Theorem on the origin of phase transitions

For physical systems described by smooth, finite-range, and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that, unless the equipotential hypersurfaces of configuration space Sum(v)=[(q(1),...,q(N)) subset R(N)/V(q(1),...,q(N))=v], v subset R, change topology at some v(c) in a given interval [v(0),v(1)] of values v of V, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature (beta(v(0)),beta(v(1))) also in the N--> infinity limit. Thus, the occurrence of a phase transition at some beta(c)=beta(v(c)) is necessarily the consequence of the loss of diffeomorphicity among the [Sigma(v)](vv(c)), which is the consequence of the existence of critical points of V on Sigma(v=v(c)), that is, points where inverted Delta V=0.     

High-Resolution Fourier Transform Emission Spectroscopy of the B(2)Sigma(+) (v = 0)-X(2)Sigma(+) (v = 0) Transition of the PN(+) Ion

Ultraviolet emission spectrum of the B(2)Sigma(+) (v = 0)-X(2)Sigma(+) (v = 0) transition of the PN(+) ion has been observed at a resolution of 0.05 cm(-1) by a Fourier transform spectrometer. The rotational analysis led to a great improvement of rotational constants in the B(2)Sigma(+) (v = 0) and X(2)Sigma(+) (v = 0) states as well as to the first determination of centrifugal distortion constants for both levels and spin-rotation interaction constant in the X(2)Sigma(+) (v = 0) state. Rotational perturbation in the B(2)Sigma(+) (v = 0) state was observed. Copyright 2000 Academic Press.     

Laser-Excited Fluorescence Spectra of Strontium Monoiodide

Fluorescence spectra of strontium monoiodide excited by Ar++ and Kr+ laser lines have been analyzed by Fourier transform spectrometry. Rotational levels have been populated either directly or after collisional relaxation: (i) in D2Sigma+ (v = 0, 1) by ultraviolet lines of Ar++, inducing numerous fluorescence transitions ending in the levels v = 0-3 of the strongly interacting A2Pi and B2Sigma+ states, (ii) in A2Pi3/2 (v = 0-4) by Kr+ line at 676.44 nm, de-exciting into transitions to X2Sigma+ (v = 0-6). Deperturbed constants for A2Pi and B2Sigma+ states and A approximately B interaction parameter are calculated from the numerical treatment of D2Sigma+ (v = 0, 1) --> A2Pi (v = 0-3) approximately B2Sigma+ (v = 0-3) transitions. Rotational constants for D2Sigma+ (v = 0, 1) are obtained for the first time. The wavenumbers of some 670 fluorescence lines are cataloged. Copyright 1999 Academic Press.     

Fourier Transform Spectroscopy of the A'(1)Pi-X(1)Sigma(+) System of CaO

The A'(1)Pi-X(1)Sigma(+) near-infrared system of CaO was observed for the first time at high resolution using a Fourier transform spectrometer. The A'(1)Pi-X(1)Sigma(+) chemiluminescence was excited in a Ca + N(2)O flame produced in a Broida-type oven. More than 3000 rotational lines, classified into 19 bands involving the A'(1)Pi 0 /= 2) levels with the nearby b(3)Sigma(+) (v-2) levels has been detected. An extended set of A'(1)Pi (v = 0-3) data has been obtained which is suitable for use in a future multistate deperturbation analysis of the a(3)Pi approximately A'(1)Pi approximately b(3)Sigma(+) approximately A(1)Sigma(+) complex of excited states. The new near-infrared spectra of the A'(1)Pi-X(1)Sigma(+) transition of CaO also permits the first direct high-resolution linkage between the orange and green systems and the near-infrared bands. Copyright 2000 Academic Press.     

High-Resolution Study of the BaI A(2)Pi Electronic State

Near-infrared and visible spectra of the A(2)Pi-X(2)Sigma(+), C(2)Pi(1/2)-A(2)Pi(1/2), C(2)Pi(1/2)-B(2)Sigma(+), and C(2)Pi(1/2)-X(2)Sigma(+) band systems of the BaI molecule were recorded by using Fourier transform spectroscopy (FTS). The spectra were produced from the chemiluminescent reaction Ba + I(2) and also by using laser-induced fluorescence (LIF) technique in which the laser sources were a Ti:sapphire single-mode laser, a dye single-mode laser, and a Kr(+) multimode ion laser. Resolved rotational data, originating from 19 vibrational levels (0 相似文献   

Search for pair production of scalar bottom quarks in pp collisions at square root of s = 1.96 TeV

A search for direct production of scalar bottom quarks (b) is performed with 310 pb(-1) of data collected by the D0 experiment in pp collisions at square root s = 1.96 TeV at the Fermilab Tevatron Collider. The topology analyzed consists of two b jets and an imbalance in transverse momentum due to undetected neutralinos (chi(1)0), with chi(1)0 assumed to be the lightest supersymmetric particle. We find the data consistent with standard model expectations, and set a 95% C.L. exclusion domain in the (m(b), m(chi(1)0)) mass plane, improving significantly upon the results from run I of the Tevatron.     

