Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe MIT Bag Model as an infinite mass limit
117
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass $m>0$ lies outside a smooth and bounded open set $OmegasubsetR^3$, it is proved that its spectrum is approximated by the one of the Dirac operator on $Omega$ with the MIT bag boundary condition. The approximation, which is developed up to and error of order $o(1/sqrt m)$, is carried out by introducing tubular coordinates in a neighborhood of $partialOmega$ and analyzing the corresponding one dimensional optimization problems in the normal direction.
rate research
Read More
We study spectral properties of Dirac operators on bounded domains $Omega subset mathbb{R}^3$ with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter $tauinmathbb{R}$; the case $tau = 0$ corresponds to the MIT bag model. We show that the eigenvalues are parametrized as increasing functions of $tau$, and we exploit this monotonicity to study the limits as $tau to pm infty$. We prove that if $Omega$ is not a ball then the first positive eigenvalue is greater than the one of a ball with the same volume for all $tau$ large enough. Moreover, we show that the first positive eigenvalue converges to the mass of the particle as $tau downarrow -infty$, and we also analyze its first order asymptotics.
In this work we study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular to the plane. We focus on the infinite-mass boundary condition (also called MIT bag condition). In the case of bounded domains, we establish the asymptotic behavior of the low-lying (positive and negative) energies in the limit of strong magnetic field. Moreover, for a constant magnetic field $B$, we study the problem on the half-plane and find that the Dirac operator has continuous spectrum except for a gap of size $a_0sqrt{B}$, where $a_0in (0,sqrt{2})$ is a universal constant. Remarkably, this constant characterizes certain energies of the system in a bounded domain as well. We discuss how these findings, together with our previous work, give a fairly complete description of the eigenvalue asymptotics of magnetic two-dimensional Dirac operators under general boundary conditions.
Quantum chromodynamics (QCD) is the theory of strong interaction and accounts for the internal structure of hadrons. Physicists introduced phe- nomenological models such as the M.I.T. bag model, the bag approximation and the soliton bag model to study the hadronic properties. We prove, in this paper, the existence of excited state solutions in the symmetric case and of a ground state solution in the non-symmetric case for the soliton bag and the bag approximation models thanks to the concentration compactness method. We show that the energy functionals of the bag approximation model are Gamma -limits of sequences of soliton bag model energy functionals for the ground and excited state problems. The pre- compactness, up to translation, of the sequence of ground state solutions associated with the soliton bag energy functionals in the non-symmetric case is obtained combining the Gamma -convergence theory and the concentration-compactness method. Finally, we give a rigorous proof of the original derivation of the M.I.T. bag equations done by Chodos, Jaffe, Johnson, Thorn and Weisskopf via a limit of bag approximation ground state solutions in the spherical case. The supersymmetry property of the Dirac operator is the key point in many of our arguments.
The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic hypo-elliptic diffusion. This diffusion solves a kinetic Fokker-Planck equation based on an Ornstein-Uhlenbeck Gaussian process. The long time diffusive behavior of this model was recently studied by Degond & Motsch using partial differential equations techniques. This model is however intrinsically probabilistic. In the present paper, we show how the long time diffusive behavior of this model can be essentially recovered and extended by using appropriate tools from stochastic analysis. The approach can be adapted to many other kinetic probabilistic models.
In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously justifies formal arguments and numerical simulations present in the Physics literature.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
