On a generalization of Jacobi's elliptic functions and the double sine-Gordon kink chain

Pawellek, Michael

doi:10.1063/1.3656873

Cited by 6 publications

(6 citation statements)

References 11 publications

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“…where am N (t, m 1 , • • • m N ) is the generalized Jacobi amplitude and K N the generalized elliptic integral of the first kind (see Ref. [66] for a complete description of these functions in the case N = 2 and Appendix B for the necessary properties). Again, increasing ν improves the robustness, while the extra parameters m i can be used to shape the pulse.…”

Section: Broadband Pulsesmentioning

confidence: 99%

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

Van Damme,

Sugny,

Glaser

2021

Preprint

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We apply the Small Tip-Angle Approximation in the Toggling Frame in order to analytically design robust pulses against resonance offsets for state to state transfer in two-level quantum systems. We show that a broadband or a local robustness up to an arbitrary order can be achieved. We provide different control parameterizations to satisfy experimental constraints and limitations on the amplitude or energy of the pulse. A comparison with numerical optimal solutions is made.

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Section: Broadband Pulsesmentioning

confidence: 99%

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

Van Damme,

Sugny,

Glaser

2021

Preprint

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“…The solutions to (2.21) were first found in [101]. They are given by generalized Jacobi elliptic functions, which are hyperelliptic but can be viewed as single-valued meromorphic functions on a Riemann surface of genus two [109]. Using (C.4), the solutions can be expressed in terms of Jacobi elliptic functions…”

Section: Examples Of Solutions To the Basu-harvey Equationmentioning

confidence: 99%

“…The function S(s, k 1 , k 2 ) is hyperelliptic but can be viewed as a single-valued meromorphic function on a Riemann surface of genus two [109]. It has been shown to be related to the Jacobi elliptic functions by…”

Section: String Lie 2-algebrasmentioning

confidence: 99%

Higher Gauge Theory and M-Theory

Palmer

2014

Preprint

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In this thesis, the emerging field of higher gauge theory will be discussed, particularly in relation to problems arising in M-theory, such as selfdual strings and the so-called (2,0) theory. This thesis will begin with a Nahm-like construction for selfdual strings using loop space, the space of loops on spacetime. This construction maps solutions of the Basu-Harvey equation, the BPS equation arising in the description of multiple M2-branes, to solutions of a selfdual string equation on loop space. Furthermore, all ingredients of the construction reduce to those of the ordinary Nahm construction when compactified on a circle with all loops restricted to those wrapping the circle. The rest of this thesis, however, will not involve loop space. We will see a Nahm-like construction for the case of infinitely many selfdual strings, suspended between two M5-branes. This is possible since the limit taken renders the fields describing the M5-branes abelian. This avoids the problem which the rest of this thesis focuses on: What fields describe multiple M5-branes? The answer is likely to involve higher gauge theory, a categorification of gauge theory which describes the parallel transport of extended objects. Any theories which involves 3-algebras, including current M2-brane models and the Lambert-Papageorgakis M5-brane model, are examples of higher gauge theories. Recently, a class of models with N = (1, 0) supersymmetry have been found, with significant overlap with algebraic structures in higher gauge theory. This overlap suggests that the full N = (2, 0) theory could involve semistrict L ∞ -algebras. Finally, we will see some explicit selfdual string solutions, which may fit into these frameworks.

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“…The function S(s, k 1 , k 2 ) is hyperelliptic but can be viewed as a single-valued meromorphic function on a Riemann surface of genus two [31]. It has been shown to be related to the Jacobi elliptic functions by S(s, k 1 , k 2 ) = sn κ (k 2 s)…”

Section: (C3)mentioning

confidence: 99%

“…The solutions to (2.20) were first found in [30]. They are given by generalized Jacobi elliptic functions, which are hyperelliptic but can be viewed as single-valued meromorphic functions on a Riemann surface of genus two [31]. Using (C.4), the solutions can be expressed in terms of Jacobi elliptic functions…”

Section: Examples Of Solutions To the Basu-harvey Equationmentioning

confidence: 99%

Constructing generalized self-dual strings

Palmer

Sämann

2011

J. High Energ. Phys.

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We generalize a recently developed ADHMN-like construction of self-dual string solitons using loop space. In particular, we present two extensions: The first one starts from solutions to the Basu-Harvey equation for the ABJM model, the second one starts from solutions to a corresponding BPS equation in an N = 2 supersymmetric deformation of the BLG model. Both constructions yield solutions to the abelian and the nonabelian self-dual string equation transgressed to loop space. These equations might provide an effective description of M2-branes suspended between M5-branes.arXiv:1105.3904v2 [hep-th]

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On a generalization of Jacobi's elliptic functions and the double sine-Gordon kink chain

Cited by 6 publications

References 11 publications

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

Higher Gauge Theory and M-Theory

Constructing generalized self-dual strings

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