Dynamical mean-field theory for pairing and spin gap in the attractive hubbard model

We solve the attractive Hubbard model for arbitrary interaction strengths within dynamical mean-field theory. We compute the transition temperature for superconductivity and analyze electron pairing in the normal phase. The normal state is a Fermi liquid at weak coupling and a non-Fermi-liquid state with a spin gap at strong coupling. Away from half filling, the quasiparticle weight vanishes discontinuously at the transition between the two normal states.     

Self-synchronization of coupled oscillators with hysteretic responses

We analyze a large system of nonlinear phase oscillators with sinusoidal nonlinearity, uniformly distributed natural frequencies and global all-to-all coupling, which is an extension of Kuramoto's model to second-order systems. For small coupling, the system evolves to an incoherent state with the phases of all the oscillators distributed uniformly. As the coupling is increased, the system exhibits a discontinuous transition to the coherently synchronized state at a pinning threshold.of the coupling strength, or to a partially synchronized oscillation coherent state at a certain threshold below the pinning threshold. If the coupling is decreased from a strong coupling with all the oscillators synchronized coherently, this coherence can persist until the depinning threshold which is less than the pinning threshold, resulting in hysteretic synchrony depending on the initial configuration of the oscillators. We obtain analytically both the pinning and depinning threshold and also expalin the discontinuous transition at the thresholds for the underdamped case in the large system size limit. Numerical exploration shows the oscillatory partially coherent state bifurcates at the depinning threshold and also suggests that this state persists independent of the system size. The system studied here provides a simple model for collective behaviour in damped driven high-dimensional Hamiltonian systems which can explain the synchronous firing of certain fireflies or neural oscillators with frequency adaptation and may also be applicable to interconnected power systems.     

Synchronized cluster formation in coupled laser networks

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.     

Spin-orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas

Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin-orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin-orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin-orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin-orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.     

Non trivial overlap distributions at zero temperature

We explore the consequences of Replica Symmetry Breaking at zero temperature. We introduce a repulsive coupling between a system and its unperturbed ground state. In the Replica Symmetry Breaking scenario a finite coupling induces a non trivial overlap probability distribution among the unperturbed ground state and the one in presence of the coupling. We find a closed formula for this probability for arbitrary ultrametric trees, in terms of the parameters defining the tree. The same probability is computed in numerical simulations of a simple model with many ground states, but no ultrametricity: polymers in random media in 1+1 dimension. This gives us an idea of what violation of our formula can be expected in cases when ultrametricity does not hold. Received 16 June 2000     

Inhomogeneous Ising models with diagonal structure on a square lattice

We study inhomogeneous Ising models on a square lattice. The nearest neighbour couplings are allowed to be of arbitrary strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate the partition function and free energy for a random coupling distribution of finite period. The phase transition is universally of Ising type. The transition temperature is independent of specific details of the coupling distribution. In particular, unexpected results for the absence of a phase transition are derived. Special examples are considered in detail, phase diagrams and critical temperature are determined. We calculate ground state energy and ground state degeneracy or, equivalently, rest entropy for “pure” frustration models, i.e. models with couplings of fixed strength but arbitrary sign, which never show a phase transition at a finite temperature.     

Fluctuation theorem for entropy production at strong coupling

Fluctuation theorems have been applied successfully to any system away from thermal equilibrium, which are helpful for understanding the thermodynamic state evolution. We investigate fluctuation theorems for strong coupling between a system and its reservoir, by path-dependent definition of work and heat satisfying the first law of thermodynamics. We present the fluctuation theorems for two kinds of entropy productions. One is the informational entropy production, which is always non-negative and can be employed in either strong or weak coupling systems. The other is the thermodynamic entropy production, which differs from the informational entropy production at strong coupling by the effects regarding the reservoir. We find that, it is the negative work on the reservoir, rather than the nonequilibrium of the thermal reservoir,which invalidates the thermodynamic entropy production at strong coupling. Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.     

