A GENERAL METHOD FOR CALCULATING PARTITION FUNCTION OF QCD AT FINITE CHEMICAL POTENTIAL

2007 ◽  
Vol 22 (19) ◽  
pp. 3201-3209 ◽  
Author(s):  
WEI-MIN SUN ◽  
HONG-SHI ZONG
Keyword(s):  
Partition Function ◽  
Chemical Potential ◽  
Baryon Number ◽  
Quark Propagator ◽  
General Situation ◽  
Multiplicative Constant ◽  
First Case ◽  
Free Quark ◽  
Quark Theory ◽  
General Method

In this paper we propose a general method for calculating the partition function of QCD at finite chemical potential. It is found that the partition function is totally determined by the dressed quark propagator at finite chemical potential up to a multiplicative constant. From this a criterion for the phase transition between the Nambu and the Wigner phase is obtained. This general method are applied to two specific cases: the free quark theory and QCD with a model dressed quark propagator proposed in H . Pagels and S. Stokar, Phys. Rev. D20, 2947 (1979). In the first case, the standard Fermi distribution at T = 0 are reproduced. In the second case, a particular form of baryon number distribution is obtained. It is found that when μ is below a critical value, the baryon number density is identically zero, which agrees with the general conclusion in M. A. Halasz et al., Phys. Rev. D58, 096007 (1998). All the results in the present paper are obtained under the condition T = 0 and μ ≠ 0. However, they can be generalized to the the general situation T ≠ 0 and μ ≠ 0 without fundamental difficulty.

scholarly journals GENERAL FORMULA FOR THE FOUR-QUARK CONDENSATE AND VACUUM FACTORIZATION ASSUMPTION

2008 ◽  
Vol 23 (10) ◽  
pp. 1507-1520 ◽  
Author(s):  
HONG-SHI ZONG ◽  
DENG-KE HE ◽  
FENG-YAO HOU ◽  
WEI-MIN SUN
Keyword(s):  
General Formula ◽  
Linear Response ◽  
Chemical Potential ◽  
Background Field ◽  
Quark Propagator ◽  
Quark Condensate ◽  
Sum Rule ◽  
Factorization Problem ◽  
Field Approach ◽  
General Method

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate [Formula: see text]. This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for [Formula: see text] holds only when the dressed vertex is taken to be the bare one. This property also holds for all other types of four-quark condensate. By comparing this formula with the general expression for the corresponding vacuum susceptibility, it is found that there exists some intrinsic relation between these two quantities, which are usually treated as independent phenomenological inputs in the QCD sum rule external field approach. The above results are also generalized to the case of finite chemical potential and the factorization problem of the four-quark condensate at finite chemical potential is discussed.

THE EQUATION OF STATE OF QUASI-PARTICLE MODEL OF QUARK–GLUON PLASMA AT FINITE CHEMICAL POTENTIAL

2010 ◽  
Vol 25 (01) ◽  
pp. 47-54 ◽  
Author(s):  
A-MENG ZHAO ◽  
JING CAO ◽  
LIU-JUN LUO ◽  
WEI-MIN SUN ◽  
HONG-SHI ZONG
Keyword(s):  
Equation Of State ◽  
Effective Mass ◽  
Quark Gluon Plasma ◽  
Chemical Potential ◽  
Gluon Plasma ◽  
Quark Propagator ◽  
Particle Model ◽  
Quasi Particle ◽  
Model Independent ◽  
Free Quark

In this letter we propose a new method of calculating the equation of state (EOS) of quasi-particle model of quark–gluon plasma at finite chemical potential. In the quasi-particle model the quark propagator has the form of a free quark propagator with a temperature and density dependent effective mass. From this quark propagator the EOS at finite chemical potential is calculated using the model-independent formula proposed in Refs. 16 and 17. A comparison between our EOS and the cold, perturbative EOS of QCD proposed in Ref. 23 is made.

