February 2013
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Day February 22, 2013

Quantum fragile matter: mechanical excitations of a Reggeon ion chain

Philipp Strack, Vincenzo Vitelli

This paper proposes to study quantum fragile materials with small linear elasticity and a strong response to zero-point fluctuations. As a first model, we consider a non-unitary (but PT-symmetric) massive quantum chain with a Reggeon-type cubic nonlinearity. At the critical point, the chain supports neither the ordinary quantum phonons of a Luttinger liquid, nor the supersonic solitons that arise in classical fragile critical points in the absence of fluctuations. Quantum fluctuations, approximately captured within a one-loop renormalization group, give rise to mechanical excitations with a nonlinear dispersion relation and dissipative spectral behavior. Models of similar complexity should be realizable with trapped ions.

http://arxiv.org/abs/1302.4453
Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)

Hermitian versus non-Hermitian representations for minimal length uncertainty relations

Sanjib Dey, Andreas Fring, Boubakeur Khantoul

We investigate four different types of representations of deformed canonical variables leading to generalized versions of Heisenberg’s uncertainty relations resulting from noncommutative spacetime structures. We demonstrate explicitly how the representations are related to each other and study three characteristically different solvable models on these spaces, the harmonic oscillator, the manifestly non-Hermitian Swanson model and an intrinsically noncommutative model with Poeschl-Teller type potential. We provide an analytical expression for the metric in terms of quantities specific to the generic solution procedure and show that when it is appropriately implemented expectation values are independent of the particular representation. A recently proposed inequivalent representation resulting from Jordan twists is shown to lead to unphysical models. We suggest an anti-PT-symmetric modification to overcome this shortcoming.

http://arxiv.org/abs/1302.4571

Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)