Spin 1/2 Fermions in 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction

Following the general theory developed in our earlier papers I [Chin. Phys. Lett. 26 （2009） 120506] and II [Chin. Phys. Left. 27 （2010） 020506] for Bosons, we extend the investigation to trapped spin 1/2 Fermions.     

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 →∞.     

A Particle Interacting with V-shaped Potential Decorated by a Dirac Delta Function Interaction at Center

The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.     

Statistical Interaction Description of Pauli Crystals in 2D Systems of Harmonically Confined Fermions

It is conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures, called Pauli crystals, are predicted for a two‐dimensional (2D) system of free fermions under harmonic confinement. In this work, the possibility of this outcome is pursued and a theoretical model is considered that may capture both qualitatively and quantitatively, the key features of the abovementioned setup. The results for $N=3$ and 6 particles show that the minimum energy configuration corresponds to and is in good quantitative agreement with the reported values of Pauli crystals seen in single‐shot imaging data obtained via the configuration density technique. Numerical results for larger systems of $N=15$ and 30 particles show that the crystalline configurations observed are not the same as the classical Wigner crystal structures that emerge should the confined charged particles interact with a Coulomb potential. An important question floated is whether such crystalline structures do really exist in a quantum system or whether they are artifacts of the methods used to analyze them.     

Static Dielectric Function and Interaction Potential in Strong Coupling with AdS/CFT

In this paper, we study the static dielectric function and interaction potential in strong coupling limit with AdS/CFT correspondence. The dielectric function is depressed compared with that in weak coupling. The interaction potential then presents a weaker screening characteristics in strong coupling, which indicates a smaller Debye mass compared with weak coupling.     

Static Dielectric Function and Interaction Potential in Strong Coupling with AdS/CFT

In this paper, we study the static dielectric function and interaction potential in strong coupling limit with AdS/CFT correspondence. The dielectric function is depressed compared with that in weak coupling. The interaction potential then presents a weaker screening characteristics in strong coupling, which indicates a smaller Debye mass compared with weak coupling.     

New Exact Solutions and Dynamics in （3＋1）-Dimensional Gross-Pitaevskii Equation with Repulsive Harmonic Potential

Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the （3＋1）-dimensional Gross-Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.     

Effective Two-Loop Thermodynamic Potential with Fermions in the Real-Time Formalism of Thermal Field Theory

Within the real-time formalism of thermal field theory, we apply the hard thermal loop resummation technique to calculate effective two-loop thermodynamic potential in quarkgluon and its renormalization. The result with collective effects is obtained, which is valid for an arbitrary number of quark flavors with masses.     

Bose-Einstein Condensate in a Linear Trap with a Dimple Potential

We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.     

The (2+1) Dirac Equation with a Delta Potential

In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric (r–r ₀) potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of r ₀ can be established by an SO(2) transformation. We obtain a transcendental equation for calculating the energy of the bound state from the matching condition in the configuration space. The condition for existence of bound states is determined by the Sturm-Liouville theorem.     

Low-Lying States of Four-Boson Systems with a Repulsive Core and an Attractive Tail in the Interaction

 The Schr?dinger equation of a four-boson model system is solved via a variational procedure. The pairwise interaction contains a repulsive core and an attractive tail. The features of the low-lying states are extracted via an analysis of the wave functions. The decisive effect of symmetry is demonstrated. A classification of states based on the inherent nodal structures of the internal wave functions is proposed. Received May 10, 1999; revised June 20, 2000; accepted for publication August 16, 2000     

U(1)-Gauge Theory of Fermions in Spacetimes with Horizons

A U(1)-gauge theory of fermions is obtained inspacetimes having horizons, including physicallyinteresting black-hole spacetimes as well as unphysicalspacetimes like NUT.     

Low-lying Collective Modes of a 1D Dipolar Quantum Gas in an Anharmonic Trap

The low-lying collective modes of an anharmonically confined one-dimensional ultracold dipolar Bose gas are investigated by using time-dependent variational method. The frequencies of dipole mode and breathing mode are obtained analytically in the full crossover regime from a Tonks-Girardeau gas to a dipolar density wave state. We find that the frequency shifts caused by quartic distortion of the potential can be amplified by interparticle interaction and the collapse and revival of the collective excitations can be observed in the anharmonic trap.     

Injected Power Fluctuations in 1D Dissipative Systems

Using fermionic techniques, we compute exactly the large deviation function (ldf) of the time-integrated injected power in several one-dimensional dissipative systems of classical spins. The dynamics are T=0 Glauber dynamics supplemented by an injection mechanism, which is taken as a poissonian flipping of one particular spin. We discuss the physical content of the results, specifically the influence of the rate of the Poisson process on the properties of the ldf.     

强非局域介质中1+1维高斯型损耗空间双孤子的相互作用

研究了1+1维高斯型双光束在含小损耗的强非局域非线性介质中的传输特性。通过对该介质中光束传输遵循的非局域非线性薛定谔方程进行近似简化,得到了含小损耗强非局域非线性介质中1+1维高斯型双光束传输模型。在此基础上运用解析的方法研究了双光束传输的演化规律,得到了准双孤子解。经过进一步分析发现,在传输过程中两光束中心的轨迹为艾里函数;两光束会准周期性地碰撞、分离;随着传输距离的增大,两光束中心之间的最大距离会越来越大。另一方面,当损耗逐渐增大时,两光束的碰撞空间周期将变短,同时两光束中心之间的最大距离也越来越大。     

强非局域介质中1+1维高斯型损耗空间双孤子的相互作用

研究了1+1维高斯型双光束在含小损耗的强非局域非线性介质中的传输特性。通过对该介质中光束传输遵循的非局域非线性薛定谔方程进行近似简化,得到了含小损耗强非局域非线性介质中1+1维高斯型双光束传输模型。在此基础上运用解析的方法研究了双光束传输的演化规律,得到了准双孤子解。经过进一步分析发现,在传输过程中两光束中心的轨迹为艾里函数;两光束会准周期性地碰撞、分离;随着传输距离的增大,两光束中心之间的最大距离会越来越大。另一方面,当损耗逐渐增大时,两光束的碰撞空间周期将变短,同时两光束中心之间的最大距离也越来越大。