Smooth Crossover Research Articles

Multiply quantized vortices and finite temperature effects in the BEC/BCS crossover regime

The interatomic interaction strength in ultracold fermionic gases can be manipulated using Feshbach resonances, allowing to probe both the regime where atoms form molecules that Bose condense (BEC) and the Bardeen–Cooper–Schrieffer (BCS) regime. We use a path-integral formalism to investigate the properties of multiply quantized vortices in these systems. Although the vortex core region expands when more quanta of circulation are present, the qualitative result is the same: in the BEC regime, the atoms do not penetrate into the vortex core, whereas in the BCS regime they do. The system undergoes a smooth crossover between the two regimes. When the temperature is increased, the penetration of atoms into the vortex core becomes more pronounced.

Sound modes at the BCS-BEC crossover

First and second sound speeds are calculated for a uniform superfluid gas of fermi atoms as a function of temperature, density and interaction strength. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature. The sound modes and their dependence on density, scattering length and temperature are calculated in the BCS, molecular BEC and unitarity limits and a smooth crossover is extrapolated. It is found that first and second sound undergo avoided crossing on the BEC side due to mixing. Consequently, they are detectable at crossover both as density and thermal waves in traps.

Kertész Line and Embedded Monopoles in QCD

We propose a new class of defects in QCD which can be viewed as embedded monopoles made of quark and gluon fields. These objects are explicitly gauge invariant and they closely resemble the Nambu monopoles in the standard electroweak model. We argue that the "embedded QCD monopoles" are proliferating in the quark-gluon plasma phase while in the low-temperature hadronic phase the spatial proliferation of these objects is suppressed. At realistic quark masses and zero chemical potential the hadronic and quark-gluon phases are generally believed to be connected by a smooth crossover across which all thermodynamic quantities are nonsingular. We argue that these QCD phases are separated by a well-defined boundary-known as the Kertész line in condensed matter systems-associated with the onset of the proliferation of the embedded QCD monopoles in the quark-gluon plasma phase.

Spicules and the Effect of Rigid Rods on Enclosing Membrane Tubes

Membrane tubes (spicules) arise in cells, or artificial membranes, in the nonlinear deformation regime due to, e.g., the growth of microtubules, actin filaments, or sickle hemoglobin fibers towards a membrane. We calculate the axial force f exerted by the tube, and its average radius, taking into account steric interactions between the fluctuating membrane and the enclosed rod. We find a smooth crossover of the axial force between f approximately square root of (sigma) and f approximately sigma as the membrane tension sigma increases and the tube radius shrinks. This crossover occurs around the most physiologically relevant membrane tensions. Our work may be important in (i) interpreting experiments in which axial force is related to the tube radius or membrane tension, and (ii) constructing dynamical theories for biopolymer growth in narrow tubes where these fluctuation effects control the tube radius.

Simple mean-field model for condensates in the BEC-BCS crossover regime

We present a mean field approach based on pairs of fermionic atoms to describe condensates in the BEC-BCS crossover regime. By introducing an effective potential, the mean field equation allows us to calculate the chemical potential, the equation of states and the atomic correlation function. The results agree surprisingly well with recent quantum Monte Carlo calculations. We show that the smooth crossover from the bosonic mean field repulsion between molecules to the Fermi pressure among atoms is associated with the evolution of the atomic correlation function.

Structures of Metastable States in Phase Transitions with a High-Spin Low-Spin Degree of Freedom

Difference of degeneracy of the low-spin (LS) and high-spin (HS) states causes interesting entropy effects on spin-crossover phase transitions and charge transfer phase transitions in materials composed of the spin-crossover atoms. Mechanisms of the spin-crossover (SC) phase transitions have been studied by using Wajnflasz model, where the degeneracy of the spin states (HS or LS) is taken into account and cooperative natures of the spin-crossover phase transitions have been well described. Recently, a charge transfer (CT) phase transition due to electron hopping between LS and HS sites has been studied by using a generalized Wajnflasz model. In the both systems of SC and CT, the systems have a high temperature structure (HT) and a low temperature structure (LT), and the change between them can be a smooth crossover or a discontinuous first order phase transition depending on the parameters of the systems. Although apparently the standard SC system and the CT system are very different, it is shown that both models are equivalent under a certain transformation of variables. In both systems, the structure of metastable state at low temperatures is a matter of interest. We study temperature dependence of fraction of HT systematically in a unified model, and find several structures of equilibrium and metastable states of the model as functions of system parameters. In particular, we find a reentrant type metastable branch of HT in a low temperature region, which would play an important role to study the photo-irradiated processes of related materials.

Phase Transitions in Traffic Models

It is suggested that the question of existence of a jamming phase transition in a broad class of single-lane cellular-automaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between free-flow and jammed states, as the car density is increased.

