Symmetries of Schrödinger Operator with Point Interactions

The transformations of all the Schrödinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling W are presented. In particular, those operators which are invariant (possibly up to a scale) are selected. Some recent papers on related topics are commented upon.     

Time resolved simultaneous detection of 14NO and 15NO via mid-infrared cavity leak-out spectroscopy

We present a ring-down absorption spectrometer based on a continuous-wave CO laser in the mid-infrared spectral region near lambda = 5 microm. Using a linear ring-down cavity (length: 0.5 m) with high reflective mirrors (R = 99.988 %), we observed a noise-equivalent absorption coefficient of 3 x 10(-10) cm(-1)Hz(-1/2). This corresponds to a noise-equivalent concentration of 800 parts per trillion (ppt) for (14)NO and 40 ppt for (15)NO in 1 s averaging time. We achieve a time resolution of 1 s which allows time resolved simultaneous detection of the two N isotopes. The delta(15)N value was obtained with a precision of +/-1.2 per thousand in a sample with a NO fraction of 11 ppm. The simultaneous detection enables the use of (15)NO as a tracer molecule for endogenous biomedical processes.     

Ergodic Properties of the Quantum Geodesic Flow on Tori

We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on . We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10.     

Four-family ${ \mathcal N }=1$ supersymmetric Pati–Salam models from intersecting D6-branes

We investigate the construction of four-family ${ \mathcal N }=1$ supersymmetric Pati–Salam models from Type IIA ${{\mathbb{T}}}^{6}/{{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{2}$ orientifold with intersecting D6-branes. Utilizing the deterministic algorithm introduced in He W, Li T and Sun R (2021 arXiv: hep-th/2112.09632), we obtain 274 types of models with three rectangular tori and distinct gauge coupling relations at string scale, while 6 types of models with two rectangular tori and one tilted torus. In both cases, there exists a class of models with gauge coupling unification at string scale. In particular, for the models with two rectangular tori, one tilted torus and gauge coupling unification, the gaugino condensations are allowed, and thus supersymmetry breaking and moduli stabilization are possible for further phenomenological study.     

Exponentially Small Splitting of Separatrices Under Fast Quasiperiodic Forcing

We consider fast quasiperiodic perturbations with two frequencies (1/ɛ,γ/$epsiv;) of a pendulum, where γ is the golden mean number. The complete system has a two-dimensional invariant torus in a neighbourhood of the saddle point. We study the splitting of the three-dimensional invariant manifolds associated to this torus. Provided that the perturbation amplitude is small enough with respect to ɛ, and some of its Fourier coefficients (the ones associated to Fibonacci numbers), are separated from zero, it is proved that the invariant manifolds split and that the value of the splitting, which turns out to be exponentially small with respect to ɛ, is correctly predicted by the Melnikov function. Received: 19 February 1996 / Accepted: 14 February 1997     

Evidence for a nodeless gap from the superfluid density of optimally doped Pr(1.855)Ce(0.145)CuO(4-y) films

We present measurements of the ab-plane magnetic penetration depth, lambda(T), in five optimally doped Pr(1.855)Ce(0.145)CuO(4-y) films for 1.6 K< or =T < or =T(c) approximately 24 K. Low resistivities, high superfluid densities n(s)(T) proportional, variant lambda(-2)(T), high T(c)'s, and small transition widths are reproducible and indicative of excellent film quality. For all five films, lambda(-2)(T)/lambda(-2)(0) at low T is well fitted by an exponential temperature dependence with a gap, Delta(min), of 0.85k(B)T(c). This behavior is consistent with a nodeless gap and is incompatible with d-wave superconductivity.     

Microwave electrodynamics of electron-doped cuprate superconductors

We report microwave cavity perturbation measurements of the temperature dependence of the penetration depth, lambda(T), and conductivity, sigma(T) of Pr(2-x)Ce(x)CuO(4-delta) (PCCO) crystals, as well as parallel-plate resonator measurements of lambda(T) in PCCO thin films. Penetration depth measurements are also presented for a Nd(2-x)Ce(x)CuO(4-delta) (NCCO) crystal. We find that Deltalambda(T) has a power-law behavior for T相似文献   

Superexponential stability of KAM tori

We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/)], being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.     

Study on the variations of the apparent diffusion coefficient in areas of solid tumor in high grade gliomas

Present knowledge suggests that in glioblastoma multiforme the value of the apparent diffusion coefficient (ADC) is elevated in the solid part and hyperintense in T1, in spite of the elevated cellularity, and also in areas where peritumoral vasogenic edema is present. The purpose of our study has been to verify in vivo if the ADC increases in areas of solid tumor because of an increased presence of edema, like it happens in areas surrounding the tumor. Sixteen patients with histologically verified glioblastoma multiforme underwent a magnetic resonance (MR) examination with sequences: T1-weighted pre and post contrast, diffusion-weighted at b = 0 and b = 1000 s/mm(2), perfusion-weighted. One hundred sixty-five regions of interest (ROI) have been obtained for all set of patients. In each ROI we have estimated 4 parameters: ADC, intensity of T2-signal normalised to the white matter (SI(T2W)(n)), regional cerebral blood volume (rCBV), T1-signal enhancement (E%). With the SI(T2W)(n) the presence of edema was estimated. For each pair of measured parameters a statistical test of linear regression on the set of all ROI was made. A directed linear correlation between: ADC and SI(T2W)(n) (p 相似文献   

The transition to explosive solitons and the destruction of invariant tori

We investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncaré sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.     

