Nonlinear supersymmetric quantum mechanics: concepts and realizations
TLDR
The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed in this paper, its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described.Abstract:
The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described. It is elaborated how the nonlinear SUSY approach provides two new methods of SUSY separation of variables for various two-dimensional models. In the framework of these methods, a partial and/or complete solution of some two-dimensional models becomes possible. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. The emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of the nonlinear SUSY in one-dimensional stationary and non-stationary, as well as in two-dimensional QM.read more
Citations
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Bloch-like waves in random-walk potentials based on supersymmetry.
TL;DR: Inspired by isospectrality, this work reveals a deterministic pathway to bandgaps in random-walk potentials by applying the notion of supersymmetry to the wave equation and enables the formation of band gaps in extremely disordered potentials analogous to Brownian motion.
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Deformed supersymmetric mechanics
E. Ivanov,S. Sidorov +1 more
TL;DR: In this paper, a new type of, d = 1 supersymmetric systems were constructed by employing superfields defined on the cosets of the supergroup SU(2|1).
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Dirac electron in graphene under supersymmetry generated magnetic fields
TL;DR: In this paper, supersymmetry transformations were used to obtain new one parameter families of inhomogeneous magnetic fields for which the massless Dirac electron possesses exact solutions, and the inhomogeneity appearing in can be controlled by the parameter λ.
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Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
TL;DR: In this paper, a supersymmetry of the pairs of reflectionless quantum mechanical systems described by soliton potentials of a general form that depends on scaling and translation parameters is investigated.
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Factorization method and new potentials from the inverted oscillator
TL;DR: In this paper, the first and second-order supersymmetric quantum mechanics were applied to obtain new exactly solvable real potentials departing from the inverted oscillator potential, and it was shown that these transformations turn out to be the so-called complex ones.
References
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Journal ArticleDOI
Dynamical Breaking of Supersymmetry
TL;DR: In this article, general conditions for dynamical supersymmetry breaking are discussed and examples are given (in 0 + 1 and 2 + 1 dimensions) in which such a program in four dimensions is possible.
Book
Darboux transformations and solitons
V. B. Matveev,Mikhail A. Salle +1 more
TL;DR: In this paper, the authors developed a systematic algebraic approach to solve linear and non-linear partial differential equations arising in soliton theory, such as the non-stationary linear Schrodinger equation, Korteweg-de Vries and Kadomtsev-Petviashvili equations, the Davey Stewartson system, Sine-Gordon and nonlinearSchrodinger equations 1+1 and 2+1 Toda lattice equations, and many others.
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Supersymmetry and quantum mechanics
TL;DR: In this article, the authors review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications, including shape invariance and operator transformations, and show that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials.