Algebraic solution of the Hubbard model on the infinite interval

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2) ) and that the bound states are Yangian singlet.     

Concurrence, tangle and fully entangled fraction

We show that although we cannot distil a singlet from many pairs of bound entangled states, the concurrence and the tangle of two entangled quantum states are always strictly larger than those of one of them, even both entangled quantum states are bound entangled. We present a relation between the concurrence and the fidelity of optimal teleportation. We also give new upper and lower bounds for concurrence and tangle.     

Origin of excess low-energy states in a disordered superconductor in a Zeeman field

Tunneling density of states measurements of disordered superconducting Al films in high Zeeman fields reveal a significant population of subgap states which cannot be explained by standard BCS theory. We provide a natural explanation of these excess states in terms of a novel disordered Larkin-Ovchinnikov phase that occurs near the spin-paramagnetic transition at the Chandrasekhar-Clogston critical field. The disordered Larkin-Ovchinnikov superconductor is characterized by a pairing amplitude that changes sign at domain walls. These domain walls carry magnetization and support Andreev bound states that lead to distinct spectral signatures at low energy.     

Motion of bound domain walls in a spin ladder

The elementary excitation spectrum of the spin- \frac12\frac{1}{2} antiferromagnetic (AFM) Heisenberg chain is described in terms of a pair of freely propagating spinons. In the case of the Ising-like Heisenberg Hamiltonian spinons can be interpreted as domain walls (DWs) separating degenerate ground states. In dimension d > 1, the issue of spinons as elementary excitations is still unsettled. In this paper, we study two spin- \frac12\frac{1}{2} AFM ladder models in which the individual chains are described by the Ising-like Heisenberg Hamiltonian. The rung exchange interactions are assumed to be pure Ising-type in one case and Ising-like Heisenberg in the other. Using the low-energy effective Hamiltonian approach in a perturbative formulation, we show that the spinons are coupled in bound pairs. In the first model, the bound pairs are delocalized due to a four-spin ring exchange term in the effective Hamiltonian. The appropriate dynamic structure factor is calculated and the associated lineshape is found to be almost symmetric in contrast to the 1d case. In the case of the second model, the bound pair of spinons lowers its kinetic energy by propagating between chains. The results obtained are consistent with recent theoretical studies and experimental observations on ladder-like materials.     

Generation of bound solitons in actively phase modulation mode-locked fiber ring resonators

Bound solitons generated in actively mode-locked lasers enable new forms of pulse pairs and multiple pairs or groups of solitons in optical transmission or logics. In this paper, we present the generation of stable bound states of multiple solitons in an active mode-locked fiber laser using continuous phase modulation for wideband phase matching. Not only that dual-soliton bound states but also the triple- and quadruple-soliton pulses can be established. Simulation of the generated solitons are demonstrated. We have also prove by simulation that experimental relative phase difference and chirping caused by phase modulation of LiNbO₃ modulator in the fiber loop significantly influences the interaction between the solitons and hence their stability as they circulate in the anomalous path-averaged dispersion fiber loop.     

Multi-soliton complexes in mode-locked fiber lasers

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers in the normal dispersion domain. In the distributed mathematical model (complex cubic-quintic Ginzburg–Landau equation), we observe a discrete family of soliton pairs with equidistantly increasing peak separation. We show that stabilization of previously unstable bound states can be achieved when the finite relaxation time of the saturable absorber is taken into account. The domain of stability can be controlled by varying this relaxation time. Furthermore, we investigate the parameter domain where the region of stable bound states does not shrink to zero for vanishing absorber recovery time corresponding to a laser with an instantaneous saturable absorber. For a certain domain of the small-signal gain, we obtain a robust first level bound state with almost constant separation where the phase of the two pulses evolves independently. Moreover, their phase difference can evolve either periodically or chaotically depending on the small signal gain. Interestingly, higher level bound states exhibit a fundamentally different dynamics. They represent oscillating solutions with a phase difference alternating between zero and π.     

