Quasi-Stable Configurations of Torus Vortex Knots and Links

The dynamics of torus vortex configurations V_{n, p, q} in a superfluid liquid at zero temperature (n is the number of quantum vortices, p is the number of turns of each filament around the symmetry axis of the torus, and q is the number of turns of the filament around its central circle; radii R₀ and r₀ of the torus at the initial instant are much larger than vortex core width ξ) has been simulated numerically based on the regularized Biot–Savart law. The lifetime of vortex systems till the instant of their substantial deformation has been calculated with a small step in parameter B₀ = r₀/R₀ for various values of parameter Λ = ln(R₀/ξ). It turns out that for certain values of n, p, and q, there exist quasi-stability regions in the plane of parameters (B₀, Λ), in which the vortices remain almost invariable during dozens and even hundreds of characteristic lengths.

     

On Noncommutative Nahm Transform

Motivated by the recently observed relation between the physics of D-branes in the background of B-field and the noncommutative geometry we study the analogue of the Nahm transform for the instantons on the noncommutative torus. Received: 2 November 1999 / Accepted: 2 November 1999     

Minimum dissipative relaxed states in toroidal plasmas

Relaxation of toroidal discharges is described by the principle of minimum energy dissipation together with the constraint of conserved global helicity. The resulting Euler-Lagrange equation is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex domain. The C-K eigenfunctions are obtained as hypergeometric functions that are solutions of scalar Helmholtz equation in toroidal coordinates in the large aspect-ratio approximation. Equilibria are constructed by assuming the current to vanish at the edge of plasma. For the m=0, n=0 (m and n are the poloidal and toroidal mode numbers respectively) relaxed states, the magnetic field, current, q (safety factor) and pressure profiles are calculated for a given value of aspect-ratio of the torus and for different values of the eigenvalue λ _{r 0}. The new feature of the present model is that solutions allow for both tokamak as well as RFP-like behaviour with increase in the values of λ _{r 0}, which is related directly to volt-sec in the experiment.     

Fractional quantum numbers via complex orbifolds

This paper studies both the conductance and charge transport on 2D orbifolds in a strong magnetic field. We consider a family of Landau Hamiltonians on a complex, compact 2D orbifold Y that are parametrised by the Jacobian torus J(Y) of Y. We calculate the degree of the associated stable holomorphic spectral orbibundles when the magnetic field B is large and obtain fractional quantum numbers as the conductance and a refined analysis also gives the charge transport. A key tool studied here is a nontrivial generalisation of the Nahm transform to 2D orbifolds.

     

Stark ladders of resonances: Wannier ladders and perturbation theory

LetH _B be any fixed one-dimensional Bloch Hamiltonian with only the firstm gaps open andH _F=H_B+F_x be the corresponding Stark Hamiltonian. For any positiveF small enoughH _F has onlym ladders of sharp resonances given by the analytic translation method, the decoupled band approximation and the regular perturbation theroy. This way, the Wannier conjecture becomes a definite regular perturbation theory for the Stark ladders as eigenvalues of the translated Hamiltonian.     

Quasi Linear Flows on Tori:¶Regularity of their Linearization

Under suitable conditions a flow on a torus C ^(p) -close, with p large enough, to a quasi periodic diophantine rotation is shown to be “linearizable”, i.e. conjugable to the quasi periodic rotation, by a map that is analytic in the perturbation size. This result is parallel to Moser's theorem stating conjugability in class C ^(p') for some p'<p. The extra conditions restrict the class of perturbations that are allowed. Received: 5 September 1996 / Accepted: 4 August 1997     

On generalized Lax equations of the Lax triple of the BKP and CKP hierarchies

Based on the Lax triple (B_m, B_n, L) of the BKP and CKP hierarchies, we derive the nonlinear evolution equations from the generalized Lax equation. The solutions of some evolution equations are presented, such as soliton and rational solutions.     

Ground state of a spin-phonon system. III. Small-B limit

The ground state of the spin-one-half acoustic phonon system is studied in the limitB1. The technique is to combine the Brillouin-Wigner variational perturbation theory with a source canonical transformation. With theB=0 source transform the energy is calculated as a function of coupling constant through terms of orderB ². To this order there is no phase transition. The theory gives the crossover from perturbation theory to an improved classical theory with quantum fluctuations. With a source transform with a nonzero inverse length the energy estimate is further improved to next order in the coupling constant and for larger values ofB. The soft, infinite-order transition of the modified source theory is removed in the limitB1.     

Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions

We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state pressure and the ground state energy density to second order in the quantum loop expansion. The renormalization group is used to sum up leading and subleading logarithms from all orders in perturbation theory. In the dilute limit, the renormalization group improved pressure and energy density are expansions in powers of the T ^2B and T ^2Bln(T ^2B), respectively, where T ^2B is the two-body T-matrix. Received 19 April 2002 Published online 13 August 2002     

Stability of the Boltzmann equation with potential forces on torus

In this paper, we are concerned with the stability of solutions to the Cauchy problem of the Boltzmann equation with potential forces on torus. It is shown that the natural steady state with the symmetry of origin is asymptotically stable in the Sobolev space with exponential rate in time for any initially smooth, periodic, origin symmetric small perturbation, which preserves the same total mass, momentum and mechanical energy. For the non-symmetric steady state, it is also shown that it is stable in L¹-norm for any initial data with the finite total mass, mechanical energy and entropy.     

Dynamic surface critical behavior of systems with conserved bulk order parameter: Detailed RG analysis of the semi-infinite extensions of modelB with and without nonconservative surface terms

The dynamic surface critical behavior of macroscopic systems whose dynamic bulk critical behavior is described by modelB is investigated. The semi-infinite extensions of bulk modelB introduced in a previous treatment [Phys. Rev. B49, 2846 (1994)] and called modelsB _A andB _B are studied in detail by means of field-theoretic RG methods. The distinctive feature of these models is the presence or absence of relevant nonconservative surface terms. The earlier results on the structure of the required counterterms, the flow equations, and the representation of the surface critical exponents of dynamic quantities at the ordinary and special phase transitions in terms of static bulk and surface exponents are corroborated by means of an explicit two-loop calculation for 4- dimensions. For parameter values corresponding to a given static surface universality class, modelsB _A andB _B represent distinct dynamic surface universality classes. Differences between these manifest themselves in the behavior of scaling functions for dynamic surface susceptibilities. RG-improved perturbation theory is used to compute some of these susceptibilities to one-loop order.Dedicated to Prof. Dr. Herbert Wagner, Ludwig-Maximilians-Universität München, on the occasion of his 60th birthday     

Nil-instantons associated with the classical torus CP 2 model

Finite energy solutions of the classical torus C P ² model are associated with certain analytic maps W C ³ where W is compact three-dimensional nilmanifold.     

Modulation instability of electromagnetic excitations for a Josephson unction in a finite-thickness slab

The modulation instability of finite-amplitude uniform plane waves oscillating with a Josephson frequency and experiencing a nonlinear frequency shift in a finite-thickness slab is studied in terms of the nonlocal electrodynamics of Josephson junction. A dispersion relation for the growth rate of small amplitude perturbation is derived. The domains of modulation instability for these waves are found. Modulation instability of the waves is shown to arise when the wavevectors of long-wave amplitude perturbations fall into the finite range 0 < Q < Q _B (A, D, L). In the range Q ≥ Q _B (A, D, L), the waves are stable.     

微扰的耦合非线性薛定谔方程的近似求解

将直接微扰方法应用于可积的含修正项的非线性薛定谔方程，通过近似解与精确解的比较确定了直接微扰方法的可靠性.继而，将该方法应用于微扰的耦合非线性薛定谔方程，并获得了该微扰方程的可靠的近似解. 关键词： 直接微扰方法 微扰 耦合非线性薛定谔方程 近似解     

An anharmonic force field for carbonyl sulphide

A 16-parameter force field for OCS based on curvilinear coordinates is presented in table 2 and the agreement between observed and calculated transitions and rotational constants is indicated in tables 4, 5 and 6. The computational approach differs from that of Morino and Nakagawa [2] and similar work on other molecules by other authors, in that perturbation theory is eschewed and the calculated vibrational transitions and rotational constants are derived via the numerical solution of a large matrix. The usual parameters x_ij , y_ijk , α _i ^B and γ _ij ^B are thereby rendered inappropriate intermediates. The approach also leads to estimates of B _e - B ₀ for each isotopic species and thence suggests equilibrium distances r _CO = 1·155386(21) Å and r _CS = 1·562021(17) Å.     

Multiple Existence of the Multivortex Solutions of the Self-Dual Chern–Simons CP(1) Model on a Doubly Periodic Domain

In this Letter, we investigate multiple existence of the multivortex solutions of the self-dual Chern–Simons CP(1) model on a flat torus for each range of the symmetry breaking parameter. We also study asymptotics of solutions as the Chern–Simons coupling constant goes to zero.     

On the effect of injection of gas in the numerical simulation of accretion flows

We investigate the effects of various ways of injection of gas at the outer boundary in the numerical simulations of non-viscous accretion flows. We study three models. In Model A, we inject material around the equatorial plane. In Models B and C, fullrange θ injection is used (we employ spherical coordinates). In all three models, the injected material has the same density distribution with polar angle θ. From the equatorial region to the polar regions, angular momentum of the injected material of Model B decreases faster than that in Model C. For all of the models, after a transient episode of infall at the beginning of the simulations, the gas piles up in the equatorial regions outside the black hole and forms a thick torus bounded by a centrifugal barrier. We find that the accretion rates of Models B and C are more than ten times higher than that in Model A. In Model A, there is weak accretion only in the torus and outflows are found on the surface of the torus. In Model B, we find strong inflows on the surface of its torus, and the accretion in the torus is weak. In Model C, strong inflows also occur on the surface of its torus, but the accretion regions are narrower and there are strong outflows in its torus. In all of our models, the time-averaged density, pressure and angular momentum in the equatorial region can be described by a radial power law, with P ∝r ^−3/2, P ∝r ⁻² and l∝r ⁰.

     

On generalized Lax equation of the Lax triple of KP Hierarchy

In terms of the operator Nambu 3-bracket and the Lax pair (L, B_n) of the KP hierarchy, we propose the generalized Lax equation with respect to the Lax triple (L, B_n, B_m). The intriguing results are that we derive the KP equation and another integrable equation in the KP hierarchy from the generalized Lax equation with the different Lax triples (L, B_n, B_m). Furthermore we derive some no integrable evolution equations and present their single soliton solutions.     

Lattice dynamics and the ferroelectric phase transition in ordered Pb2B′B″O6 (B′ = Ga, In, Lu; B″ = Nb, Ta) solid solutions

The lattice vibration spectrum, rf permittivity, and dynamic Born charges have been calculated for ordered Pb₂ B′B″O₃ (B′=Ga, In, Lu; B″=Nb, Ta) solid solutions in terms of the generalized Gordon—Kim model. It has been shown that all compounds exhibit a ferroelectric instability and that the frequencies of “soft” ferroelectric modes are close in magnitude. The ferroelectric phase-transition temperatures and the spontaneous polarization in the ferroelectric phase of the solid solutions under consideration have been calculated by the Monte Carlo method using the model Hamiltonian in the local mode approximation. The transition temperature is found to increase with increasing atomic number of the B′ ion.