Related papers: The Fermi Function Beyond The Second Order Perturb…
From classical stochastic equations of motion we derive the quantum Schr\"odinger equation. The derivation is carried out by assuming that the real and imaginary parts of the wave function $\phi$ are proportional to the coordinates and…
Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and…
In this paper, the acceleration of particles in astrophysical sources by the Fermi mechanism is revisited under the assumption of Lorentz invariance violation (LIV). We calculate the energy spectrum and the acceleration time of particles…
We propose a multipole representation of the Fermi-Dirac function and the Fermi operator, and use this representation to develop algorithms for electronic structure analysis of metallic systems. The new algorithm is quite simple and…
Boltzmann's differential equation is replaced by the corresponding reciprocal symmetric finite difference equation. Finite difference translates discreteness of energy. Boltzmann's function, then, splits into two reciprocally related…
We solve the Wigner equation for massless spin-1/2 charged fermions near global equilibrium. The Wigner function can be obtained order by order in the power expansion of the vorticity and electromagnetic field. The Wigner function has been…
Some elaborations regarding the Hilbert and Fourier transforms of Fermi function are presented. The main result shows that the Hilbert transform of the difference of two Fermi functions has an analytical expression in terms of the $\Psi$…
The derivation becomes possible when we find a new formalism which connects the relativistic mechanics with the quantum mechanics. In this paper, we explore the quantum wave nature from the Newtonian mechanics by using a concept: velocity…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…
The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of…
We construct models for first- and second-order Fermi acceleration of particles, incorporating generic frame transformations, dispersion relations, and conservation laws. Within this framework, we study deformations of Lorentz symmetry via…
A compact method for amplitude calculations in theories with Dirac and Majorana effective operators is discussed. Using the renormalizable formalism of Denner et al., [1,2] for propagators, vertices and fermion (number) flow and introducing…
Regularity of the deformation of the Fermi surface under short-range interactions is established to all orders in perturbation theory. The proofs are based on a new classification of all graphs that are not doubly overlapping. They turn out…
First-order Fermi acceleration process at a relativistic shock wave is investigated by means of Monte Carlo simulations involving numerical integration of particle equations of motion in a turbulent magnetic field near the shock. In…
Fermi helped establish a new framework for understanding matter, based on quantum theory. This framework refines and improves traditional atomism in two crucial respects. First, the elementary constituents of matter belong to a very small…
Smooth, highly accurate analytical representations of Fermi-Dirac (FD) integral combinations important in free-energy density functional calculations are presented. Specific forms include those that occur in the local density approximation…
The concept of photon is not necessary only applied to the relativistic Doppler theory. It may also work well for classical theory. As conservation of momentum and energy are physical laws, if applying these laws gives the exact…
The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…
Fermi-edge absorption theory predicting the spectrum, A(\omega)\propto \omega^{-2\delta_0/\pi+\delta^2_0/\pi^2}, relies on the assumption that scattering phase, \delta_0, is frequency-independent. Dependence of \delta_0 on \omega becomes…