Supersymmetric quantum mechanics on non-commutative space

Abstract

We construct supersymmetric quantum mechanics in terms of two real supercharges on noncommutative space in arbitrary dimensions. We obtain the exact eigenspectra of the two and three dimensional noncommutative superoscillators. We further show that a reduction in the phase-space occurs for a critical surface in the space of parameters. At this critical surface, the energy-spectrum of the bosonic sector is infinitely degenerate, while the degeneracy in the spectrum of the fermionic sector gets enhanced by a factor of two for each pair of reduced canonical coordinates. For the two dimensional noncommutative 'inverted superoscillator', we find exact eigenspectra with a welldefined groundstate for certain regions in the parameter space, which have no smooth limit to the ordinary commutative space.

Supersymmetry breaking in noncommutative quantum mechanics

“…In contrast to the noncommutative harmonic oscillator on which a considerable body of literature exists (see e.g. [10,11,12]), the noncommutative supersymmetric harmonic oscillator only received some attention recently [13,14]. Here we follow a different approach, based on [15], and rather focus on the issue of supersymmetry breaking, which was not discussed in these papers.…”

Quantum phase transition in a pseudo-Hermitian Dicke model

“…an operator that is related to its adjoint through a similarity transformation. Both the approaches involving pseudo-hermiticity and PT -invariance are complementary to each other and open up several new directions in the study of nonhermitian operators [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. It may be mentioned here that operators which are non-hermitian with respect to the conventional inner product in the Hilbert space are generally used to simulate dissipative processes.…”