The dynamical entropy of the quantum Arnold cat map

We present a rigorous computation of the dynamical entropyh of the quantum Arnold cat map. This map, which describes a flow on the noncommutative two-dimensional torus, is a simple example of a quantum dynamical system with optimal mixing properties, characterized by Lyapunov exponents ± 1n ⁺, ⁺ > 1. We show that, for all values of the quantum deformation parameter,h coincides with the positive Lyapunov exponent of the dynamics.     

An Analytical Approach to the Turbulence-Relaxed State in Tokamak Plasmas

Starting from the continuity, temperature, and motion equations of the trapped electron fluid in generaltokamak magnetic field with positive or reversed shear and the definition of Lagrangian invariant, dL / dt = ( t u. )L =0, where u is convective velocity, the trapped electron dynamics is considered in the following two assumptions: (i) theturbulence is low frequency electrostatic, and (ii) L is a functional only of the density n, temperature T, and magneticfield B, and the effect of perturbation potential φ is included in the convective velocity u, i.e., u is a functional of n,T, B, and φ. The Lagrangian invariant hidden in the trapped electron dynamics is strictly found: L= ln[(n/B)c1(T/B2/3)c2], where c1 and c2 are dimensionless changeable parameters and c1 ∝ c2. From this Lagrangian invariant thewhich, in the limit of large aspect ratio, reduce to n(r)q(r) = const. and T3/2(r)q(r) = const., respectively. The lattertwo scaling laws are compared with existent experimental results, being in good agreement.     

Harmonic measure and winding of conformally invariant curves

The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance r as H approximately r(alpha) while the curve logarithmically spirals with a rotation angle phi=lambdalnr. It obeys the scaling law f(alpha,lambda)=(1+lambda(2))f(alpha)-blambda(2) with alpha=alpha/(1+lambda(2)) and b=(25-c)/12, and where f(alpha) identical with f(alpha,0) is the pure harmonic measure spectrum, and c the conformal central charge. The results apply to O(N) and Potts models, as well as to stochastic L?wner evolution.     

Evidence of two dimensionality in quasi-one-dimensional cobalt oxides

The quasi-one-dimensional (Q1D) cobalt oxides A(N + 2)Co(n + 1)O(3n + 3) (A = Ca, Sr, and Ba, n = 1 - infinity) were investigated by muon-spin spectroscopy under applied pressures of up to 1.1 GPa. The relationship between the onset Néel temperature T(on)(N) and the interchain distance (d(ic)), which increases monotonically with n, is well fitted by the formula T(N)/T(N,0) = (1 - d(ic)/d(ic,o)(beta), here for T(on)(N) approximately 100 K for Ca(3)Co(2)O(6) (n = 1) and approximately 15 for BaCoCoO(3) (n = infinity at ambient P. The T(on)(N) - d(ic) curve also predicts a large dependence of Y(N) for the compounds with n > or = 5, i.e., in the vicinity of , while the compounds show only a very small effect. Indeed, our high-pressure mu(+) results show that of BaCoO(3) is enhanced by with a slope of 2.2 K(Gpa), whereas no detectable changes by P for both Ca(3)Co(2)O(6) and Sr(4)Co(3)O(9) (n = 2). This clearly confirms the role of the 2D-antiferromagnetic interaction on T(on)(N) in the Q1D cobalt oxides.     

A large volume flat coil probe for oriented membrane proteins

15N detection of mechanically aligned membrane proteins benefits from large sample volumes that compensate for the low sensitivity of the observe nuclei, dilute sample preparation, and for the poor filling factor arising from the presence of alignment plates. Use of larger multi-tuned solenoids, however, is limited by wavelength effects that lead to inhomogeneous RF fields across the sample, complicating cross-polarization experiments. We describe a 600 MHz 15N-1H solid-state NMR probe with large (580 mm3) RF solenoid for high-power, multi-pulse sequence experiments, such as polarization inversion spin exchange at the magic angle (PISEMA). In order to provide efficient detection for 15N, a 4-turn solenoidal sample coil is used that exceeds 0.27 lambda at the 600 MHz 1H resonance. A balanced tuning-matching circuit is employed to preserve RF homogeneity across the sample for adequate magnetization transfer from 1H to 15N. We describe a procedure for optimization of the shorted 1/4 lambda coaxial trap that allows for the sufficiently strong RF fields in both 1H and 15N channels to be achieved within the power limits of 300 W 1H and 1 kW 15N amplifiers. The 8 x 6 x 12 mm solenoid sustains simultaneous B1 irradiation of 100 kHz at 1H frequency and 51 kHz at 15N frequency for at least 5 ms with 265 and 700 W of input power in the respective channels. The probe functionality is demonstrated by 2D 15N-1H PISEMA spectroscopy for two applications at 600 MHz.     

