اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the Manifestly Covariant Juttner Distribution and Equipartition Theorem
111
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Juttners as the relativistic generalization of Maxwells distribution for d=1,2,3 spatial dimensions and pointed to an invariant temperature. In this work we argue an invariant temperature naturally follows from manifest covariance. We present a new derivation of the manifestly covariant Juttners distribution and Equipartition Theorem. The standard procedure to get the equilibrium distribution as a solution of the relativistic Boltzmanns equation is here adopted. However, contrary to previous analysis, we use cartesian coordinates in d+1 momentum space, with d spatial components. The use of the multiplication theorem of Bessel functions turns crucial to regain the known invariant form of Juttners distribution. Since equilibrium kinetic theory results should agree with thermodynamics in the comoving frame to the gas the covariant pseudo-norm of a vector entering the distribution can be identified with the reciprocal of temperature in such comoving frame. Then by combining the covariant statistical moments of Juttners distribution a novel form of the Equipartition Theorem is advanced which also accommodates the invariant comoving temperature and it contains, as a particular case, a previous not manifestly covariant form.
قيم البحث
اقرأ أيضاً
Stochastic inflation is an effective theory describing the super-Hubble, coarse-grained, scalar fields driving inflation, by a set of Langevin equations. We previously highlighted the difficulty of deriving a theory of stochastic inflation that is in
variant under field redefinitions, and the link with the ambiguity of discretisation schemes defining stochastic differential equations. In this paper, we solve the issue of these inflationary stochastic anomalies by using the Stratonovich discretisation satisfying general covariance, and identifying that the quantum nature of the fluctuating fields entails the existence of a preferred frame defining independent stochastic noises. Moreover, we derive physically equivalent It^o-Langevin equations that are manifestly covariant and well suited for numerical computations. These equations are formulated in the general context of multifield inflation with curved field space, taking into account the coupling to gravity as well as the full phase space in the Hamiltonian language, but this resolution is also relevant in simpler single-field setups. We also develop a path-integral derivation of these equations, which solves conceptual issues of the heuristic approach made at the level of the classical equations of motion, and allows in principle to compute corrections to the stochastic formalism. Using the Schwinger-Keldysh formalism, we integrate out small-scale fluctuations, derive the influence action that describes their effects on the coarse-grained fields, and show how the resulting coarse-grained effective Hamiltonian action can be interpreted to derive Langevin equations with manifestly real noises. Although the corresponding dynamics is not rigorously Markovian, we show the covariant, phase-space Fokker-Planck equation for the Probability Density Function of fields and momenta when the Markovian approximation is relevant [...]
We explain dark energy with equipartition theorem in string landscape.
We discuss the no-ghost theorem in the massive gravity in a covariant manner. Using the BRST formalism and St{u}ckelberg fields, we first clarify how the Boulware-Deser ghost decouples in the massive gravity theory with Fierz-Pauli mass term. Here we
find that the crucial point in the proof is that there is no higher (time) derivative for the St{u}ckelberg `scalar field. We then analyze the nonlinear massive gravity proposed by de Rham, Gabadadze and Tolley, and show that there is no ghost for general admissible backgrounds. In this process, we find a very nontrivial decoupling limit for general backgrounds. We end the paper by demonstrating the general results explicitly in a nontrivial example where there apparently appear higher time derivatives for St{u}ckelberg scalar field, but show that this does not introduce the ghost into the theory.
Non-Gaussianities of primordial perturbations in the soft limit provide the important information about the light degrees of freedom during inflation. The soft modes of the curvature perturbations, unobservable for a local observer, act as rescaling
the spatial coordinates. We determine how the trispectrum in the collapsed limit is shifted by the rescaling due to the soft modes. We find the form of the inequality between $f_{rm NL}$ and $tau_{rm NL}$ parameters is not affected by the rescaling, demonstrating that the role of the inequality as an indicator of the light degrees of freedom remains intact. We also comment on the local observer effect on the consistency relation for ultra slow-roll inflation.
A phenomenological approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts model. The d
uality symmetry of the 2D Potts model together with the known results on its critical exponent {alpha} allow to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
