اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA new discrete calculus of variations and its applications in statistical physics
107
0
0.0
(
0
)
تأليف
Q. H. Liu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
For a discrete function $fleft( xright) $ on a discrete set, the finite difference can be either forward and backward. However, we observe that if $ fleft( xright) $ is a sum of two functions $fleft( xright) =f_{1}left( xright) +f_{2}left( xright) $ defined on the discrete set, the first order difference of $Delta fleft( xright) $ is equivocal for we may have $ Delta ^{f}f_{1}left( xright) +Delta ^{b}f_{2}left( xright) $ where $ Delta ^{f}$ and $Delta ^{b}$ denotes the forward and backward difference respectively. Thus, the first order variation equation for this function $ fleft( xright) $ gives many solutions which include both true and false one. A proper formalism of the discrete calculus of variations is proposed to single out the true one by examination of the second order variations, and is capable of yielding the exact form of the distributions for Boltzmann, Bose and Fermi system without requiring the numbers of particle to be infinitely large. The advantage and peculiarity of our formalism are explicitly illustrated by the derivation of the Bose distribution.
قيم البحث
اقرأ أيضاً
The observation of coherent elastic neutrino nucleus scattering (CE$ u$NS) by the COHERENT collaboration in 2017 has opened a new window to both test Standard Model predictions at relatively low energies and probe new physics scenarios. Our investiga
tions show, however, that a careful treatment of the statistical methods used to analyze the data is essential to derive correct constraints and bounds on new physics parameters. In this manuscript we perform a detailed analysis of the publicly available COHERENT CsI data making use of all available background data. We point out that Wilks theorem is not fulfilled in general and a calculation of the confidence regions via Monte Carlo simulations following a Feldman-Cousins procedure is necessary. As an example for the necessity of this approach to test new physics scenarios we quantify the allowed ranges for several scenarios with neutrino non-standard interactions. Furthermore, we provide accompanying code to enable an easy implementation of other new physics scenarios as well as data files of our results.
Einstein utilized Lorentz invariance from Maxwells equations to modify mechanical laws and establish the special theory of relativity. Similarly, we may have a different theory if there exists another covariance of Maxwells equations. In this paper,
we find such a new transformation where Maxwells equations are still unchanged. Consequently, Veselagos metamaterial and other systems have negative phase velocities without double negative permittivity and permeability can be described by a unified theory. People are interested in the application of metamaterials and negative phase velocities but do not appreciate the magnitude and significance to the spacetime conception of modern physics and philosophy.
These notes provide a concise introduction to important applications of the renormalization group (RG) in statistical physics. After reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena, Wilsons momentum shell RG method is
presented, and the critical exponents for the scalar Phi^4 model are determined to first order in an eps expansion about d_c = 4. Subsequently, the technically more versatile field-theoretic formulation of the perturbational RG for static critical phenomena is described. It is explained how the emergence of scale invariance connects UV divergences to IR singularities, and the RG equation is employed to compute the critical exponents for the O(n)-symmetric Landau-Ginzburg-Wilson theory. The second part is devoted to field theory representations of non-linear stochastic dynamical systems, and the application of RG tools to critical dynamics. Dynamic critical phenomena in systems near equilibrium are efficiently captured through Langevin equations, and their mapping onto the Janssen-De Dominicis response functional, exemplified by the purely relaxational models with non-conserved (model A) / conserved order parameter (model B). The Langevin description and scaling exponents for isotropic ferromagnets (model J) and for driven diffusive non-equilibrium systems are also discussed. Finally, an outlook is presented to scale-invariant phenomena and non-equilibrium phase transitions in interacting particle systems. It is shown how the stochastic master equation associated with chemical reactions or population dynamics models can be mapped onto imaginary-time, non-Hermitian `quantum mechanics. In the continuum limit, this Doi-Peliti Hamiltonian is represented through a coherent-state path integral, which allows an RG analysis of diffusion-limited annihilation processes and phase transitions from active to inactive, absorbing states.
The first three years of the LHC experiments at CERN have ended with the nightmare scenario: all tests, confirm the Standard Model of Particles so well that theorists must search for new physics without any experimental guidance. The supersymmetric t
heories, a privileged candidate for new physics are nearly excluded. As a potential escape from the crisis, we propose thinking about a series of astonishing relations suggesting fundamental interconnections between the quantum world and the large scale Universe. It seems reasonable that, for instance, the equation relating a quark-antiquark pair with the fundamental physical constants and cosmological parameters must be a sign of new physics. One of the intriguing possibilities is interpreting our relations as a signature of the quantum vacuum containing the virtual gravitational dipoles.
The Euler-Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler-Maclaurin summation formula and the Poission summation formul
a as special cases. By making use of the modified formula, a numerical summation method is obtained and the error can be controlled. The modified formula is also generalized from one dimention to two dimentions. Examples of its applications in statistical physics are also discussed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