Bound states and Cooper pairs of molecules in 2D optical lattices bilayer

We investigate the formation of Cooper pairs, bound dimers and the dimer‐dimer elastic scattering of ultracold dipolar Fermi molecules confined in a 2D optical lattice bilayer configuration. While the energy and their associated bound states are determined in a variational way, the correlated two‐molecule pair is addressed as in the original Cooper formulation. We demonstrate that the 2D lattice confinement favors the formation of zero center mass momentum bound states. Regarding the Cooper pairs binding energy, this depends on the molecule populations in each layer. Maximum binding energies occur for non‐zero (zero) pair momentum when the Fermi system is polarized (unpolarized). We find an analytic expression for the dimer‐dimer effective interaction in the deep BEC regime. The present analysis represents a route for addressing the BCS‐BEC crossover in dipolar Fermi gases confined in 2D optical lattices within the current experimental panorama.     

The pseudogap mode as long-lived states of noncoherent pairs with large momenta

The mirror nesting of the Fermi contour of a quasi-two-dimensional electronic system and the presence of at least one negative eigenvalue of the Fourier transform of interaction energy are sufficient conditions for the formation of bound states of the relative motion of pairs with large total momenta. As distinct from pairing by attractive interactions, the wave functions of such pairs have alternating signs and lines of zeros that twice intersect the Fermi contour in the regions of definition of relative motion momenta. The total number of intersection points between the line of zeros and the Fermi contour is determined by symmetry of a linear combination of the wave functions of crystallographically equivalent pairs. Long-lived quasi-stationary states exist in the form of noncoherent pairs with different but close momenta and cause substantial suppression of the density of one-particle states (the appearance of a pseudogap) over a fairly wide energy range. The upper tempereture bound of the pseudogap is determined by the decay of pairs, and the lower bound, by phase coherence disturbance when pairs leave the condensate that is formed at some optimum pair momentum value owing to mirror nesting.     

Dynamics of domain walls in pattern formation with traveling-wave forcing

We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.     

Correlated trapped bosons and the many-body Efimov effect

We study two-body correlations in systems of identical bosons. We use a Faddeev type of decomposition of the wave function where all pairs of particles are treated equally. At large scattering length appears a series of Efimov-like states, i.e., spatially extended, model-independent many-body bound states inside the trap. They may play a role in the decay of Bose-Einstein condensates.     

Breather states in magnetic domain wall racetrack memory samples

Magnetic domain wall racetrack memory samples allow for the controlled motion of isolated magnetic domain walls in a quasi one-dimensional geometry. Here we consider the possibility of the dynamical formation of bound states of domain walls that can be prepared via a suitably chosen external field. Upon switching off the external field, these domain walls oscillate around their common center of mass, with a frequency depending on the relative initial handedness of the domain wall. Such breather states may be observed by detecting the resulting magnetization oscillations.     

正反重强子对构成的强子分子态能谱

近二十年来,世界上众多高能物理实验发现了大量超出传统夸克模型的共振结构。为了理解 这些性质奇特的共振结构,科学家们提出了很多方法和模型。其中,因为实验上发现的这些奇特态 大多处在一对强子阈值附近,强子分子态的观点得到了很多关注。本文我们将以粲{反粲强子对为例 来探究哪些系统可以形成分子态,进而给出粲{反粲强子分子态的能谱。我们考虑了所有由 S 波粲 介子、粲重子以及窄的 P 波粲介子构成的粲{反粲强子对。我们假定它们之间的相互作用由介子交 换主导,在最低阶近似下可简化为常数。通过求解常数相互作用的 Bethe---Salpeter 方程,我们可以 找到振幅的极点进而确定该系统分子态的质量。最终我们发现,那些通过轻矢量介子交换在阈值附 近产生吸引力的系统,会存在一个靠近阈值的极点。不同的系统,由于其相互作用强度不同,极点 可能会处于能量复平面的第一黎曼面或者第二黎曼面,分别对应于束缚态或者虚态。我们总共发现 了 229 个强子分子态。很多实验上发现的那些位于粲---反粲强子对阈值附近的共振结构可以很好地 与我们的结果吻合。另外,我们需要强调所预言的一个 ΛcΛc  分子态,这个态可以很好地解释北京正负电子谱仪 (BESIII) 上测量的数据。     

Raising and Lowering of Generalized Hulthén Potential from Supersymmetry Approaches

