Peter N. Meisinger

PT-symmetric quantum mechanics

This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition H†=H on the Hamiltonian, where † represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian H has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement H‡=H, where ‡ represents combined parity reflection and time reversal PT, one obtains new classes of complex Hamiltonians whose spectra are still real and positive. This generalization of Hermiticity is investigated using a complex deformation H=p2+x2(ix)e of the harmonic oscillator Hamiltonian, where e is a real parameter. The system exhibits two phases: When e⩾0, the energy spectrum of H is real and positive as a consequence of PT symmetry. However, when −1<e<0, the spectrum contains an infinite number of complex eigenvalues and a finite number of real, positive eigenvalues b...

Complex periodic potentials with real band spectra

Abstract This paper demonstrates that complex P T-symmetric periodic potentials possess real band spectra. However, there are significant qualitative differences in the band structure for these potentials when compared with conventional real periodic potentials. For example, while the potentials V(x) = i sin2N+1 (x) (N = 0, 1, 2,…) have infinitely many gaps, at the band edges there are periodic wave functions but no antiperiodic wave functions. Numerical analysis and higher-order WKB techniques are used to establish these results.

Phenomenological equations of state for the quark-gluon plasma

Two phenomenological models describing an

Chiral symmetry restoration and ZN symmetry

\mathrm{SU}(N)

Quantum complex Hénon–Heiles potentials

quark-gluon plasma are presented. The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range

Calculation of the hidden symmetry operator in -symmetric quantum mechanics

{T}_{d}\ensuremath{-}{5T}_{d},

Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians

and has the correct blackbody behavior for large temperatures. The

Variational ansatz for PT-symmetric quantum mechanics

N=2

Complex correspondence principle.

deconfinement transition is second order in both models, while

Complete high temperature expansions for one loop finite temperature effects

N=3, 4,