T invariance/ solvable PT-symmetric Hamiltoniansexactly solvable modelsaperiodicperiodiccompletely solvablepartially solvable/ A0365G Solutions of wave equations: bound state in quantum theory A1130E Charge conjugation, parity, time reversal and other discrete symmetries...
A Hamiltonian H is said to be PT-symmetric if it commutes with the operator PT. The key point of PT-symmetric quantum theory is to build a new positive definite inner product on the given Hilbert space so that the given Hamiltonian is Hermitian with respect to the new inner product. The...
将这个哈密顿量变换到momentum space,Hamiltonian将变成这样: H=d1Γ1+d12Γ12+d15Γ15+iγΓ13 where d1=t(1+2cos(kx/2)cos(3ky/2)) d12=−2tcos(kx/2)sin(3ky/2) d15=λSO(2sinkx−4sin(kx/2)cos(3ky/2)) Γ(1,2,3,4,5)=(σx⊗I,σz⊗I,σy⊗sx,σy⊗...
InvestigationofPT—symmetricHamiltonianSystemsfromanAlternativePointof View LIJunQing( 军青),LIQian(牟倩),andMIAOYan—Gang(缪炎川) SchoolofPhysics,NankaiUniversity,Tianjin300071,China (ReceivedMay2,2012;revisedmanuscriptreceivedJuly5,2012) AbstractTwononHermitianPT—symmetricHamiltoniansystemsarereconsideredbymean...
The system is described by a pseudo-Hermitian Hamiltonian and subject to certain conditions, the Hamiltonian shows parity-time (PT) symmetry. The probability amplitudes of various atomic levels both below and above the PT-theshold is worked out....
Physicists are always riveted in predicting how a physical system behaves as a function of time. We begin this review article by understanding various formalisms to study the dynamics of the systems. The once-accepted belief that the Hamiltonian had to be Hermitian to ensure real eigenvalues got...
In recent years, the properties of parity-time (PT) symmetric system are revealed to realize plenty of counterintuitive phenomena[1]. In particular, encircling the exceptional point (EP) in a PT symmetric system for asymmet...
This is unlike the common PT-symmetry breaking, where the intercavity coupling affects the reality of the energy-level spectrum of a PT-symmetric Hamiltonian. By using Supplementary Equations S11d–S11e, the ratio of n_{{\mathrm{ss}},1} to n_{{\mathrm{ss}},2} is derived as n_{{\...
The classical trajectories of the family of complex PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric). The periods o
As mentioned above2, the usual one-dimensional (1D) PT-symmetric Hamiltonian is H=−∂x2+V(x)+iW(x), with V(−x) = V(x) and W(−x) = −W(x). However, physics of semiconductors gives rise to a Hamiltonian in which the effective mass of collective excitations58...