arXiv subjects

Tai-Hua Heng

Publications and source records attributed to Tai-Hua Heng.

6 recordsLinked to original sources

arXiv2026

Deformation quantization for systems with second-class constraints in deformed fermionic phase space

In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket. In this way an oscillator system in a deformed fermionic phase space is analyzed and the corresponding energy level and Wigner functions are evaluated according to scheme of deformation quantization. We also study the entanglement entropy induced by the deformation of the fermionic phase space.

math-ph↗

arXiv2025

Connes spectral distance and nonlocality of generalized noncommutative phase spaces

We study the Connes spectral distance of quantum states and analyse the nonlocality of a 4D generalized noncommutative phase space. By virtue of the Hilbert-Schmidt operatorial formulation, we obtain the Dirac operator and construct a spectral triple corresponding to the noncommutative phase space. Based on the ball condition, we obtain some constraint relations about the optimal elements, and then calculate the Connes spectral distance between two Fock states. Due to the noncommutativity, the spectral distances between Fock states in generalized noncommutative phase spaces are shorter than those in normal phase spaces. This shortening of distances implies some type of nonlocality caused by the noncommutativity. These spectral distances in the 4D generalized noncommutative phase space are additive and satisfy the normal Pythagoras theorem. When the noncommutative parameters go to zero, the results return to those in normal quantum phase spaces.

math-ph↗

arXiv2020

Connes distance of $2D$ harmonic oscillators in quantum phase space

We study the Connes distance of quantum states of $2D$ harmonic oscillators in phase space. Using the Hilbert-Schmidt operatorial formulation, we construct a boson Fock space and a quantum Hilbert space, and obtain the Dirac operator and a spectral triple corresponding to a $4D$ quantum phase space. Based on the ball condition, we obtain some constraint relations about the optimal elements. We construct the explicit expressions of the corresponding optimal elements and then derive the Connes distance between two arbitrary Fock states of $2D$ quantum harmonic oscillators. We prove that these two-dimensional distances satisfy the Pythagoras theorem.

math-ph↗

arXiv2019

Induced entanglement entropy of harmonic oscillators in noncommutative phase space

We study the entanglement entropy of harmonic oscillators in noncommutative phase space. We propose a new definition of quantum Rényi entropy based on Wigner functions in noncommutative phase space. Using the Rényi entropy, we calculate the entanglement entropy of the ground state of the 2D isotropic harmonic oscillators. We find that for some values of the noncommutative parameters, the harmonic oscillators can be entangled in noncommutative phase space. This is a new entanglement-like effect caused by the noncommutativity of the phase space.

math-ph↗

arXiv2017

Research on the halo in $^{31}$Ne with complex momentum representation method

Halo is one of the most interesting phenomena in exotic nuclei especially for $^{31}$Ne, which is deemed to be a halo nucleus formed by a $p-$wave resonance. However, the theoretical calculations don't suggest a $p-$wave resonance using the scattering phase shift approach or complex scaling method. Here, we apply the complex momentum representation method to explore resonances in $^{31}$Ne. We have calculated the single-particle energies for bound and resonant states together with their evolutions with deformation. The results show that the $p-$wave resonances appear clearly in the complex momentum plane accompanied with the $p-f$ inversion in the single-particle levels. As it happens the $p-f$ inversion, the calculated energy, width, and occupation probabilities of major components in the level occupied by valance neutron support a $p-$wave halo for $^{31}$Ne.

nucl-th↗

arXiv2009

Deformation quantization for coupled harmonic oscillators on a general noncommutative space

Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and Wigner functions, which are intrinsic important quantities in the deformation quantization theory. Then based on this observation we investigate a two coupled harmonic oscillators system on the general noncommutative phase space by requiring both spatial and momentum coordinates do not commute each other. We derive all the Wigner functions and the corresponding energy spectra for this system, and consider several interesting special cases, which lead to some significant results.

math-ph↗