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Day November 8, 2010

Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems

Henning Schomerus

(a) Sketch of a nonhermitian PT-symmetric system, where a region with absorption rate μ (and mean level spacing, left) is coupled symmetrically via a tunnel barrier (supporting N channels with transmission probability T) to an amplifying region with a matching amplification rate (right). Below this, the scattering description of the system. (b) Two routes to spontaneous PT-symmetry breaking, depending on whether the hermitian limit μ = 0 is T -symmetric (orthogonal class displaying level crossings, left) or not (unitary class displaying avoided crossings, right). Shown are real eigenvalues of a random Hamiltonian H [Eq. (4)] as function of T for fixed μ = 0 (left of dashed line), and then as a function of μ for fixed T = 1 (right of dashed line). Complex-valued levels (formed by level coalescence at μ > 0) are not shown. Here μ0 = √N/2, and we set N = 10.PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous PT-symmetry breaking can occur via two distinct mechanisms, whose predominance is associated to different universality classes. Present optical experiments fall into the orthogonal class, where symmetry-induced level crossings render the characteristic absorption rate independent of the coupling strength between the symmetry-related parts of the system.
Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics)