AN EXISTENCE CRITERION FOR THE PT-SYMMETRIC PHASE TRANSITION

作者：Caliceti Emanuela^*; Graffi Sandro

来源：Discrete and Continuous Dynamical Systems-Series B, 2014, 19(7): 1955-1967.

DOI：10.3934/dcdsb.2014.19.1955

We consider on L-2(R) the Schrodinger operator family H(g) with domain and action defined as follows
F(H(g)) =(HR)-R-2() boolean AND L-2M(2) (R); H(g)u -(-d(2)/dx(2) + x(2M)/(2M) -g(xM-1)/(M-1))u
where g epsilon C, M = 2, 4,.... H(g) is self-adjoint if g E I, while H(ig) is PTsymmetric. We prove that H(ig) exhibits the so-called PT-symmetric phase transition. Namely, for each eigenvalue E (ig) of H(ig), g E I, there exist (i7,) epsilon R(m) > 0 such that epsilon (ig) epsilon r for g < R(m) and turns into a pair of complex conjugate eigenvalues for g > Ri(n).

• 出版日期2014-9