Resonance tongues in a system of globally coupled FitzHugh-Nagumo oscillators with time-periodic coupling strength

We investigate the dynamics of a population of globally coupled FitzHugh-Nagumo oscillators with a time-periodic coupling strength. While for synchronizing global coupling, the in-phase state is always stable, the oscillators split into several cluster states for desynchronizing global coupling, most commonly in two, irrespective of the coupling strength. This confines the ability of the system to form n:m locked states considerably. The prevalence of two and four cluster states leads to large 2:1 and 4:1 subharmonic resonance regions, while at low coupling strength for a harmonic 1:1 or a superharmonic 1:m time-periodic coupling coefficient, any resonances are absent and the system exhibits nonresonant phase drifting cluster states. Furthermore, in the unforced, globally coupled system the frequency of the oscillators in a cluster state is in general lower than that of the uncoupled oscillator and strongly depends on the coupling strength. Periodic variation of the coupling strength at twice the natural frequency causes each oscillator to keep oscillating with its autonomous oscillation period.     

Competition of spin fluctuations and phonons in superconductivity of ZrZn(2)

It has long been suspected that spin fluctuations in ZrZn2 may lead to a triplet superconductivity. We point out another possibility, an inhomogeneous singlet (Fulde-Ferrell) state. We calculated the electronic structure, as well as the zone center phonons and their coupling with electrons. We find that the exchange splitting is nonuniform and the Fermi surface exhibits substantial nesting. Both factors favor a Fulde-Ferrell state at parts of the Fermi surface. We find a substantial coupling of Zr rattling modes with electrons, which can provide the necessary pairing in the s-channel.     

Stability of incoherence in a population of coupled oscillators

We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is incoherent, with all the oscillators running at their natural frequencies, but when the coupling exceeds a certain threshold, the system spontaneously synchronizes. We obtain the first rigorous stability results for this model by linearizing the Fokker-Planck equation about the incoherent state. An unexpected result is that the system has pathological stability properties: the incoherent state is unstable above threshold, butneutrally stable below threshold. We also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise.     

The Labusch parameter of a driven flux line lattice in YBa Cu O superconducting films

We have investigated the influence of a driving force on the elastic coupling (Labusch parameter) of the field-cooled state of the flux line lattice (FLL) in 400 nm thick YBa₂Cu₃O₇ superconducting films. We found that the FLL of a field-cooled state without driving forces is not in an equilibrium state. Results obtained for magnetic fields applied at and 30 relative to CuO₂ planes, show an enhancement of the elastic coupling of the films at driving current densities several orders of magnitude smaller than the critical one. Our results indicate that the FLL appears to be in a relatively ordered, metastable state after field cooling without driving forces. Received 21 December 1999     

Effects of the spin–orbit coupling on magnetic and superconducting properties in iron-based superconductors

We analyze the magnetic properties through two-orbital Hubbard model with the spin–orbit coupling (SOC) interaction in the iron-based superconductors. With the help of the Ising approximation for the Hund’s coupling between the itinerant electrons and the localized spins, we give a self-consistent account of the various magnetic orders observed in pnictides and the pairing symmetry. We also calculate the local density of states (LDOS) of the vortex state when a magnetic field is applied. The LDOS without SOC shows no resonant peak at the vortex core center in the superconducting state, while it shows an obvious resonant peak when SOC is applied.     

Kondo state of Co impurities at noble metal surfaces

We use scanning tunneling microscopy and spectroscopy to study the properties of magnetic Co adatoms on noble metal surfaces at 6 K. Due to spin-flip scattering of the substrate electrons at the impurity the many-body Kondo state forms. This state is characterized by an energy, the Kondo temperature T_K. We measure T_K of adatom systems and a resonant scattering phase shift locally and are thus able to discuss the coupling of the Co adatom to the metal electronic system. From the resonant scattering phase shift of the surface-state electrons scattering off a Co adatom on Ag(111), we find that the coupling to the surface state is rather weak. On the other hand, increasing the number of nearest neighbor substrate atoms increases the coupling of a Co adatom to the host metal and increases T_K. This shows the dominant character of the coupling of the Co atom to the bulk states of the substrate crystal. PACS 72.10.Fk; 68.37,Ef; 72.15.Qm     

Three-step approach to Fokker-Planck equation for an interacting open waveguide system and localizable entanglement dynamics

We consider a system of three coupled single-mode waveguides each locally interacting with its own Gaussian environment and present a general solution for this coupled system initially in any Gaussian state using the symplectic operations. We investigate the dynamics of two-mode localizable entanglement contained in the evolved state when the system is initially in three-mode bisymmetric Gaussian state in contact with the independent decoherence. We show that such an entanglement exhibits a damped oscillation in a regime of weak waveguide-waveguide coupling and small mean photon numbers of the bath. Remarkably, we find that the entanglement can reappear after the long-time death and arrives at a steady-state oscillation, whose maximum depends strongly on both the squeezing of the bath and the coupling strength between these waveguides. Finally, we generalize the approach to a common squeezed environment case.     