The Radial Hamiltonians for the X(1)Sigma(+) and B(1)Sigma(+) States of HCl

All literature vibration-rotational and pure rotational transition energies for the ground X(1)Sigma(+) electronic state of H(35)Cl, H(37)Cl, D(35)Cl, and D(37)Cl, along with the entire collection of electronic B(1)Sigma(+) --> X(1)Sigma(+) emission data for the four isotopomers, have been used in a least-squares fit of compact analytic Born-Oppenheimer potential functions for the B(1)Sigma(+) and X(1)Sigma(+) electronic states. Additional functions related to the adiabatic and nonadiabatic corrections have also been determined. Separate least-squares fits were made according to the hamiltonian operators of J. K. G. Watson (J. Mol. Spectrosc. 80, 411 (1980)) and R. M. Herman and J. F. Ogilvie (Adv. Chem. Phys. 103, 187 (1998)). The results from the separate analyses demonstrate clearly that the two hamiltonian operators are essentially equivalent, both achieving equally satisfactory representations of the spectral data, and furnishing virtually identical Born-Oppenheimer potential functions. Fully quantum-mechanical vibrational eigenvalues and rotational perturbation series parameters B(v)-O(v) are presented for the lower levels of the X(1)Sigma(+) ground state for which infrared and/or microwave data are available (v" 相似文献   

Complexity of random energy landscapes, glass transition, and absolute value of the spectral determinant of random matrices

Finding the mean of the total number N(tot) of stationary points for N-dimensional random energy landscapes is reduced to averaging the absolute value of the characteristic polynomial of the corresponding Hessian. For any finite N we provide the exact solution to the problem for a class of landscapes corresponding to the "toy model" of manifolds in a random environment. For N>1 our asymptotic analysis reveals a phase transition at some critical value mu(c) of a control parameter mu from a phase with a finite landscape complexity: N(tot) approximately e(N Sigma), Sigma(mu0 to the phase with vanishing complexity: Sigma(mu>mu(c))=0. Finally, we discuss a method of dealing with the modulus of the spectral determinant applicable to a broad class of problems.     

Observation of direct dissociative ionization in molecular hydrogen

Direct dissociative ionization is the simplest three-body breakup process in H2. We describe the experimental verification of direct dissociative ionization to the repulsive A2Sigma(+)(u) state by resolving the kinetic energy and angular distributions of the formed protons. A (2+1) resonant enhanced multiphoton ionization process via the isotropic E,F (1)Sigma(+)(g)(v = 6,J = 0) level is employed. The structure in the kinetic energy spectrum is well described by a projection of the vibrational wave function of the E,F (1)Sigma(+)(g)(v = 6,J = 0) state onto the repulsive ionic state. The electronic character of the ionization continuum is revealed by the proton angular distribution.     

The Rotational Spectrum of SO(2) and the Determination of the Hyperfine Constants and Nuclear Magnetic Shielding Tensors of (33)SO(2) and SO(17)O

Rotational analyses of the B(2)Sigma(+)(u) --> X(2)Sigma(+)(g) system of the (14)N(+)(2) molecule have been extended to include the vibrational levels up to v' = 4. Spectral data from 20 bands obtained from high-resolution Fourier transform spectrometry of a hollow-cathode and a Pointolite lamp were included in the analysis. A global deperturbation yielded molecular parameters of the highly perturbed B(2)Sigma state and interaction parameters A(2)Pi(u) approximately B(2)Sigma(u) with a standard deviation of 0.011 cm(-1). Rotational term values of the B(2)Sigma(+) state were also determined. New perturbations in the B(2)Sigma(+) (v = 0) level have been observed at N approximately 85 and N approximately 96. Copyright 2000 Academic Press.     

Laser-Induced Fluorescence and Fourier Transform Spectroscopy of NiCl: Identification of a Low-Lying (2)Sigma(+) State (1768 cm(-1))

From a comparison with the spectrum of NiF, a low-lying (2)Sigma(+) state is expected to lie in the first 2000 cm(-1) above the ground X(2)Pi(3/2) state of NiCl. The identification of this (2)Sigma(+) (v = 0) state (at 1768 cm(-1)) has been carried out through the analysis of two electronic transitions (2)Pi(3/2)-(2)Sigma(+) (22 720 cm(-1)) and (2)Pi(1/2)-(2)Sigma(+) (23 210 cm(-1)) recorded by high-resolution Fourier transform spectroscopy. Dispersed fluorescence spectroscopy allowed these transitions to be located on an absolute energy-level diagram that includes the previously studied electronic states. Copyright 2000 Academic Press.     

