scholarly journals Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons

2015 ◽  
Vol 92 (5) ◽  
Author(s):  
Chang-Woo Lee ◽  
Paweł Kurzyński ◽  
Hyunchul Nha
Keyword(s):  
Nonlinear Dynamics ◽  
Dirac Equation ◽  
Quantum Walk ◽  
Nonlinear Dirac Equation

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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