Spin-orbit coupled Fermi gases across a Feshbach resonance

In this Letter we study both ground state properties and the superfluid transition temperature of a spin-1/2 Fermi gas across a Feshbach resonance with a synthetic spin-orbit coupling, using the mean-field theory and the exact solution of two-body problem. We show that a strong spin-orbit coupling can significantly enhance the pairing gap for negative scattering length a(s), due to increased density of state at Fermi surface. Strong spin-orbit coupling can also significantly enhance the superfluid transition temperature Tc to a sizable fraction of Fermi temperature when a(s) ≤ 0, while it suppresses Tc slightly for positive a(s). The interaction energy and pair size at resonance are also discussed.     

Ground-states and rotational properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate in a concentrically coupled toroidal trap

We investigate the ground states of an antiferromagnetic spin-1 Bose–Einstein condensate with spin–orbit coupling in a concentrically coupled toroidal trap. A new necklace-type state with double-ring structure is created in the system due to the spin–orbit coupling. The petal number of the necklace state is increased with enhancing the strength of the spin–orbit coupling. When the rotation is introduced, the condensate can be dragged into the outer trough of the trap by increasing the rotation frequency, which makes it possible to realize the exotic ground state combined by the necklace state at the inner trough and the persistent flow at the outer one. Once the two troughs of the toroidal trap are populated by the persistent flow at the specific effective interactions between atoms, the hidden vortices may occur in the central region of the trap and at the barrier between the two troughs. In addition, the visible vortex with the laminar structure can be generated under the more effective atomic interaction.     

One-dimensional δ-function attractive Fermi gas in an external magnetic field

We investigate the ground-state properties of a one-dimensional spin-1/2 fermionic atoms interacting through the attractive δ-function potential in an external magnetic field. By the thermal Bethe ansatz method, the integral equations for the dressed energies are formulated. Those integral equations at zero-temperature are solved in the power series forms of rapidity and momentum for both strong and weak coupling cases. The magnetization as a function of the coupling constant and the external field is also obtained explicitly. Based on the analytic results, quantum phase transitions are identified among three phases, an unpolarized fully paired state, a fully polarized normal ferromagnetic state and a mixed state of paired and unpaired atoms.     

Zn1-xMnxS(001)稀磁半导体薄膜的能量稳定性、磁性和电子结构

通过基于广义梯度近似的总能密度泛函理论研究不同Mn掺杂浓度的ZnS(001)薄膜的电学和磁学特性. 计算单个Mn原子和两个Mn原子处于各种掺杂位置及不同的磁耦合状态时的能量稳定性.计算了单个Mn原子掺杂和两个Mn原子掺杂的ZnS(001)薄膜的态密度. 不同掺杂组态的p-d杂化的程度不同. 不同掺杂组态,Mn原子所处的晶场环境不同,所以不同掺杂组态的Mn的3d分波态密度峰的劈裂有很大的不同. 掺杂两个Mn原子时,得到三种稳定组态的基态都是反铁磁态. 分析了以上三种能量稳定的组态中,两个Mn原子在不同磁耦合状态下的3d态密度图. 当两原子为铁磁耦合时,由于d-d电子相互作用,使反键态的态密度峰明显加宽. 随着Mn掺杂浓度的增加,Mn原子有相互靠近,并围绕S原子形成団簇的趋势. 对于这样的组态,Mn原子之间为反铁磁耦合能量更低.     

Ground State of a Quantum Particle Coupled to a Scalar Bose Field

We use methods from functional integration to prove the existence and uniqueness of the ground state of a confined quantum particle coupled to a scalar massless Bose field. For an external potential growing at infinity, the ground state exists under fairly general conditions while, for a decaying potential, an unphysical condition on the coupling strength is still needed.     

Athermal dynamics of strongly coupled stochastic three-state oscillators

We study the behavior of globally coupled ensembles of cyclic stochastic three-state units with transition rates from i-1 to i proportional to the number of units in state i. Contrary to mean-field theory predictions, numerical simulations show significant stochastic oscillations for sufficiently large coupling strength. The order parameter characterizing units synchrony increases monotonically with coupling while the coherence of oscillations has a maximum at a certain coupling strength. We find the exact formulas for the stationary probability distribution and the order parameter.