scholarly journals Modular invariance in finite temperature Casimir effect

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich
Keyword(s):  
Partition Function ◽  
Chemical Potential ◽  
Casimir Effect ◽  
Temperature Inversion ◽  
Massless Scalar ◽  
Partition Functions ◽  
Parallel Plates ◽  
Modular Transformations ◽  
Real Analytic ◽  
Set Up

Abstract The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell’s theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.

scholarly journals Quark Number Susceptibilities and Equation of State in QCD at Finite μB

Proceedings ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 5
Author(s):  
Saumen Datta ◽  
Rajiv Gavai ◽  
Sourendu Gupta
Keyword(s):  
Equation Of State ◽  
Taylor Series ◽  
Chemical Potential ◽  
Baryon Number ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collider ◽  
Quark Number ◽  
Monte Carlo Studies ◽  
Essential Input ◽  
Beam Energy Scan

One of the main goals of the cold baryonic matter (CBM) experiment at FAIR is to explore the phases of strongly interacting matter at finite temperature and baryon chemical potential μ B . The equation of state of quantum chromodynamics (QCD) at μ B > 0 is an essential input for the CBM experiment, as well as for the beam energy scan in the Relativistic Heavy Ion Collider(RHIC) experiment. Unfortunately, it is highly nontrivial to calculate the equation of state directly from QCD: numerical Monte Carlo studies on lattice are not useful at finite μ B . Using the method of Taylor expansion in chemical potential, we estimate the equation of state, namely the baryon number density and its contribution to the pressure, for two-flavor QCD at moderate μ B . We also study the quark number susceptibilities. We examine the technicalities associated with summing the Taylor series, and explore a Pade resummation. An examination of the Taylor series can be used to get an estimate of the location of the critical point in μ B , T plane.

scholarly journals Notes on massless scalar field partition functions, modular invariance and Eisenstein series

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich ◽  
Martin Bonte
Keyword(s):  
Scalar Field ◽  
Partition Function ◽  
Low Temperature ◽  
Eisenstein Series ◽  
Chemical Potential ◽  
Proper Time ◽  
Series Representation ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spacetime Manifold

Abstract The partition function of a massless scalar field on a Euclidean spacetime manifold ℝd−1 × 𝕋2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝp × 𝕋q+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On 𝕋d+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

The Methods to Study the Influence of the Clearance in the Case of Great Speeds and Small Speeds

2013 ◽  
Vol 837 ◽  
pp. 88-92
Author(s):  
Jan Cristian Grigore
Keyword(s):  
Dynamic Behavior ◽  
Reaction Force ◽  
Accurate Method ◽  
Angular Speed ◽  
Connecting Rod ◽  
Lagrange Equations ◽  
Joint Rotation ◽  
First Case ◽  
Multi Body ◽  
General Method

In kinematic couplings, clearances are inevitable for their operation. The size of these clearances but as a consequence of use, causes a malfunction of the mechanism to which it belongs. The law of motion of driveline changes, big clearances, non-technological system causes vibration, leading to discomfort, uncertainty, and thus reach its degradation. In the paper we shall make a few of geometric and mechanical type considerations about the clearances in the linkages, linkages planes with joint rotation links. Based on mathematical algorithm developed and applied crank mechanism, the model presented in [1], this paper scientifically developed mathematical model, proposing mathematical models to study the influence of the size of the clearance in general dynamic calculation mechanisms. Mechanism considered is crank connecting rod mechanism with clearance cinematic coupling between rod and crank rotation. The paper makes a study of the influence on the dynamic behavior of the crank rod mechanism at high speeds, but also general method algorithm is developed and accurate method to assess the dynamic behavior of multi-body mechanism. The first case is considered a constant angular speed motor and thus determine the elemental expressions that establish the mechanism position, velocity and acceleration expressions in the two directions heads elements. Finally we obtain the expression of the normal reaction force, as well as position expression that defines its angle. With reaction force can specify phase (contact, flight, impact) [1], the behavior of the journal. For the case of general method - the method multi-body - the exact method are established liaison relationships between the parameters , write matrices , inertia matrix. Use Lagrange equations, if non-holonomic constraints. Matrix differential equation of motion is written and it can be solved numerically using Runge-Kutta method of order four. Of the iterative method, we obtain the parameters used in calculating the reaction force expression that can be evaluated accurately in journal bearings behaviour. Any would be their source of appearance, they usually produce unwished effects during the mechanisms functioning.