Entropy conservation as h(T(&mgr;) ) approximately lambda(&mgr;) (+)d(&mgr;) in neurobiological dynamical systems

That the topological entropy, h(T(&mgr;) ), of a C(1M, of a surface, M, upon which invariant measure(s) &mgr; are concentrated, varies as the product of its average leading Lyapunov characteristic exponent, lambda(&mgr;), and the Hausdorff dimension of its support, d(&mgr;),was proven by Pesin [Russ. Math Surveys 32, 55-114 (1977)] for nonuniform partial hyperbolic systems and by Ledreppier and Young [Ergod. Theor. Dyn. Syst. 2, 109-123 (1982)], and Manning [Ergod. Theor. Dyn. Syst. 1, 451-459 (1981)] for uniformly hyperbolic (Axiom A) diffeomorphisms. When considered in conjunction with the post-Shannon information encoding theorems of Adler [Trans. Am. Math. Soc. 114, 309-319 (1965); Mem. Am. Math. Soc., No. 219 (1979)] and others, this suggests a way to differentiate equal entropy behaviors in systems with varying patterns of dynamical behaviors. Here we show this relation to be useful in the quantitative discrimination among the behaviors of abstract neuronal models and two real, finite time, partially and nonuniformly hyperbolic, brain-related dynamical systems. We observe a trade-off in finite time between two competing dynamical processes, jittery sticking (tending to increase d(&mgr;)) and convective escaping (more prominently incrementing lambda(&mgr;) (+)). In finite time systems, these changes in combination can statistically conserve the dynamical entropy, h(T(&mgr;) ), while altering the Levy characteristic exponent, alpha (describing the tail of the density distribution of observables, rho(x) approximately exp-gammamid R:xmid R:(alpha),10.5 implicates sequential correlations and H(*)<0.5 sequential anticorrelation. When the relation h(T(&mgr;) )=lambda(&mgr;) (+)d&mgr; fails, the way it does so provides information about the system. (c) 1997 American Institute of Physics.     

Effective wavelength scaling for optical antennas

In antenna theory, antenna parameters are directly related to the wavelength lambda of incident radiation, but this scaling fails at optical frequencies where metals behave as strongly coupled plasmas. In this Letter we show that antenna designs can be transferred to the optical frequency regime by replacing lambda by a linearly scaled effective wavelength lambda(eff)=n(1)+n(2)lambda/lambda(p), with lambda(p) being the plasma wavelength and n(1), n(2) being coefficients that depend on geometry and material properties. It is assumed that the antenna is made of linear segments with radii R < lambda. Optical antennas hold great promise for increasing the efficiency of photovoltaics, light-emitting devices, and optical sensors.     

Resolution of the orthopositronium-lifetime puzzle

The long-standing discrepancy [G. S. Adkins, R. N. Fell, and J. Sapirstein, Ann. Phys. (N.Y.) 295, 136 (2002)]] between the theoretical calculations of the orthopositronium (o-Ps) annihilation decay rate (lambda(T)=1/lifetime) and some of the experimental measurements has been resolved. A focused beam of positrons incident on a special nanoporous silica film produces near-thermal energy o-Ps in vacuum that is slow enough to be virtually free of perturbing interactions. The fitted decay rate requires only a 500 ppm correction for nonthermal o-Ps effects. The new value of lambda(T)=7.0404(10)(8) micros(-1) is in excellent agreement with theory.     

Exclusive measurement of the nonmesonic weak decay of the lambda(5)He hypernucleus

We performed a coincidence measurement of two nucleons emitted from the nonmesonic weak decay of lambda(5)He formed via the 6Li(pi+, K+) reaction. The energies of the two nucleons and the pair number distributions in the opening angle between them were measured. In both np and nn pairs, we observed a clean back-to-back correlation coming from the two-body weak reactions of lambda p --> np and lambda n --> nn, respectively. The ratio of the nucleon pair numbers was N(nn)/N(np) = 0.45 +/- 0.11(stat) +/- 0.03(syst) in the kinematic region of cos theta(NN) < -0.8. Since each decay mode was exclusively detected, the measured ratio should be close to the ratio of gamma(lambda p --> np)/gamma(lambda n --> nn). The ratio is consistent with recent theoretical calculations based on the heavy meson and/or direct-quark exchange picture.     

Renormalization-group analysis for the transition to chaos in Hamiltonian systems

We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of invariant tori for Hamiltonian systems with two degrees of freedom. The analysis of this transformation indicates that the break-up of invariant tori is a universal mechanism. The properties of invariant tori are described by the renormalization flow. A trivial attractive set of the renormalization transformation characterizes the Hamiltonians that have a smooth invariant torus. The set of Hamiltonians that have a non-smooth invariant torus is a fractal surface. This critical surface is the stable manifold of a single strange set encompassing all irrational frequencies. This hyperbolic strange set characterizes the Hamiltonians that have an invariant torus at the threshold of the break-up. From the critical strange set, one can deduce the critical properties of the tori (self-similarity, universality classes).