Chon-Fai Kam

University of Macau · Department of Mathematics

The quantum phase transitions of spin‐1 Heisenberg chains with an easy‐axis anisotropy Δ and a uniaxial single‐ion anisotropy D are studied using a multipartite entanglement approach. The genuine tripartite entanglement between the spin blocks, measured by the tripartite qutrit hyperdeterminant, is calculated within the quantum renormalization grou...

Majorana stars, the antipodal directions associated with the coherent states that are orthogonal to a spin state, provide a visualization and a geometric understanding of the structures of general quantum states. For example, the Berry phase of a spin-1/2 is given by half the solid angle enclosed by the close path of its Majorana star. It is concei...

We study the quantum phase transitions of spin-1 Heisenberg chains with an easy-axis anisotropy $\Delta$ and a uniaxial single-ion anisotropy $D$ using a multipartite entanglement approach. The genuine tripartite entanglement between the spin blocks, measured by the tripartite qutrit hyperdeterminant, is calculated within the quantum renormalizatio...

We study the dynamics of a two-level crossing model with a polynomial modification of the linear Landau–Zener tunneling. For a cubic modification, we express the non-adiabatic transition amplitudes analytically via the bi-confluent Heun functions. We find a closed-form series expression of the transition probability at the long time limit, and deri...

Exceptional points, which are spectral degeneracy points in the complex parameter space, are fundamental to non‐Hermitian quantum systems. The dynamics of non‐Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here, non‐adiabatic transitions in non‐Hermitian PT‐symmetric systems are investigat...

Majorana stars, the antipodal directions associated with the coherent states that are orthogonal to a spin state, provide a visualization and a geometric understanding of the structures of general quantum states. For example, the Berry phase of a spin-1/2 is given by half the solid angle enclosed by the close path of its Majorana star. It is concei...

Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-sy...

Majorana stars, the 2j spin coherent states that are orthogonal to a spin-j state, offer a visualization of general quantum states and may disclose deep structures in quantum states and their evolutions. In particular, the genuine tripartite entanglement—the three-tangle of a symmetric three-qubit state, which can be mapped to a spin-3/2 state—is m...

We study the dynamics of a two-level crossing model with a parabolic separation of the diabatic energies. The solutions are expressed in terms of the tri-confluent Heun equations - the generalization of the confluent hypergeometric equations. We obtain analytical approximations for the state populations in terms of Airy and Bessel functions. Applic...

We study the dynamics of a nonlinear two-level crossing model with a cubic modification of the linear Landau-Zener diabatic energies. The solutions are expressed in terms of the bi-confluent Heun functions --- the generalization of the confluent hypergeometric functions. We express the finial transition probability as a convergent series of the par...

We study the dynamics of a two-level crossing model with a parabolic separation of the diabatic energies. The solutions are expressed in terms of the tri-confluent Heun equations-the generalization of the confluent hyper-geometric equations. We obtain analytical approximations for the state populations in terms of Airy and Bessel functions. Applica...

We study the dynamics of a two-level crossing model with a parabolic separation of the diabatic energies. The solutions are expressed in terms of the tri-confluent Heun equations --- the generalization of the confluent hypergeometric equations. We obtain analytical approximations for the state populations in terms of Airy and Bessel functions. Appl...

Majorana stars, the $2j$ spin coherent states that are orthogonal to a spin-$j$ state, offer a geometric representation of the quantum state and many interesting quantum characteristics. In particular, the genuine tripartite entanglement - the three-tangle of a symmetric three-qubit state, which can be mapped to a spin-3/2 state, is measured by the...

Berry phases and gauge structures are fundamental quantum phenomena. In linear quantum mechanics the gauge field in parameter space presents monopole singularities where the energy levels become degenerate. In nonlinear quantum mechanics, which is an effective theory of interacting quantum systems, there can be phase transitions and hence critical...