Bosons or Fermions in 1D Power Potential Trap with Repulsive Delta Function Interaction

We study the ground state of a 1D many Boson or Fermion system with repulsive delta function interparticle interaction trapped in an external potential V （x） =｜x｜a/2 where a 〉 0.     

Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction

Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.     

Spin-1/2 Fermion Gas in One-Dimensional Harmonic Trap with Attractive Delta Function Interaction

In terms of the Thomas-Fermi method, we solve the ground state energy of the N-body 1 D harmonically trapped spin-1/2 fermion gas with the attractive δ-function interaction in the limit N →∞.     

Antiferromagnetism of Repulsively Interacting Fermions in a Harmonic Trap

We propose a real-space Gutzwiller variational approach and apply it to a system of repulsively interacting ultracold fermions with spin-1/2 trapped in an optical lattice with a harmonic confinement. Using the realspace Gutzwiller variational approach, we find that in a system with balanced spin-mixtures on a square lattice, antiferromagnetism either appears in a checkerboard pattern or forms a ring, and the antiferromagnetie order is stable in the regions where the particle density is close to one, which is consistent with the recent results obtained by the real-space dynamical mean-field theory approach. We also investigate the imbalanced case and find that the antiferromagnetic order is suppressed there.     

Polar-Core Spin Vortex of Quasi-2D Spin-2 Condensate in a Flat-Bottomed Optical Trap

Motivated by the recent experiments realized in a flat-bottomed optical trap [Science 347(2015) 167;Nat. Commun. 6(2015) 6162], we study the ground state of polar-core spin vortex of quasi-2D spin-2 condensate in a homogeneous trap plus a weak magnetic field. The exact spatial distribution of local spin is obtained and the vortex core are observed to decrease with the growth of the effective spin-spin interaction. For the larger effective spin-spin interaction, the spatial distribution of spin magnitude in spin-2 condensate we obtained agrees well with that of spin-1 condensate in a homogeneous trap, where a polar-core spin vortex was schematically demonstrated as a fully-magnetized planar spin texture with a zero-spin core. The effective spin-spin interaction is proportional to both the bare spin-spin interaction and the radius of the homogeneous trap, simultaneously. Thus the polar-core spin vortex we obtained can be easily controlled by the radius of the trap.     

Efimov Physics with {1/2} Spin-Isospin Fermions

The structure of few-fermion systems having \({1/2}\) spin-isospin symmetry is studied using potential models. The strength and range of the two-body potentials are fixed to describe low energy observables in the angular momentum \({L=0}\) state and spin \({S=0,1}\) channels of the two-body system. Successively the strength of the potentials are varied in order to explore energy regions in which the two-body scattering lengths are close to the unitary limit. This study is motivated by the fact that in the nuclear system the singlet and triplet scattering lengths are both large with respect to the range of the interaction. Accordingly we expect evidence of universal behavior in the three- and four-nucleon systems that can be observed from the study of correlations between observables. In particular we concentrate in the behavior of the first excited state of the three-nucleon system as the system moves away from the unitary limit. We also analyze the dependence on the range of the three-body force of some low-energy observables in the three- and four-nucleon systems.     

谐振子势与高斯势的联合势阱中两分量旋转玻色爱因斯坦凝聚体的基态特性和自旋纹理

研究了两分量旋转玻色爱因斯坦凝聚体在谐振子势与高斯势的联合势阱中的基态特性和自旋纹理。通过托马斯-费米近似得到每组分凝聚体在相混合态时密度分布首次形成中心洞的临界旋转角频率,并根据旋转角频率与临界旋转角频率的关系,给出了两分量凝聚体的三种不同的基态密度分布:两个都是盘、一个是盘和另一个是环、两个都是环。对于相分离的情况,针对两分量粒子数严重不平衡的凝聚体分别作托马斯费米近似,解析地给出了两分量凝聚体的两种对称基态密度分布。同时研究了凝聚体在两分量的界面处形成的两种赝自旋纹理,它们分别是巨斯格明子和同轴双环斯格明子。     

Self-Dual Transitive Spin 1/2 Models

Most general self-dual spin 1/2 models in any dimension, with interaction that is translation-invariant in a suitable sense (‘transitive models’), are determined. In the process of classification of such systems, a class of models which are self-dual in a particularly strong sense is introduced.     

Quantum Communication in Spin Chain with Multiple Spin Exchange Interaction

The transmission of quantum states in the anisotropic Heisenberg XXZ chain model with three-spin exchange interaction is studied. The average fidelity is used to evaluate the state transfer. It is found that quantum communication can be enhanced by the anisotropic coupling and multiple spin interaction. Such spin model can reduce the time required for the perfect state transmission where the fidelity is unity. The maximally entangled Bell states can be generated and separated from the whole quantum systems.     

Semiclassical Expectation Values for Relativistic Particles with Spin 1/2

For relativistic particles with spin 1/2, which are described by the Dirac equation, a semiclassical trace formula is introduced that incorporates expectation values of observables in eigenstates of the Dirac-Hamiltonian. Furthermore, the semiclassical limit of an average of expectation values is expressed in terms of a classical average of the corresponding classical observable.     

A Generalized Talmi-Moshinsky Transformation for 1D Harmonic Oscillator Functions and Interaction Matrix Elements

A generalized Talmi-Moshinsky transformation relating one-dimensional harmonic oscillator product states with different sets of Jacobian coordinates is derived for systems composed of an arbitrary number of particles with arbitrary masses. With the help of our method the multidimensional integral which must be performed to evaluate an N-particle matrix element can be transformed into a sum of products of one-dimensional integrals.     

The Hawking Effect for Spin 1/2 Fields

We prove the Hawking effect, for a gravitational collapse of charged star in the case of a charged massive Dirac field.     

Non-Universality in Ising Models with Four Spin Interaction

We consider two bidimensional classical Ising models, coupled by a weak interaction bilinear in the energy densities of the two systems; the model contains, as limiting cases, the Ashkin–Teller and the Eight-vertex models for certain values of their parameters. We write the energy–energy correlations and the specific heat as Grassman integrals formally describing Dirac 1+1 dimensional interacting massive fermions on a lattice, and an expansion based on Renormalization Group is written for them, convergent up to temperatures very close to the critical temperature for small coupling. The asymptotic behaviour is determined by critical indices which are continuous functions of the coupling.