Nonlinear Schrödinger-type field equation for the description of dissipative systems. II. Frictionally damped motion in a magnetic field

1984 ◽  
Vol 25 (2) ◽  
pp. 391-410 ◽  
Author(s):  
D. Schuch ◽  
K.-M. Chung ◽  
H. Hartmann
Keyword(s):  
Magnetic Field ◽  
Field Equation ◽  
Dissipative Systems ◽  
Nonlinear Schrödinger

scholarly journals Fluctuation Relations for Dissipative Systems in Constant External Magnetic Field: Theory and Molecular Dynamics Simulations

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 146
Author(s):  
Alessandro Coretti ◽  
Lamberto Rondoni ◽  
Sara Bonella
Keyword(s):  
Magnetic Field ◽  
Molecular Dynamics ◽  
External Magnetic Field ◽  
Molecular Dynamics Simulations ◽  
Nonequilibrium Molecular Dynamics ◽  
Dissipative Systems ◽  
Common Belief ◽  
Fluctuation Relations ◽  
Dynamics Simulations ◽  
Constant External Magnetic Field

We illustrate how, contrary to common belief, transient Fluctuation Relations (FRs) for systems in constant external magnetic field hold without the inversion of the field. Building on previous work providing generalized time-reversal symmetries for systems in parallel external magnetic and electric fields, we observe that the standard proof of these important nonequilibrium properties can be fully reinstated in the presence of net dissipation. This generalizes recent results for the FRs in orthogonal fields—an interesting but less commonly investigated geometry—and enables direct comparison with existing literature. We also present for the first time a numerical demonstration of the validity of the transient FRs with nonzero magnetic field via nonequilibrium molecular dynamics simulations of a realistic model of liquid NaCl.

scholarly journals Einstein’s Notational Equation of Electro-Magnetic Field Equation in Rindler spacetime

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Field Equation ◽  
Electromagnetic Fields ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Electro Magnetic Field ◽  
Rindler Space ◽  
Electro Magnetic

We find Einstein’s notational equation of the electro-magnetic field equation and the electromagneticfield in Rindler space-time. Because, electromagnetic fields of the accelerated frame include in general relativity theory.

scholarly journals NEW TREATMENT OF THE NONCOMMUTATIVE DIRAC EQUATION WITH A COULOMB POTENTIAL

2012 ◽  
Vol 27 (19) ◽  
pp. 1250100 ◽  
Author(s):  
LAMINE KHODJA ◽  
SLIMANE ZAIM
Keyword(s):  
Magnetic Field ◽  
Field Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Hyperfine Structure ◽  
Coulomb Potential ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
New Treatment

Using the approach of the modified Euler–Lagrange field equation together with the corresponding Seiberg–Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification to the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the Hamiltonian of the hydrogen atom is obtained, and we show that the noncommutativity plays the role of spin and magnetic field which gives the hyperfine structure.

On nonlinear circularly polarized Alfvén waves

1988 ◽  
Vol 40 (2) ◽  
pp. 281-287 ◽  
Author(s):  
G. Mann
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Periodic Solutions ◽  
Type Equation ◽  
Finite Amplitude ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Circularly Polarized ◽  
Ambient Magnetic Field ◽  
Nonlinear Schrödinger

Finite-amplitude circularly polarized Alfvén waves propagating along the ambient magnetic field are described by a derivative nonlinear Schrödinger-type equation. It leads to stationary, solitary and periodic solutions with phase modulations. The amplitude–width relation for these solitons is shown to be an inequality. The relevance of the results is briefly discussed for particular phenomena in the solar wind.

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