Lagrangian form of Schrödinger equation

Arsenović, D.; Burić, Nikola; Davidović, Dragomir; Prvanović, Slobodan

doi:10.1007/s10701-014-9810-4

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…ξ = 0 corresponds to a kinetic term and resembles the kinetic part of the Schrödinger Lagrangian [61]. Indeed, there is a one-to-one correspondence between Eq.…”

Section: Viscous Maxwell-chern-simons Theorymentioning

confidence: 99%

Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter

Van Mechelen,

Jacob

2019

Preprint

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We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. Our model applies to a quantum Hall fluids with viscosity. We solve both continuum and lattice regularized systems to demonstrate that this is the minimal (exactly solvable) gauge theory with a nontrivial photonic Chern number (C = 0) for electromagnetic waves coupled to a quantum Hall fluid. The interplay of symmetry and topology is also captured by the spin-1 representations of a photonic skyrmion at high-symmetry points in the Brillouin zone. To rigorously analyze the topological physics, we introduce the viscous Maxwell-Chern-Simons Lagrangian and derive the equations of motion, as well as the boundary conditions, from the principle of least action. We discover topologically-protected chiral (unidirectional) edge states which minimize the surface variation and correspond to massless photonic excitations costing an infinitesimal amount of energy. Physically, our predicted electromagnetic phases are connected to a dynamical photonic mass in the integer quantum Hall fluid. This arises from viscous (nonlocal) Hall conductivity and we identify the nonlocal Chern-Simons coupling with the Hall viscosity. The electromagnetic phase is topologically nontrivial C = 0 when the Hall viscosity inhibits the total bulk Hall response. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of spin-1 quantization in nontrivial photonic phases.

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“…ξ = 0 corresponds to a kinetic term and resembles the kinetic part of the Schrödinger Lagrangian [61]. Indeed, there is a one-to-one correspondence between Eq.…”

Section: Viscous Maxwell-chern-simons Theorymentioning

confidence: 99%

Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter

Van Mechelen,

Jacob

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Many other modifications of variation methods exist to find relevant calculus to obtain the correct equations of motion . The duplication of the variables-introduction the complex conjugted field variables-is also an applicable method in the case of Schrödinger field [43,44], other quantum fields [45], moreover the transport equations such as Fourier heat conduction [46][47][48]. A promising solution is usage of potential (generator) functions in different ways for electrodynamics [49,50], for the field theory of thermodynamics [51], or for dissipative mechanical systems [52].…”

Section: Introductionmentioning

confidence: 99%