We obtain the exact bound states of the generalized of Hulthén potential with negative energy levels using an analytic approach. In order to obtain bound states, we use the associated Jacobi differential equation. Using the supersymmetry approach to quantum mechanics, we show that these bound states, via four pairs of first order differential operators, represent four types of ladder equations. Two types of these supersymmetric structures suggest derivation of algebric solutions for the bound states using two different approaches. PACS 21.60.Cs; 21.60.Fw; 21.60.-n; 03.65.Fd; 03.65.Ge; 03.65.-w     

Striped phase in the cuprates as a semiclassical phenomenon

The striped phase, a novel type of electron solid, has been observed recently in a number of doped Mott-Hubbard insulators (including cuprates). This solid consists of a parallel array of charged-domain walls, bound states of carriers and Néel walls in the antiferromagnetic spin system. The existence of these states has been predicted well in advance of their experimental observation on the basis of semiclassical (‘Hartree-Fock’) theory. Nevertheless, it is not at all clear whether semiclassics yields a correct explanation. In this paper we will focus especially on the variety of striped phases realized in the cuprates, characterized by a domain wall filling of half a hole per domain wall unit cell. We will unfold the reasons why semiclassics, as applied to simple Hubbard models, favours strongly a filling of one hole per domain wall unit cell, as is for instance the case in the nickelates. Nevertheless, the occurrence of half-filled walls as semiclassical ground states cannot be excluded on general grounds. It might be that Hubbard models do not incorporate the microscopic situation correctly. Instead, we derive a qualitative criterion: in order to acquire a special stability on the semiclassical level, the half-filled domain walls should be characterized by a quadrupling of the period along the walls, involving a modulation in the longitudinal spin- and/or charge channel. 64.60. - i, 71.27. + a, 74.72. - h, 75.10. - b     

Creation dynamics of bound States in supercritical fields

Using space-time resolved solutions to relativistic quantum field theory, we analyze the electron-positron creation process from vacuum in the long-time regime in which multiple pairs are produced. We find that for a supercritical potential of finite extension, the time dependence of the production rate of pairs is described by four distinct regimes that have their direct counterparts in the time evolved spatial density of the particles. These regimes include the shape-invariant birth process, an entanglement-induced reduction of interference, a recurrent Pauli suppression of pair production induced by electron-potential scattering, and finally a production halt associated with a population of supercritical and a partial population of subcritical bound states.     

Fermion states on domain-wall junctions and the flavor number

In this paper we address the problem of localizing fermion states on stable domain-wall junctions. The study focus on the consequences of intersecting six independent 8d domain walls to form 4d junctions in a ten-dimensional spacetime. This is related to the mechanism of relaxing to three space dimensions through the formation of domain-wall junctions. The model is based on six bulk real scalar fields, the φ ⁴ model in its broken phase, the prototype of the Higgs field, and is such that the fermion and scalar modes bound to the domain walls are the zero mode and a single massive bound state, which can be regarded as a two-level system, at least at sufficiently low energy. Inside the junction, we use the fact that some states are statistically more favored to address the possibility of constraining the flavor number of the elementary fermions.     

Chern number spins of Mn acceptor magnets in GaAs

We determine the effective total spin J of local moments formed from acceptor states bound to Mn ions in GaAs by evaluating their magnetic Chern numbers. When individual Mn atoms are close to the sample surface, the total spin changes from J=1 to J=2, due to quenching of the acceptor orbital moment. For Mn pairs in bulk, the total J depends on pair orientation in the GaAs lattice and on the separation between the Mn atoms. We point out that Berry curvature variation as a function of local moment orientation can profoundly influence the quantum-spin dynamics of these magnetic entities.     

Asymmetric bound states of spiral pairs in excitable media

We present a stable regime of asymmetric bound states for spiral pairs in a generic numerical model of a homogeneous excitable medium. In this regime, one spiral tip (slave) rotates around the other (master). Master-slave dynamics occur for both same-chirality and opposite-chirality spiral pairs in a range of parameters and initial conditions. We study the dependency of master-slave characteristics on the medium's excitation threshold and present a phenomenological model that accounts for the qualitative properties of master-slave dynamics.     

Bogolubov–Hartree–Fock Theory for Strongly Interacting Fermions in the Low Density Limit

We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose–Einstein condensate of fermion pairs. The latter can be described by means of the Gross–Pitaevskii energy functional.