arXiv subjects

Xiao-Lei Hao

Publications and source records attributed to Xiao-Lei Hao.

3 recordsLinked to original sources

arXiv2022

Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system

We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time-dependent transformation operator has to be $PT$ symmetric and non-unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of non-Hermitian Hamiltonian. We obtain analytically the wave functions and associated non-adiabatic Berry phase $γ_{n}$ for the $n$th eigenstate. The classical version of the non-Hermitian Hamiltonian becomes a complex function of canonical variables and time. The corresponding kernel Hamiltonian is derived with $PT$ symmetric canonical-variable transfer in the classical gauge transformation. Moreover, with the change of position-momentum to angle-action variables it is revealed that the non-adiabatic Hannay's angle $Δθ_{H}$ and Berry phase satisfy precisely the quantum-classical correspondence,$γ_{n}=$ $(n+1/2)Δθ_{H}$.

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arXiv2022

$PT$-symmetric non-Hermitian Hamiltonian and invariant operator in periodically driven $SU(1,1)$ system

We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schrödinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a scheme to construct the non-Hermitian invariant with a $PT$-symmetric but non-unitary transformation operator. The eigenstates of invariant and its complex conjugate form a bi-orthogonal basis to formulate the exact solution. We obtain the non-adiabatic Berry phase, which reduces to the adiabatic one in the slow time-variation limit. A non-unitary time-evolution operator is found analytically. As an consequence of the non-unitarity the ket ($|ψ(t)\rangle $) and bra ($\langle ψ(t)|$) states are not normalized each other. While the inner product of two states can be evaluated with the help of a metric operator. It is shown explicitly that the model can be realized by a periodically driven oscillator.

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arXiv2021

Generalized Bell-like inequality and maximum violation for multiparticle entangled Schrödinger-cat-states of spin-s

This paper proposes a generalized Bell-like inequality (GBI) for multiparticle entangled Schrödinger-cat--states of arbitrary spin-$s$. Based on quantum probability statistics the GBI and violation are formulated in an unified manner with the help of state density operator, which can be separated to local and non-local parts. The local part gives rise to the inequality, while the non-local part is responsible for the violation. The GBI is not violated at all by quantum average except the spin-$1/2$ entangled states. If the measuring outcomes are restricted in the subspace of spin coherent state (SCS), namely, only the maximum spin values $\pm s$, the GBI is still meaningful for the incomplete measurement. With the help of SCS quantum probability statistics, it is proved that the violation of GBI can occur only for half-integer spins but not integer spins. Moreover, the maximum violation bound depends on the number parity of entangled particles, that it is $1/2$ for the odd particle-numbers while $1$ for even numbers.

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