scholarly journals Exact stationary solutions of the parametrically driven and damped nonlinear Dirac equation

2019 ◽  
Vol 29 (9) ◽  
pp. 093129
Author(s):  
Niurka R. Quintero ◽  
Bernardo Sánchez-Rey
Keyword(s):  
Dirac Equation ◽  
Stationary Solutions ◽  
Nonlinear Dirac Equation

Charged spinor solitons

1986 ◽  
Vol 64 (3) ◽  
pp. 232-238 ◽  
Author(s):  
P. Mathieu ◽  
T. F. Morris
Keyword(s):  
Dirac Equation ◽  
Mass Parameter ◽  
Structure Constant ◽  
Finite Energy ◽  
Stationary Solutions ◽  
Fine Structure Constant ◽  
Many Body ◽  
Nonlinear Dirac Equation ◽  
Frequency Relation ◽  
Static Energy

A nonlinear Dirac equation for which all finite-energy stationary solutions are nontopological solitons with compact support is coupled to the electromagnetic field. In a many-body situation, it is shown that the equilibrium is reached when all the solitons have the same value of the charge. This implies the de Broglie frequency relation and a relation for the fine-structure constant. In specific domains and to a very good approximation, the model reduces to the linear Dirac equation for a particle whose mass parameter is the static energy of the soliton.

scholarly journals On the nonlinear Dirac equation on noncompact metric graphs

2021 ◽  
Vol 278 ◽  
pp. 326-357
Author(s):  
William Borrelli ◽  
Raffaele Carlone ◽  
Lorenzo Tentarelli
Keyword(s):  
Dirac Equation ◽  
Metric Graphs ◽  
Nonlinear Dirac Equation

scholarly journals Solitary waves in the nonlinear Dirac equation in the presence of external driving forces

2016 ◽  
Vol 49 (6) ◽  
pp. 065402 ◽  
Author(s):  
Franz G Mertens ◽  
Fred Cooper ◽  
Niurka R Quintero ◽  
Sihong Shao ◽  
Avinash Khare ◽  
...  
Keyword(s):  
Dirac Equation ◽  
Solitary Waves ◽  
Driving Forces ◽  
Nonlinear Dirac Equation ◽  
External Driving

Existence and asymptotics of ground states to the nonlinear Dirac equation with Coulomb potential

2021 ◽  
pp. 1-26
Author(s):  
Tianfang Wang ◽  
Wen Zhang ◽  
Jian Zhang
Keyword(s):  
Dirac Equation ◽  
Coulomb Potential ◽  
Ground State ◽  
Continuous Dependence ◽  
Energy Functional ◽  
Ground State Solution ◽  
State Solution ◽  
Nonlinear Dirac Equation ◽  
Relationship Of ◽  
Least Energy

In this paper we study the Dirac equation with Coulomb potential − i α · ∇ u + a β u − μ | x | u = f ( x , | u | ) u , x ∈ R 3 where a is a positive constant, μ is a positive parameter, α = ( α 1 , α 2 , α 3 ), α i and β are 4 × 4 Pauli–Dirac matrices. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. Under some suitable conditions, we prove that the problem possesses a ground state solution which is exponentially decay, and the least energy has continuous dependence about μ. Moreover, we are able to obtain the asymptotic property of ground state solution as μ → 0 + , this result can characterize some relationship of the above problem between μ > 0 and μ = 0.

scholarly journals Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity

2020 ◽  
Vol 53 (7) ◽  
pp. 075203 ◽  
Author(s):  
Fred Cooper ◽  
Avinash Khare ◽  
Niurka R Quintero ◽  
Bernardo Sánchez-Rey ◽  
Franz G Mertens ◽  
...  
Keyword(s):  
Dirac Equation ◽  
Nonlinear Dirac Equation

ONE-DIMENSIONAL QUANTUM LATTICE BOLTZMANN SCHEME FOR THE NONLINEAR DIRAC EQUATION

2013 ◽  
Vol 24 (12) ◽  
pp. 1340001 ◽  
Author(s):  
SILVIA PALPACELLI ◽  
PAUL ROMATSCHKE ◽  
SAURO SUCCI
Keyword(s):  
Dirac Equation ◽  
Lattice Boltzmann ◽  
Spontaneous Breaking ◽  
Mass Generation ◽  
Quantum Lattice ◽  
One Dimensional ◽  
Dynamic Mass ◽  
Nonlinear Dirac Equation ◽  
Njl Model ◽  
Lattice Boltzmann Scheme

We develop a quantum lattice Boltzmann (QLB) scheme for the Dirac equation with a nonlinear fermion interaction provided by the Nambu–Jona-Lasinio (NJL) model. Numerical simulations in 1 + 1 space-time dimensions, provide evidence of dynamic mass generation, through spontaneous breaking of chiral symmetry.

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