On the Essential Features of Metastability: Tunnelling Time and Critical Configurations

We consider Metropolis Markov chains with finite state space and transition probabilities of the form $$P(\eta ,\eta ')=q(\eta ,\eta ')e^{- \beta [H(\eta ') - H(\eta)]_+}$$ for given energy function H and symmetric Markov kernel q. We propose a simple approach to determine the asymptotic behavior, for large β, of the first hitting time to the ground state starting from a particular class of local minima for H called metastable states. We separate the asymptotic behavior of the transition time from the determination of the tube of typical paths realizing the transition. This approach turns out to be useful when the determination of the tube of typical paths is too difficult, as for instance in the case of conservative dynamics. We analyze the structure of the saddles introducing the notion of “essentiality” and describing essential saddles in terms of “gates.” As an example we discuss the case of the 2D Ising Model in the degenerate case of integer ${\tfrac{{2j}}{h}}$ .     

Abelian cosmic string in the extended Starobinsky model of gravity

We analyze numerically the behaviour of the solutions corresponding to an Abelian cosmic string taking into account an extension of the Starobinsky model, where the action of general relativity is replaced by \(f(R) = R - 2\Lambda + \eta R^2 + \rho R^m\), with \(m > 2\). As an interesting result, we find that the angular deficit which characterizes the cosmic string decreases as the parameters \(\eta \) and \(\rho \) increase. We also find that the cosmic horizon due to the presence of a cosmological constant is affected in such a way that it can grows or shrinks, depending on the vacuum expectation value of the scalar field and on the value of the cosmological constant.     

High-temperature expansion for nonequilibrium steady states in driven lattice gases

We develop a controlled high-temperature expansion for nonequilibrium steady states of the driven lattice gas, the "Ising model" for nonequilibrium physics. We represent the steady state as P(eta) alpha e(-betaH(eta)-psi(eta)) and evaluate the lowest order contribution to the nonequilibrium effective interaction psi(eta). We see that, in dimensions d > or = 2, all models with nonsingular transition rates yield the same summable psi(eta), suggesting the possibility of describing the state as a Gibbs state similar to equilibrium. The models with the Metropolis rule show exceptional behavior.     

Glassy conformations in wrinkled membranes

Partially polymerized membranes display a striking mechanical transition at low temperature known as the wrinkling transition. Fluorescence and scanning electron microscopy as well as profile measurements using an atomic force microscope revealed the existence of three degrees of wrinkling depending on the degree of the membrane polymerization. At low polymerization the membrane undergoes a cascade of wrinkling to form a folded phase with a characteristic exponent eta equal to 3, at intermediate polymerization, the membrane is in an intermediate-wrinkled phase (similar to the crumpling of an elastic sheet) with eta approximately 2.5, while at high polymerization the membrane undergoes an abrupt "compaction" to the wrinkled-rough phase with eta approximately 2.     

Numerical renormalization-group study of the Bose-Fermi Kondo model

We extend the numerical renormalization-group method to Bose-Fermi Kondo models (BFKMs), describing a local moment coupled to a conduction band and a dissipative bosonic bath. We apply the method to the Ising-symmetry BFKM with a bosonic bath spectral function eta(omega) proportional omega(s), of interest in connection with heavy-fermion criticality. For 0 < s < 1, an interacting critical point, characterized by hyperscaling of exponents and omega/T scaling, describes a quantum phase transition between Kondo-screened and localized phases. A connection is made to other results for the BFKM and the spin-boson model.     

An interstitialcy theory of structural relaxation and related viscous flow of glasses

A theory of isothermal structural relaxation and creep of glasses below the glass transition temperature is given. According to the interstitialcy theory, the supercooled liquid state does not exist below a Kauzmann "pseudocritical" temperature T(k), which lies above the temperature T(K), commonly called the "Kauzmann temperature." Structural relaxation is simply a reduction with time of the interstitialcy concentration to the crystalline state for TT(k). The predicted viscosity eta is universal, given by eta=eta(0) + eta(T)t, in agreement with experiment. eta is continuous in T, with eta discontinuous at T(k) but linear in 1/T above and below T(k). The dependence of eta on the shear modulus directly connects kinetic and thermodynamic properties of glasses and liquids.     

Two-particle microrheology of quasi-2D viscous systems

We study the spatially correlated motions of colloidal particles in a quasi-2D system (human serum albumin protein molecules at an air-water interface) for different surface viscosities eta s. We observe a transition in the behavior of the correlated motion, from 2D interface dominated at high eta s to bulk fluid dependent at low eta s. The correlated motions can be scaled onto a master curve which captures the features of this transition. This master curve also characterizes the spatial dependence of the flow field of a viscous interface in response to a force. The scale factors used for the master curve allow for the calculation of the surface viscosity eta s that can be compared to one-particle measurements.     

