Professor Chen Ping Yang's early significant contributions to mathematical physics

In the 60's Professor Chen Ping Yang with Professor Chen Ning Yang published several seminal papers on the study of Bethe's hypothesis for various problems of physics. The works on the lattice gas model, critical behaviour in liquid-gas transition, the one-dimensional (1D) Heisenberg spin chain, and the thermodynamics of 1D delta-function interacting bosons are significantly important and influential in the fields of mathematical physics and statistical mechanics. In particular, the work on the 1D Heisenberg spin chain led to subsequent developments in many problems using Bethe's hypothesis. The method which Yang and Yang proposed to treat the thermodynamics of the 1D system of bosons with a delta-function interaction leads to significant applications in a wide range of problems in quantum statistical mechanics. The Yang and Yang thermodynamics has found beautiful experimental verifications in recent years.Comment: 5 pages + 3 figure

Exact Entanglement dynamics in Three Interacting Qubits

Motivated by recent experimental study on coherent dynamics transfer in three interacting atoms or electron spins \cite{Barredo:2015,Rosenfeld:2018}, here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. So that dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer, characterized by the quantum mutual information and concurence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind.Comment: 6 pages + 5 figure

The spin-s homogeneous central spin model: exact spectrum and dynamics

We consider the problem of a central spin with arbitrary spin s that interacts pairwise and uniformly with a bath of N spins with s=1/2. We present two approaches for determining the exact spectrum of this model, one based on properties of SU(2), and the other based on integrability. We also analyze the exact time evolution of a spin coherent state, and compute the time evolution of various quantities of physical interest, including the entanglement entropy, spin polarization and Loschmidt echo.Comment: 19 page

Determining the nature of white dwarfs from low-frequency gravitational waves

An extreme-mass-ratio system composed of a white dwarf (WD) and a massive black hole can be observed by the low-frequency gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA). When the mass of the black hole is around $10^4 \sim 10^5 M_\odot$, the WD will be disrupted by the tidal interaction at the final inspiraling stage. The event position and time of the tidal disruption of the WD can be accurately determined by the gravitational wave signals. Such position and time depend upon the mass of the black hole and especially on the density of the WD. We present the theory by using LISA-like gravitational wave detectors, the mass-radius relation and then the equations of state of WDs could be strictly constrained (accuracy up to $0.1\%$). We also point out that LISA can accurately predict the disruption time of a WD, and forecast the electromagnetic follow-up of this tidal disruption event.Comment: 7 pages, 2 figure

Exact quantum dynamics of XXZ central spin problems

We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with few to many bath spins, and for a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field $B$, coupling constant $A$ and longitudinal interaction $\Delta$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the resonance condition $B=\Delta=A$, the location of the $m$-th revival peak in time reaches a simple relation $t_{r} \simeq\frac{\pi N}{A} m$ for a large $N$. For $\Delta =0$, $N\to \infty$ and a small polarization in the initial spin coherent state, our analytical result for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problems and the light-matter interacting systems in quantum nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes, while disappearing at strong inhomogeneity.Comment: added new result on inhomogeneous central spin problem and added new references and supplementary material, 6 pages + 15 pages; 4 figures + 14 figure

Multiple discrete soluble aggregates influence polyglutamine toxicity in a Huntington\u27s disease model system

Huntington’s disease (HD) results from expansions of polyglutamine stretches (polyQ) in the huntingtin protein (Htt) that promote protein aggregation, neurodegeneration, and death. Since the diversity and sizes of the soluble Htt-polyQ aggregates that have been linked to cytotoxicity are unknown, we investigated soluble Htt-polyQ aggregates using analytical ultracentrifugation. Soon after induction in a yeast HD model system, non-toxic Htt-25Q and cytotoxic Htt-103Q both formed soluble aggregates 29S to 200S in size. Because current models indicate that Htt-25Q does not form soluble aggregates, reevaluation of previous studies may be necessary. Only Htt-103Q aggregation behavior changed, however, with time. At 6 hr mid-sized aggregates (33S to 84S) and large aggregates (greater than 100S) became present while at 24 hr primarily only mid-sized aggregates (20S to 80S) existed. Multiple factors that decreased cytotoxicity of Htt-103Q (changing the length of or sequences adjacent to the polyQ, altering ploidy or chaperone dosage, or deleting anti-aging factors) altered the Htt-103Q aggregation pattern in which the suite of mid-sized aggregates at 6 hr were most correlative with cytotoxicity. Hence, the amelioration of HD and other neurodegenerative diseases may require increased attention to and discrimination of the dynamic alterations in soluble aggregation processes