Entropy production and isotropization in Yang-Mills theory with use of quantum distribution function

We investigate thermalization process in relativistic heavy ion collisions in terms of the Husimi-Wehrl (HW) entropy defined with the Husimi function, a quantum distribution function in a phase space. We calculate the semiclassical time evolution of the HW entropy in Yang-Mills field theory with the phenomenological initial field configuration known as the McLerran-Venugopalan model in a non-expanding geometry, which has instabilty triggered by initial field fluctuations. HW-entropy production implies the thermalization of the system and it reflects the underlying dynamics such as chaoticity and instability. By comparing the production rate with the Kolmogorov-Sina\"i rate, we find that the HW entropy production rate is significantly larger than that expected from chaoticity. We also show that the HW entropy is finally saturated when the system reaches a quasi-stationary state. The saturation time of the HW entropy is comparable with that of pressure isotropization, which is around $1$ fm/c in the present calculation in the non-expanding geometry.Comment: 17 pages, 5 figure

Study of entropy production in Yang-Mills theory with use of Husimi function

Understanding the thermalization process in a pure quantum system is a challenge in theoretical physics. In this work, we explore possible thermalization mechanism in Yang-Mills(YM) theory by using a positive semi-definite quantum distribution function called a Husimi function which is given by a coarse graining of the Wigner function within the minimum uncertainty. Then entropy is defined in terms of the Husimi function, which is called the Husimi-Wehrl(HW) entropy. We propose two numerical methods to calculate the HW entropy. We find that it is feasible to apply the semi-classical approximation with the use of classical YM equation. It should be noted that the semi-classical approximation is valid in the systems of physical interest including the early stage of heavy-ion collisions. Using a product ansatz for the Husimi function, which is confirmed to reproduce the HW entropy within 20% error (overestimate) for a few-body quantum system, we succeed in a numerical evaluation of HW entropy of YM fields and show that it surely has a finite value and increases in time.Comment: 7 pages, 5 figures, Proceeding of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International Conference Center, Kobe, Japa

Entropy production in quantum Yang-Mills mechanics in semi-classical approximation

We discuss thermalization of isolated quantum systems by using the Husimi-Wehrl entropy evaluated in the semiclassical treatment. The Husimi-Wehrl entropy is the Wehrl entropy obtained by using the Husimi function for the phase space distribution. The time evolution of the Husimi function is given by smearing the Wigner function, whose time evolution is obtained in the semiclassical approximation. We show the efficiency and usefullness of this semiclassical treatment in describing entropy production of a couple of quantum mechanical systems, whose classical counter systems are known to be chaotic. We propose two methods to evaluate the time evolution of the Husimi-Wehrl entropy, the test-particle method and the two-step Monte-Carlo method. We demonstrate the characteristics of the two methods by numerical calculations, and show that the simultaneous application of the two methods ensures the reliability of the results of the Husimi-Wehrl entropy at a given time.Comment: 11 pages, 8 figure

Prediction of cavitation and induced erosion inside a high-pressure fuel pump

The operation of a high-pressure, piston-plunger fuel pump, oriented for use in the common rail circuit of modern Diesel engines for providing fuel to the injectors is investigated in the present study from a numerical perspective. Both the suction and pressurization phases of the pump stroke were simulated with the overall flow time be-ing in the order of 12•10-3 s. The topology of the cavitating flow within the pump con-figuration was captured through the use of an Equation of State (EoS) implemented in the framework of a barotropic, homogeneous equilibrium model. Cavitation was found to set in within the pressure chamber as early as 0.2•10-3 s in the operating cycle, while the minimum liquid volume fraction detected was in the order of 60% during the sec-ond period of the valve opening. Increase of the in-cylinder pressure during the final stages of the pumping stroke lead to the collapse of the previously arisen cavitation structures and three layout locations, namely the piston edge, the valve/valve-seat re-gion and the outlet orifice, were identified as vulnerable to cavitation-induced erosion through the use of cavitation-aggressiveness indicators

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Depsipeptide substrates for sortase-mediated N-terminal protein ligation

Technologies that allow the efficient chemical modification of proteins under mild conditions are widely sought after. Sortase-mediated peptide ligation provides a strategy for modifying the N or C terminus of proteins. This protocol describes the use of depsipeptide substrates (containing an ester linkage) with sortase A (SrtA) to completely modify proteins carrying a single N-terminal glycine residue under mild conditions in 4–6 h. The SrtA-mediated ligation reaction is reversible, so most labeling protocols that use this enzyme require a large excess of both substrate and sortase to produce high yields of ligation product. In contrast, switching to depsipeptide substrates effectively renders the reaction irreversible, allowing complete labeling of proteins with a small excess of substrate and catalytic quantities of sortase. Herein we describe the synthesis of depsipeptide substrates that contain an ester linkage between a threonine and glycolic acid residue and an N-terminal FITC fluorophore appended via a thiourea linkage. The synthesis of the depsipeptide substrate typically takes 2–3 d