Higher-dimensional black holes with Dirac–Born–Infeld (DBI) global defects

It is well-known that the exact solution of non-linear \(\sigma \) model coupled to gravity can be perceived as an exterior gravitational field of a global monopole. Here we study Einstein’s equations coupled to a non-linear \(\sigma \) model with Dirac–Born–Infeld (DBI) kinetic term in D dimensions. The solution describes a metric around a DBI global defects. When the core is smaller than its Schwarzschild radius it can be interpreted as a black hole having DBI scalar hair with deficit conical angle. The solutions exist for all D, but they can be expressed as polynomial functions in r only when D is even. We give conditions for the mass M and the scalar charge \(\eta \) in the extremal case. We also investigate the thermodynamic properties of the black holes in canonical ensemble. The monopole alter the stability differently in each dimensions. As the charge increases the black hole radiates more, in contrast to its counterpart with ordinary global defects where the Hawking temperature is minimum for critical \(\eta \). This behavior can also be observed for variation of DBI coupling, \(\beta \). As it gets stronger (\(\beta \ll 1\)) the temperature increases. By studying the heat capacity we can infer that there is no phase transition in asymptotically-flat spacetime. The AdS black holes, on the other hand, undergo a first-ordered phase transition in the Hawking–Page type. The increase of the DBI coupling renders the phase transition happen for larger radius.     

Pure nuclear quadrupole resonance determination of the electric field gradient asymmetry for broad lines

We present an angle dependent nuclear quadrupole resonance (ADNQR) method to determine the electric field gradient asymmetry parameter eta in systems where the resonance line is so broad that the radio frequency field can excite only a portion of the nuclear spins. In this situation, the recently developed spectroscopic methods are not applicable. ADNQR is useful for single crystals and oriented powders, and, for small eta determines eta4. Therefore, it can be used to evaluate fluctuations in eta due to inhomogeneities. We demonstrate the application of ADNQR experimentally to oriented superconducting YBa2Cu3O7 powder.     

Intrinsic aging and effective viscosity in the slow dynamics of a soft glass with tunable elasticity

We investigate by rheology and light scattering the influence of the elastic modulus, G0, on the slow dynamics and the aging of a soft glass. We show that the slow dynamics and the aging can be entirely described by the evolution of an effective viscosity, eta(eff), defined as the characteristic time measured in a stress relaxation experiment times G0. At all times, eta(eff) is found to be independent of G0, of elastic perturbations, and of the rate at which the sample is quenched in the glassy phase. We propose a simple model that links eta(eff) to the internal stress built up at the fluid-to-solid transition.     

The Role of Spin-Flipping Terms in Hadronic Transitions of {\Upsilon (4S)}

Recent experimental data on the \({\Upsilon(4S)\to\Upsilon(1S)\eta}\) and \({\Upsilon(4S)\to h_{b}(1P)\eta}\) processes seem to contradict the naive expectation that hadronic transitions with spin-flipping terms should be suppressed with respect those without spin-flip. We analyze these transitions using the QCD multipole expansion (QCDME) approach and within a constituent quark model framework that has been applied successfully to the heavy-quark sectors during the last years. The QCDME formalism requires the computation of hybrid intermediate states which has been performed in a natural, parameter-free extension of our constituent quark model based on the quark confining string (QCS) scheme. We show that (i) the M1–M1 contribution in the decay rate of the \({\Upsilon(4S)\to\Upsilon(1S)\eta}\) is important and its suppression until now is not justified; (ii) the role played by the \({L=0}\) hybrid states, which enter in the calculation of the M1–M1 contribution, explains the observed enhancement in the \({\Upsilon(4S)\to\Upsilon(1S)\eta}\) decay width; and (iii) the anomalously large decay rate of the \({\Upsilon(4S)\to h_{b}(1P)\eta}\) transition has the same physical origin.     

Radiative cycle with stimulated emission from atoms and ions in an astrophysical plasma

We propose that a radiative cycle operates in atoms and ions located in a rarefied gas in the vicinity of a hot star. Besides spontaneous transitions the cycle includes a stimulated transition in one very weak intermediate channel. This radiative "bottleneck" creates a population inversion, which for an appropriate column density results in amplification and stimulated radiation in the weak transition. The stimulated emission opens a fast decay channel leading to a fast radiative cycle in the atom (or ion). We apply this model by explaining two unusually bright Fe II lines at 250.7 and 250.9 nm in the UV spectrum of gas blobs close to eta Carinae, one of the most massive and luminous stars in the Galaxy.     

DMRG studies on interchain coupling model for quasi-one-dimensional organic magnet

We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase. The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays the same type of critical behavior as the pair contact process with diffusion 2A↦3A, 2A↦. Received 14 October 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: Haye.Hinrichsen@physik.uni-wuppertal.de     

Structure and properties of confined sodium nitrite

The temperature evolution of the structure of NaNO(2) nanocomposite ferroelectric material in a porous glass with 7 nm pores was studied by neutron diffraction in temperature region from room temperature up to the melting, i.e. in the ferro- and paraelectric phases. It is demonstrated that in the ferroelectric phase the structure is consistent with the structure of the bulk, but above the ferroelectric phase transition (and up to approximately 513 K) a volume premelted state is formed, manifesting itself in a growth of amplitudes of ion thermal vibrations, a steep increase of elementary cell volume and "softening" of lattice. For the first time the temperature dependence of order parameter eta for confined sodium nitrite is determined. eta (T) follows a power law with T(C)=425.6+/- 2.1 K and beta= 0.31+/- 0.04, which is essentially different from that for bulk NaNO(2). Our obtained data are in a good agreement with the results of earlier dielectric and neutron diffraction measurements.     

