اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBivelocity picture in the nonrelativistic limit of relativistic hydrodynamics
225
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We discuss the nonrelativistic limit of the relativistic Navier-Fourier-Stokes (NFS) theory. The next-to-leading order relativistic corrections to the NFS theory for the Landau-Lifshitz fluid are obtained. While the lowest order truncation of the velocity expansion leads to the usual NFS equations of nonrelativistic fluids, we show that when the next-to-leading order relativistic corrections are included, the equations can be expressed concurrently with two different fluid velocities. One of the fluid velocities is parallel to the conserved charge current (which follows the Eckart definition) and the other one is parallel to the energy current (which follows the Landau-Lifshitz definition). We compare this next-to-leading order relativistic hydrodynamics with bivelocity hydrodynamics, which is one of the generalizations of the NFS theory and is formulated in such a way to include the usual mass velocity and also a new velocity, called the volume velocity. We find that the volume velocity can be identified with the velocity obtained in the Landau-Lifshitz definition. Then, the structure of bivelocity hydrodynamics, which is derived using various nontrivial assumptions, is reproduced in the NFS theory including the next-to-leading order relativistic corrections.
قيم البحث
اقرأ أيضاً
We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) times
SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_{pi}$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the ordinary theory at long distances which we compute. This determines, in some cases, the leading dependence of the transport parameters of QCD on the pion mass. We analyze the predictions of this computation, as the system approaches the $O(4)$ critical point.
A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Gre
en-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.
The Whitham approach is a well-studied method to describe non-linear integrable systems. Although approximate in nature, its results may predict rather accurately the time evolution of such systems in many situations given initial conditions. A simil
arly powerful approach has recently emerged that is applicable to quantum integrable systems, namely the generalized hydrodynamics approach. This paper aims at showing that the Whitham approach is the semiclassical limit of the generalized hydrodynamics approach by connecting the two formal methods explicitly on the example of the Lieb-Liniger model on the quantum side to the non-linear Schr{o}dinger equation on the classical side in the $cto0$ limit, $c$ being the interaction parameter. We show how quantum expectation values may be computed in this limit based on the connection established here which is mentioned above.
We argue that different formulations of hydrodynamics are related to uncertainties in the definitions of local thermodynamic and hydrodynamic variables. We show that this ambiguity can be resolved by viewing different formulations of hydrodynamics as
particular gauge choices which lead to the same physical behavior of the system. Using the example of bulk viscosity, we show that Bemfica-Disconzi-Noronha-Kovtun (BDNK) and Israel-Stewart hydrodynamics are particular gauge choices of this type, related by a well-defined transformation of thermodynamic and hydrodynamic variables. We argue that this gauge ambiguity is necessary to ascertain the causality of stochastic hydrodynamic evolution and conjecture that it could explain the applicability of hydrodynamics outside its expected regime of validity since far from equilibrium and close to equilibrium may be related through transformations of this type.
The dynamics of Quark-gluon plasma (QGP) as a lump of deconfined free quarks and gluons is elaborated. Based on the first principal we construct the Lagrangian that represents the dynamics of QGP. To induce a hydrodynamics approach, we substitute the
gluon fields with flow fields. As a result, the derived equation of Motion (E.O.M) for gluon dominated QGP shows the form that similar to Euler equation, and the energy momentum tensor also represents explicitly the system of ideal fluid. Combining the E.O.M and energy momentum tensor, the pressure and energy density distribution as the equation of states are analytically derived.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
