Supersymmetric many-particle quantum systems with inverse-square interactions

Ghosh, Pijush K.

doi:10.1088/1751-8113/45/18/183001

Cited by 15 publications

(27 citation statements)

References 166 publications

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“…The equations of motion for the odd numbered particles in the limit γ = 0 is identical with that of rational A N +1 -type Calogero model [29,30,31,32,33] with m particles. However, the Hamiltonians for these two cases are not identical in the same limit, due to a mismatch of total degrees of freedom and γ independence of V .…”

Section: Unidirectional Coupling Between System and Bathmentioning

confidence: 86%

Integrable coupled Liénard-type systems with balanced loss and gain

Sinha¹,

Ghosh²

2019

Annals of Physics

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A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a suitable choice of co-ordinates, the Hamiltonian can always be reformulated as a many-particle system in the background of a pseudo-Euclidean metric and subjected to an analogous inhomogeneous magnetic field with a functional form that is identical with space-dependent loss/gain co-efficient.The resulting equations of motion from the Hamiltonian are a system of coupled Liénard-type differential equations. Partially integrable systems are obtained for two distinct cases, namely, systems with (i) translational symmetry or (ii) rotational invariance in a pseudo-Euclidean space. A total number of m+1 integrals of motion are constructed for a system of 2m particles, which are in involution, implying that two-particle systems are completely integrable. A few exact solutions for both the cases are presented for specific choices of the potential and spacedependent gain/loss co-efficients, which include periodic stable solutions. Quantization of the system is discussed with the construction of the integrals of motion for specific choices of the potential and gain-loss coefficients. A few quasi-exactly solvable models admitting bound states in appropriate Stoke wedges are presented.

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Section: Unidirectional Coupling Between System and Bathmentioning

confidence: 86%

Integrable coupled Liénard-type systems with balanced loss and gain

Sinha¹,

Ghosh²

2019

Annals of Physics

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“…There are various possibilities for generalizing this system to N coupled chain of nonlinear oscillators. A straightforward generalization would be to consider the potential, (37) and the representations in Eqs. (23) and (28).…”

Section: Examplesmentioning

confidence: 99%

Hamiltonian formulation of systems with balanced loss–gain and exactly solvable models

Ghosh

Sinha

2018

Annals of Physics

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A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occur in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion is constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

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“…By definition, the intertwining operators q ± l , p ∓ l , and, correspondingly, two terms in the definition (15) of h (1) ik are mutually orthogonal, q ± l p ∓ l = 0. These two terms in h (1) ik were necessary to obtain the Hamiltonian of the Schrödinger form, and the orthogonality is important to provide the intertwining relations (18), (19).…”

Section: Two-dimensional Susy Qm With First-order Superchargesmentioning

confidence: 99%

Nonlinear supersymmetric quantum mechanics: concepts and realizations

Andrianov¹,

Ioffe²

2012

J. Phys. A: Math. Theor.

128

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Abstract. Nonlinear SUSY approach to spectral problems in Quantum Mechanics is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described. For various two-dimensional models it is elaborated how Nonlinear SUSY provides two new methods of supersymmetric separation of variables. In the framework of these methods 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. Emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of Nonlinear SUSY in one-dimensional stationary and non-stationary as well as in two-dimensional QM.

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Supersymmetric many-particle quantum systems with inverse-square interactions

Cited by 15 publications

References 166 publications

Integrable coupled Liénard-type systems with balanced loss and gain

Integrable coupled Liénard-type systems with balanced loss and gain

Hamiltonian formulation of systems with balanced loss–gain and exactly solvable models

Nonlinear supersymmetric quantum mechanics: concepts and realizations

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