The (1)(3)Pi Electronic State of LaF

Rotational studies of bands of the infrared systems (1)(3)Pi-->(1)(3)Delta and (1)(3)Pi(1)-->X(1)Sigma(+) of lanthanum monofluoride were carried out with the aim of characterizing the (1)(3)Pi state, assuming the previous representations of X(1)Sigma(+) and (1)(3)Delta (1-3). The vibrational levels of (1)(3)Pi involved in the analyzed transitions were v=0, 1, 2 of the Omega=0 component, v=0, 1 of the Omega=1 component, and v=0 of the Omega=2 component. Perturbations were observed in both systems which were ascribed to spin-uncoupling interactions between (1)(3)Pi(2)(v=0) and (1)(3)Pi(1)(v=1) levels. A 9x9 matrix representation at equilibrium of the complex of interacting levels (v=0, 1, 2) was constructed, each diagonal v-block corresponding to a triplet model of the rovibrational (3)Pi Hamiltonian. The wavenumbers of some 1910 lines in the two systems were simultaneously fitted (rms error of the fit of about 0.0053 cm(-1)), thus yielding a consistent set of accurate spectroscopic constants for the (1)(3)Pi state; the spin-uncoupling interaction parameter was determined as B(Pi)(0, 1)=0.010917(13) cm(-1). Copyright 2001 Academic Press.     

Submillimeter-Wave Spectroscopy of CO in the a(3)Pi State

Submillimeter-wave absorption spectrum of CO in electronically excited a(3)Pi state was observed in the 540-830 GHz region by using a phase-locked BWO spectrometer. New rotational transitions up to J = 9-8 in the vibrational excited states up to v = 5 were analyzed accompanied with previous observations in the RF and millimeter-wave regions. A multivibrational states fit among a' (3)Sigma(+) (v = 0-3) and a(3)Pi (v = 0-7) states was performed in order to analyze overall perturbation between the a(3)Pi and a' (3)Sigma(+) states. As a result, the deperturbed rotational parameters were derived precisely to improve the RKR potential. Copyright 2000 Academic Press.     

The E(2)Sigma(+) --> C(2)Pi Transition of NO and Term Values for the A, D, E, and C Lowest Rydberg Levels

The E(2)Sigma(+) --> C(2)Pi Rydberg-Rydberg transition of (14)N(16)O near 8492 cm(-1) has been studied by Fourier transform spectrometry in the emission from a dc excited supersonic jet expansion and from a dc discharge under equilibrium conditions. The same transition has also been observed in laser-induced stimulated emission. Line wavenumbers of the 0-0, 1-1, and 2-2 bands, together with data for previously published near-infrared transitions, have been reduced to consistent sets of rovibronic term values for v = 0, 1, and 2 of the A(2)Sigma(+), D(2)Sigma(+), E(2)Sigma(+), and C(2)Pi states which frequently serve as intermediates in the multiphoton excitation of higher Rydberg levels of NO. Copyright 2000 Academic Press.     

Flow phase diagrams for concentration-coupled shear banding

After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant systems, we present flow phase diagrams spanned by shear stress Σ (or strain rate ) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS-φ) model. We also give results for the macroscopic flow curves Σ(ˉ,ˉφ) for a range of (average) concentrations ˉφ. For any concentration that is high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence “plateau” that slopes upwards, dΣ/dˉ > 0. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point [Σ_c,ˉφ_c,ˉ_c]. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, Σ(ˉ,ˉφ), measured for several different values of ˉφ. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-φ model contains two different spatial gradient terms that describe the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length ξ for equilibrium concentration-fluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio r ≡ l /ξ, with loss of unique state selection at r = 0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width (relative to l and ξ) at the critical point. Received: 20 December 2002 / Accepted: 24 April 2003 / Published online: 11 June 2003 RID="a" ID="a"e-mail: physf@irc.leeds.ac.uk RID="b" ID="b"e-mail: p.d.olmsted@leeds.ac.uk     

Time-domain measurement of spontaneous vibrational decay of magnetically trapped NH

The v=1-->0 radiative lifetime of NH(X(3)Sigma(-),v=1,N=0) is determined to be tau_(rad,exp.)=37.0+/-0.5_(stat)+2.0/-0.8_(syst) ms, corresponding to a transition dipole moment of |mu_(10)|=0.0540_(-0.0018)(+0.0009) D. To achieve sufficiently long observation times, NH(X;{3}Sigma;{-},v=1) radicals are magnetically trapped using helium buffer-gas loading. The rate constant for background helium-induced collisional quenching was determined to be k_(v=1)<3.9x10(-15) cm(3) s(-1), which yields the quoted systematic uncertainty on tau_{rad,exp.}. With a new ab initio dipole moment function and a Rydberg-Klein-Rees potential, we calculate a lifetime of 36.99 ms, in agreement with our experimental value.     