Solid-fluid transition in a granular shear flow

The rheology of a granular shear flow is studied in a quasi-2D rotating cylinder. Measurements are carried out near the midpoint along the length of the surface flowing layer where the flow is steady and nonaccelerating. Streakline photography and image analysis are used to obtain particle velocities and positions. Different particle sizes and rotational speeds are considered. We find a sharp transition in the apparent viscosity (eta) variation with rms velocity (u). Below the transition depth we find that the rms velocity decreases with depth and eta proportional to u(-1.5) for all the different cases studied. The material approaches an amorphous solidlike state deep in the layer. The velocity distribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer. The results indicate a sharp transition from a fluid to a fluid + solid state with decreasing rms velocity.     

A spatio-temporal study of rheo-oscillations in a sheared lamellar phase using ultrasound

We present an experimental study of the flow dynamics of a lamellar phase sheared in the Couette geometry. High-frequency ultrasonic pulses at 36 MHz are used to measure time-resolved velocity profiles. Oscillations of the viscosity occur in the vicinity of a shear-induced transition between a high-viscosity disordered fluid and a low-viscosity ordered fluid. The phase coexistence shows up as shear bands on the velocity profiles. We show that the dynamics of the rheological data result from two different processes: (i) fluctuations of slip velocities at the two walls and (ii) flow dynamics in the bulk of the lamellar phase. The bulk dynamics are shown to be related to the displacement of the interface between the two differently sheared regions in the gap of the Couette cell. Two different dynamical regimes are investigated under applied shear stress: one of small amplitude oscillations of the viscosity ( %) and one of large oscillations ( %). A phenomenological model is proposed that may account for the observed spatio-temporal dynamics.Received: 2 December 2003, Published online: 9 March 2004PACS: 83.10.Tv Structural and phase changes - 43.58. + z Acoustical measurements and instrumentation - 47.50. + d Non-Newtonian fluid flows     

Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions

Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.     

Ab-initio calculations of structural,phonon and thermal properties of $$\hbox {Al}_x \hbox {Ga}_{1-x} \hbox {As}$$ alloy

We provide the energy spectrum of an electron in a degenerately doped semiconductor of parabolic band. Knowing the energy spectrum, the density-of-states (DOS) functions are obtained, considering the Gaussian distribution of the potential energy of the impurity states, showing a band tail in them e.g., energy spectrum and density-of-states. Therefore, Fermi integrals (FIs) of DOS functions, having band tail, are developed by the exact theoretical calculations of the same. It is noticed that with heavy dopings in semiconductors, the total FI demonstrates complex functions, containing both real and imaginary terms of different FI functions. Their moduli possess an oscillatory function of \(\eta \) (reduced \(\hbox {Fermi energy} = E_{\mathrm{f}}/k_{\mathrm{B}}T\), \(k_{\mathrm{B}}\) is the Boltzmann constant and T is the absolute temperature) and \(\eta _{e}\) (impurity screening potential), having a series solutions of confluent hypergeometric functions, \(\Phi (a, b; z)\), superimposed with natural cosine functions of angle \(\theta \). The variation of \(\theta \) with respect to \(\eta \) indicated a resonance at \(\eta =1.5\). The oscillatory behaviour of FIs show the existence of ‘band-gaps’, both in the real as well as in the forbidden bands as new band gaps in the semiconductor.     

Transition from stick-slip to smooth sliding: an earthquakelike model

We present a detailed study of an earthquakelike model that exhibits a "transition" from stick-slip motion to smooth sliding at a velocity of the order of those observed in experiments. This contrasts with the many previous microscopic models in which the transition velocity is many orders of magnitude too large. The results show that experimentally observed smooth sliding at the macroscopic scale must correspond to microscopic-scale stick-slip motion.     

Static and dynamic heterogeneities in a model for irreversible gelation

We study the structure and the dynamics in the formation of irreversible gels by means of molecular dynamics simulation of a model system where the gelation transition is due to the random percolation of permanent bonds between neighboring particles. We analyze the heterogeneities of the dynamics in terms of the fluctuations of the self-intermediate scattering functions: in the sol phase close to the percolation threshold, we find that this dynamic susceptibility increases with the time until it reaches a plateau. At the gelation threshold this plateau scales as a function of the wave vector k as k(eta-2), with eta being related to the decay of the percolation pair connectedness function. At the lowest wave vector, approaching the gelation threshold it diverges with the same exponent gamma as the mean cluster size. These findings suggest an alternative way of measuring critical exponents in a system undergoing chemical gelation.