  
High Performance ◽  
Pediatric Patients ◽  
Plasma Concentrations ◽  
Substantial Reduction ◽  
Systemic Exposure ◽  
Pharmacokinetic Interaction ◽  
Lymphocytic Leukemia ◽  
Control Group ◽  
Systemic Clearance ◽  
The Mean

PURPOSE A possible pharmacokinetic interaction between teniposide and anticonvulsant medications was evaluated in pediatric patients. PATIENTS AND METHODS The systemic clearance of teniposide was determined in six pediatric patients with acute lymphocytic leukemia receiving concomitant therapy with anticonvulsants. Clearance was then compared with a control group of patients treated with the same protocol therapy and matched for age at diagnosis, sex, and race but not receiving anticonvulsants or other agents known to induce hepatic metabolism or alter protein binding of drugs. Eight blood samples were obtained during and after 4-hour infusions of teniposide, and plasma concentrations were measured by a specific high-performance liquid chromatography (HPLC) assay. A two-compartment model was fitted to each subject's data. RESULTS The mean systemic clearance (range) for the six anticonvulsant-treated patients studied during 22 courses of therapy was 32 mL/min/m2 (range, 21 to 54 mL/min/m2), significantly higher (P less than .001) than the mean value of 13 mL/min/m2 (range, 7 to 17 mL/min/m2) for the control patients studied during 26 courses of therapy. Clearance estimates for control patients were similar to previously published values for pediatric patients. CONCLUSION These data indicate that the systemic clearance of teniposide is consistently increased two- to three-fold by concomitant phenobarbital or phenytoin therapy. The consequent substantial reduction in systemic exposure may reduce teniposide's efficacy.

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