scholarly journals Comparisons between classical and quantum mechanical nonlinear lattice models

2014 ◽  
Author(s):  
Peter Jason ◽  
Keyword(s):  
Lattice Models ◽  
Quantum Mechanical ◽  
Nonlinear Lattice

scholarly journals Nonlinear lattice models for biopolymers: Dynamical coupling to a ionic cloud and application to actin filaments

2011 ◽  
Vol 4 (5) ◽  
pp. 1147-1166
Author(s):  
Cynthia Ferreira ◽  
◽  
Guillaume James ◽  
Michel Peyrard ◽  
◽  
...  
Keyword(s):  
Actin Filaments ◽  
Lattice Models ◽  
Ionic Cloud ◽  
Nonlinear Lattice ◽  
Dynamical Coupling

scholarly journals Arrested cracks in nonlinear lattice models of brittle fracture

1999 ◽  
Vol 60 (6) ◽  
pp. 7569-7571 ◽  
Author(s):  
David A. Kessler ◽  
Herbert Levine
Keyword(s):  
Brittle Fracture ◽  
Lattice Models ◽  
Nonlinear Lattice

ON SOLITON-MEDIATED FAST ELECTRIC CONDUCTION IN A NONLINEAR LATTICE WITH MORSE INTERACTIONS

2006 ◽  
Vol 16 (04) ◽  
pp. 1035-1039 ◽  
Author(s):  
MANUEL G. VELARDE ◽  
WERNER EBELING ◽  
DIRK HENNIG ◽  
CHRISTIAN NEIßNER
Keyword(s):  
Field Strength ◽  
Morse Potential ◽  
Tight Binding ◽  
Quantum Mechanical ◽  
Constant Field ◽  
Electric Conduction ◽  
Field Independent ◽  
Nonlinear Lattice ◽  
Morse Interactions ◽  
Potential Interactions

Assuming the quantum mechanical "tight binding" of an electron to a nonlinear lattice with Morse potential interactions we show how electric conduction can be mediated by solitons. For relatively high values of an applied electric field the current follows Ohm's law. As the field strength is lowered the current takes a finite, constant, field-independent value.

scholarly journals Continuum models and Morse Theory in the simulation, design and evaluation of magnetic Skyrmion devices

2021 ◽  
Author(s):  
P. Robert Kotiuga
Keyword(s):  
Morse Theory ◽  
Lattice Models ◽  
Energy Functional ◽  
Continuum Models ◽  
Quantum Mechanical ◽  
Simulation Design ◽  
Lattice Systems ◽  
Solid Foundation ◽  
Magnetic Skyrmions ◽  
The Continuum

Nanomagnetic devices such as computer gates and memory devices based on magnetic skyrmions are close to becoming a reality. In this paper we will explore the highly nonconvex nanomagnetic energy landscape in order to draw conclusions about the complexity of magnetic phenomena. Morse theoretic arguments show that, in a bounded energy interval, the number of critical points of the energy functional grows exponentially. To show this, we introduce a hierarchy of models for the design of nanomagnetic devices to provide a solid foundation for the introduction of topological tools. To reason in terms of lattice models, one must make a distinction between two types of lattices: the quantum mechanical model of the actual physical lattice and the lattice model that can be associated with a discretization of a continuum model of the physics. By focusing on the implications of Morse theory applied to lattice systems arising from the discretization of the continuum models, and the notion of “topological frustration”, we provide a framework for understanding “complexity” in the context of nanomagnetic systems. We conclude with some suggestions for making the analysis more qualitative.

scholarly journals Continuum models and Morse Theory in the simulation, design and evaluation of magnetic Skyrmion devices

2021 ◽  
Author(s):  
P. Robert Kotiuga
Keyword(s):  
Morse Theory ◽  
Lattice Models ◽  
Energy Functional ◽  
Continuum Models ◽  
Quantum Mechanical ◽  
Simulation Design ◽  
Lattice Systems ◽  
Solid Foundation ◽  
Magnetic Skyrmions ◽  
The Continuum

Nanomagnetic devices such as computer gates and memory devices based on magnetic skyrmions are close to becoming a reality. In this paper we will explore the highly nonconvex nanomagnetic energy landscape in order to draw conclusions about the complexity of magnetic phenomena. Morse theoretic arguments show that, in a bounded energy interval, the number of critical points of the energy functional grows exponentially. To show this, we introduce a hierarchy of models for the design of nanomagnetic devices to provide a solid foundation for the introduction of topological tools. To reason in terms of lattice models, one must make a distinction between two types of lattices: the quantum mechanical model of the actual physical lattice and the lattice model that can be associated with a discretization of a continuum model of the physics. By focusing on the implications of Morse theory applied to lattice systems arising from the discretization of the continuum models, and the notion of “topological frustration”, we provide a framework for understanding “complexity” in the context of nanomagnetic systems. We conclude with some suggestions for making the analysis more qualitative.

SOME ASPECTS OF NONLINEAR LATTICE MODELS

1981 ◽  
Vol 42 (C6) ◽  
pp. C6-111-C6-118 ◽  
Author(s):  
H. Büttner ◽  
H. Bilz
Keyword(s):  
Lattice Models ◽  
Nonlinear Lattice

ELECTRON TRAPPING BY SOLITONS: CLASSICAL VERSUS QUANTUM MECHANICAL APPROACH

2008 ◽  
Vol 18 (02) ◽  
pp. 521-526 ◽  
Author(s):  
MANUEL G. VELARDE ◽  
WERNER EBELING ◽  
ALEXANDER P. CHETVERIKOV ◽  
DIRK HENNIG
Keyword(s):  
Bound States ◽  
Tight Binding ◽  
Electron Trapping ◽  
Classical Electrodynamics ◽  
Quantum Mechanical ◽  
Repulsive Potential ◽  
Nonlinear Lattice ◽  
Mechanical Approach ◽  
Quantum Mechanical Approach ◽  
Potential Interactions

Assuming either classical electrodynamics or the quantum mechanical tight-binding of an electron to a nonlinear lattice with exponentially repulsive potential interactions we show how in both cases electron trapping can be mediated by solitons thus forming similar robust bound states (solectrons).

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