A Reinvestigation of the c(3)Pi-X(1)Sigma(+) (0-0) Absorption Band of Carbon Monoxide

The forbidden c(3)Pi-X(1)Sigma(+) (0-0) absorption band of carbon monoxide has been reinvestigated under different pressure conditions using the 10.7-m VUV spectrograph at Meudon. Overlap with the allowed C(1)Pi-X(1)Sigma(+) (0-0) band at lower transition energy has been taken into account. We have identified a new rotational branch corresponding to an S-type branch and extended the analysis to both higher and lower J. An analysis of the band structure and the low J transition lines suggests that the band gains its intensity predominantly as a result of an interaction of the c(3)Pi state with a (1)Sigma(+) state, most likely the C(1)Sigma(+) (v = 0) state. Molecular constants have been obtained for the c(3)Pi state that are in reasonable agreement with those previously published. The apparently anomalous small value for the centrifugal distortion constant is explained by a homogeneous perturbation with the k(3)Pi valence state. Copyright 2000 Academic Press.     

Enhanced Access to the Dark Triplet States of (7)Li(2) through New Singlet-Triplet A(1)Sigma(+)(u) approximately b(3)Pi(u) Perturbation Window Levels: Perturbation-Facilitated Optical-Optical Double Resonance Study of the 2(3)Sigma(+)(g) State

Two new pairs of singlet-triplet A(1)Sigma(+)(u) approximately b(3)Pi(u) mixed levels of (7)Li(2) have been observed and used here as "window" levels in cw perturbation-facilitated optical-optical double-resonance (PFOODR) experiments. Previously, only one b(3)Pi(u) vibrational level, v = 19, was known to mix with the singlet A(1)Sigma(+)(u) v = 13 level, resulting in three perturbed A approximately b pairs [L. Li, T. An, T.-J. Whang, A. M. Lyyra, W. C. Stwalley, R. W. Field, and R. A. Bernheim, J. Chem. Phys. 96, 3342 (1992)]. The scarcity of window levels and the resulting difficulty in accessing the dark triplet states of Li(2) is caused by the weak spin-orbit interaction of Li(2). The two new mixed b(3)Pi(u) v = 15 and 22 levels reported here enhance access to the dark triplet state manifold through expansion of the Franck-Condon overlap factor range. Furthermore, the earlier range of accessible rotational levels, N = 5, 7, and 10, is now expanded to include N = 8 and N = 16, thereby allowing for more reliable determination of the excited triplet states rotational structure. To demonstrate the importance of the new A(1)Sigma(+)(u) approximately b(3)Pi(u) mixed levels, we have studied the 2(3)Sigma(+)(g) state by cw PFOODR fluorescence excitation spectroscopy. New molecular constants and RKR potential curve have been determined. As previously reported [L. Li, G. Lazarov, and A. M. Lyyra, J. Mol. Spectrosc. 191, 387 (1998)], the 2(3)Sigma(+)(g) state interacts with the repulsive 1(3)Pi(g) state by L-uncoupling and predissociates. We show that some 2(3)Pi(g) levels predissociate accidentally by the 1(3)Pi(g) state via the 2(3)Sigma(+)(g) state through L-uncoupling. Copyright 2001 Academic Press.     

Dynamical response of quantum spin-glass models at t = 0

We study the behavior of two archetypal quantum spin glasses at T = 0 by exact diagonalization techniques: the random Ising model in a transverse field and the random Heisenberg model. The behavior of the dynamical spin response is obtained in the spin-glass ordered phase. In both models it is gapless and has the general form chi(")(omega) = qdelta(omega)+chi(")(reg)(omega), with chi(")(reg)(omega) approximately omega for the Ising and chi(")(reg)(omega) approximately const for the Heisenberg, at low frequencies. The method provides new insight to the physical nature of the low-lying excitations.     

The Predissociation of the 1(3)Sigma(-)(g) State of (7)Li(2)

The predissociation of the 1(3)Sigma(-)(g) v >/= 10 levels of (7)Li(2) has been observed by pulsed and continuous-wave perturbation-facilitated optical-optical double-resonance spectroscopy (PFOODR). Our ab initio calculation shows that the inner wall of the 1(3)Sigma(-)(g) potential intersects the 1(3)Pi(g) repulsive potential at internuclear distance R = 2.00 ?. The predissociation is due to a DeltaS = 0, DeltaLambda = +/-1 rotational-electronic interaction with the repulsive 1(3)Pi(g) state. Copyright 2001 Academic Press.