Confinement-deconfinement transition and spin correlations in a generalized Kitaev model

We present a spin model, namely, the Kitaev model augmented by a loop term and perturbed by an Ising Hamiltonian, and show that it exhibits both confinement-deconfinement transitions from spin liquid to antiferromagnetic/spin-chain/ferromagnetic phases and topological quantum phase transitions between gapped and gapless spin-liquid phases. We develop a fermionic resonating-valence-bonds (RVB) mean-field theory to chart out the phase diagram of the model and estimate the stability of its spin-liquid phases, which might be relevant for attempts to realize the model in optical lattices and other spin systems. We present an analytical mean-field theory to study the confinement-deconfinement transition for large coefficient of the loop term and show that this transition is first order within such mean-field analysis in this limit. We also conjecture that in some other regimes, the confinement-deconfinement transitions in the model, predicted to be first order within the mean-field theory, may become second order via a defect condensation mechanism. Finally, we present a general classification of the perturbations to the Kitaev model on the basis of their effect on it's spin correlation functions and derive a necessary and sufficient condition, within the regime of validity of perturbation theory, for the spin correlators to exhibit a long-ranged power-law behavior in the presence of such perturbations. Our results reproduce those of Tikhonov et al. [Phys. Rev. Lett. 106, 067203 (2011)] as a special case.

Theoretical analysis of photoinduced H-atom elimination in thiophenol

The photoinduced hydrogen elimination reaction in thiophenol via the conical intersections of the dissociative (1)pi sigma* excited state with the bound (1)pi pi* excited state and the electronic ground state has been investigated with ab initio electronic-structure calculations and time-dependent quantum wave-packet calculations. A screening of the coupling constants of the symmetry-allowed coupling modes at the (1)pi pi*-(1)pi sigma* and (1)pi sigma*-S-0 conical intersection shows that the SH torsional mode is by far the most important coupling mode at both conical intersections. A model including three intersecting potential-energy surfaces (S-0, (1)pi pi*, (1)pi sigma*) and two nuclear degrees of freedom (SH stretch and SH torsion) has been constructed on the basis of ab initio complete-active-space self-consistent field and multireference second-order perturbation theory calculations. The nonadiabatic quantum wave-packet dynamics initiated by optical excitation of the (1)pi pi* and (1)pi sigma* states has been explored for this three-state two-coordinate model. The photodissociation dynamics is characterized in terms of snapshots of time-dependent wave packets, time-dependent electronic population probabilities, and the branching ratio of the (2)sigma/(2)pi electronic states of the thiophenoxyl radical. The dependence of the timescale of the photodissociation process and the branching ratio on the initial excitation of the SH stretching and SH torsional vibrations has been analyzed. It is shown that the node structure, which is imposed on the nuclear wave packets by the initial vibrational preparation as well as by the transitions through the conical intersections, has a profound effect on the photodissociation dynamics. The effect of additional weak coupling modes of CC twist (nu(16a)) and ring-distortion (nu(16b)) character has been investigated with three-dimensional and four-dimensional time-dependent wave-packet calculations, and has been found to be minor. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4709608]

The Kπ form factors from analyticity and unitarity

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic K l3 decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of Kπ form factors up to an energy t in = 1GeV 2. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros.

The 27-plet contributions to the CP-conserving K -> pi l(+)l(-) decays

We revisit the rare kaon decays K -> pi l(+)l(-) which are of special interest due to the recent measurements of the charged kaon decay spectra. We compute the contribution of the 27-plet to the decay amplitudes in one loop SU(3) chiral perturbation theory. We estimate the resulting impact to be similar to 10% to the branching ratios of the charged kaon decays, and also noticeably influence the shape of the spectra. With current values of the constants G(8) associated with the octet and G(27) associated with the 27-plet, the contribution of the latter pushes the spectrum in the correct direction, towards the charged lepton spectra. We also discuss the impact for neutral decay rates and spectra.

Quasiuniversal Transient Behavior of a Nonequilibrium Mott Insulator Driven by an Electric Field

We use a self-consistent strong-coupling expansion for the self-energy (perturbation theory in the hopping) to describe the nonequilibrium dynamics of strongly correlated lattice fermions. We study the three-dimensional homogeneous Fermi-Hubbard model driven by an external electric field showing that the damping of the ensuing Bloch oscillations depends on the direction of the field and that for a broad range of field strengths a long-lived transient prethermalized state emerges. This long-lived transient regime implies that thermal equilibrium may be out of reach of the time scales accessible in present cold atom experiments but shows that an interesting new quasiuniversal transient state exists in nonequilibrium governed by a thermalized kinetic energy but not a thermalized potential energy. In addition, when the field strength is equal in magnitude to the interaction between atoms, the system undergoes a rapid thermalization, characterized by a different quasiuniversal behavior of the current and spectral function for different values of the hopping. DOI: 10.1103/PhysRevLett.109.260402

Bounds on the spacelike pion electromagnetic form factor from analyticity and unitarity

We use the recently measured accurate BaBaR data on the modulus of the pion electromagnetic form factor,Fπ(t), up to an energy of 3 GeV, the I=1P-wave phase of the π π scattering ampli-tude up to the ω−π threshold, the pion charge radius known from Chiral Perturbation Theory,and the recently measured JLAB value of Fπ in the spacelike region at t=−2.45GeV2 as inputs in a formalism that leads to bounds on Fπ in the intermediate spacelike region. We compare our constraints with experimental data and with perturbative QCD along with the results of several theoretical models for the non-perturbative contribution s proposed in the literature.

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low-frequency limit we use adiabatic theory, while in the high-frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an ``engineered'' initial state where the particles (taken to be hard-core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light-cone-like spreading of the particles in real space.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Capillary Effect on Vertically Excited Surface Wave in Circular Cylindrical Vessel

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension.

Thermocapillary flow in an annular liquid layer painted on a moving fiber

In the present paper, a theoretical model is studied on the flow in the liquid annular film, which is ejected from a vessel with relatively higher temperature and painted on the moving solid fiber. A temperature gradient, driving a thermocapillary flow, is formed on the free surface because of the heat transfer from the liquid with relatively higher temperature to the environmental gas with relatively lower temperature. The thermocapillary flow may change the radii profile of the liquid film. This process analyzed is based on the approximations of lubrication theory and perturbation theory, and the equation of the liquid layer radii and the process of thermal hydrodynamics in the liquid layer are solved for a temperature distribution on the solid fiber.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Damping of Vertically Excited Surface Wave in Weakly Viscous Fluid

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Analysis of Instabilities in Non-Equilibrium Plasmas

Plasma instabilities with charged particle production processes in non-equilibrium plasma are analysed. A criterion on plasma instabilities is deduced by 6rst-order perturbation theory. The relationship between plasma instabilities and certain factors (degree of non-equilibrium in Plasma, the electron attachment rate coefficient and electron temperature) are described.