A MODEL STUDY OF QUARK NUMBER SUSCEPTIBILITY AT FINITE CHEMICAL POTENTIAL AND ZERO TEMPERATURE

2009 ◽  
Vol 24 (12) ◽  
pp. 2241-2251 ◽  
Author(s):  
YAN-BIN ZHANG ◽  
FENG-YAO HOU ◽  
YU JIANG ◽  
WEI-MIN SUN ◽  
HONG-SHI ZONG
Keyword(s):  
General Result ◽  
Chemical Potential ◽  
Direct Method ◽  
Quark Propagator ◽  
Zero Temperature ◽  
Quark Number ◽  
Model Study ◽  
Analytic Expression ◽  
A Direct Method ◽  
Quark Number Susceptibility

In this paper, we try to provide a direct method for calculating quark number susceptibility at finite chemical potential and zero temperature. In our approach, quark number susceptibility is totally determined by G[μ](p) (the dressed quark propagator at finite chemical potential μ). By applying the general result given in Phys. Rev. C71, 015205 (2005), G[μ](p) is calculated from the model quark propagator proposed in Phys. Rev. D67, 054019 (2003). From this the full analytic expression of quark number susceptibility at finite μ and zero T is obtained.

scholarly journals Deforming charged black holes with dipolar differential rotation boundary

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Tong-Tong Hu ◽  
Shuo Sun ◽  
Hong-Bo Li ◽  
Yong-Qiang Wang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Chemical Potential ◽  
Dimensional Space ◽  
Quasinormal Modes ◽  
Fixed Temperature ◽  
First Case ◽  
Ads Black Holes ◽  
Horizon Geometry ◽  
Black Hole Solutions

Abstract Motivated by the recent studies of the novel asymptotically global $$\hbox {AdS}_4$$AdS4 black hole with deformed horizon, we consider the action of Einstein–Maxwell gravity in AdS spacetime and construct the charged deforming AdS black holes with differential boundary. In contrast to deforming black hole without charge, there exists at least one value of horizon for an arbitrary temperature. The extremum of temperature is determined by charge q and divides the range of temperature into several parts. Moreover, we use an isometric embedding in the three-dimensional space to investigate the horizon geometry. The entropy and quasinormal modes of deforming charged AdS black hole are also studied in this paper. Due to the existence of charge q, the phase diagram of entropy is more complicated. We consider two cases of solutions: (1) fixing the chemical potential $$\mu $$μ; (2) changing the value of $$\mu $$μ according to the values of horizon radius and charge. In the first case, it is interesting to find there exist two families of black hole solutions with different horizon radii for a fixed temperature, but these two black holes have same horizon geometry and entropy. The second case ensures that deforming charged AdS black hole solutions can reduce to standard RN–AdS black holes.

scholarly journals Equation of State and Freezeout in QCD with Staggered Quarks

2018 ◽  
Vol 175 ◽  
pp. 07035
Author(s):  
Saumen Datta ◽  
R. V. Gavai ◽  
Sourendu Gupta
Keyword(s):  
Equation Of State ◽  
Taylor Expansion ◽  
Chemical Potential ◽  
Baryon Number ◽  
Number Density ◽  
Statistical Errors

We report the equation of state at finite chemical potential, namely the baryon number density and the baryonic contribution to the pressure, using a resummation of the Taylor expansion. We also report the freezeout conditions for a measure of fluctuations. We examine the major sources of systematic and statistical errors in all of these measurements.

Sign in / Sign up

Export Citation Format

Share Document