Synchronization and partial synchronization of linear maps

We study synchronization of low-dimensional ( d = 2 , 3 , 4 ) chaotic piecewise linear maps that are coupled bidirectionally. For Bernoulli maps we find Lyapunov exponents and locate the synchronization transition, which numerically is found to be discontinuous (despite continuously vanishing Lyapunov exponent(s)). For tent maps, a limit of stability of the synchronized state is used to locate the synchronization transition that numerically is found to be continuous. For nonidentical tent maps at the partial synchronization transition, the probability distribution of the synchronization error is shown to develop highly singular behavior. We suggest that for nonidentical Bernoulli maps (and perhaps some other discontinuous maps) partial synchronization is merely a smooth crossover rather than a well-defined transition. More subtle analysis in the d = 4 case locates the point where the synchronized state becomes stable. In some cases, however, a riddled basin attractor appears, and synchronized and chaotic behaviors coexist.

Isotropic-nematic transition in liquid-crystalline elastomers: Lattice model with quenched disorder

When liquid-crystalline elastomers pass through the isotropic-nematic transition, the orientational order parameter and the elastic strain vary rapidly but smoothly, without the expected first-order discontinuity. This broadening of the phase transition is an important issue for applications of liquid-crystalline elastomers as actuators or artificial muscles. To understand this behavior, we develop a lattice model of liquid-crystalline elastomers, with local directors coupled to a global strain variable. In this model, we can consider either random-bond disorder (representing chemical heterogeneity) or random-field disorder (representing heterogeneous local stresses). Monte Carlo simulations show that both types of disorder cause the first-order isotropic-nematic transition to broaden into a smooth crossover, consistent with the experiments. For random-field disorder, the smooth crossover into an ordered state can be attributed to the long-range elastic interaction.

Influence of physical ageing on the excessive heat capacity of hyperquenched silicate glass fibers

Two types of hyperquenched continuous glass fibers, basaltic glass fibers and soda-lime silicate glass fibers, are thermally aged within a temperature range from 0.55Tg to 0.95Tg, where Tg is the glass transition temperature. The results show the complexity of enthalpy relaxation of the aged fibers. During up-scanning of the aged fibers in a differential scanning calorimeter, a relaxation exotherm occurs above a certain temperature, which is due to the release of the excess energy relative to that of a glass cooled at the rate 0.33K/s. At a certain ageing temperature, an endotherm occurs prior to the appearance of the exotherm. There is a smooth crossover between the endotherm and the exotherm. The gradual shift of the crossover from lower to higher temperature with increasing ageing temperature is not due to the distribution of fictive temperatures, but to a distribution of the excess potential energy over all configurational coordinates. A phenomenological equation has been proposed to describe the decrease of the remaining energy with increasing ageing temperature.

Statistical mechanics of worm-like polymers from a new generating function.

We present a mathematical approach to the worm-like chain model of semiflexible polymers. Our method is built on a novel generating function from which all the properties of the model can be derived. Moreover, this approach satisfies the local inextensibility constraint exactly. In this paper, we focus on the lowest order contribution to the generating function and derive explicit analytical expressions for the characteristic function, polymer propagator, single chain structure factor, and mean square end-to-end distance. These analytical expressions are valid for polymers with any degree of stiffness and contour length. We find that our calculations are able to capture the fully flexible and infinitely stiff limits of the aforementioned quantities exactly while providing a smooth and approximate crossover behavior for intermediate values of the stiffness of the polymer backbone. In addition, our results are in very good quantitative agreement with the exact and approximate results of five other treatments of semiflexible polymers.

Generalized minority games with adaptive trend-followers and contrarians.

We introduce a simple extension of the minority game in which the market rewards contrarian (respectively, trend-following) strategies when it is far from (respectively, close to) efficiency. The model displays a smooth crossover from a regime where contrarians dominate to one where trend-followers dominate. In the intermediate phase, the stationary state is characterized by non-Gaussian features as well as by the formation of sustained trends and bubbles.

Effect of quantum fluctuations on the dipolar motion of bose-einstein condensates in optical lattices.

We reexamine dipolar motion of condensate atoms in one-dimensional optical lattices and harmonic magnetic traps including quantum fluctuations within the truncated Wigner approximation. In the strong tunneling limit we reproduce the mean field results with a sharp dynamical transition at the critical displacement. When the tunneling is reduced, on the contrary, strong quantum fluctuations lead to finite damping of condensate oscillations even at infinitesimal displacement. We argue that there is a smooth crossover between the chaotic classical transition at finite displacement and the superfluid-to-insulator phase transition at zero displacement. We further analyze the time dependence of the density fluctuations and of the coherence of the condensate and find several nontrivial dynamical effects, which can be observed in the present experimental conditions.

Solid state Pomeranchuk effect in unstable Kondo lattice systems

In this paper we study the first order transitions which occur in Kondo lattice systems accompanied by volume instabilities. In general, in non-magnetic Kondo lattice materials there is a smooth crossover along a coherence line between a Fermi liquid and a local moment regime. We investigate here the conditions that for certain materials this crossover changes into an abrupt transition at which local moment and Fermi liquid phases coexist. The system YbInCu 4 is such a material and we point out the similarities of its thermodynamic behavior with that of 3He including the existence of a solid state Pomeranchuk effect. Finally, the possibility of constructing a cooling machine based on unstable Kondo lattice systems is discussed.

Nature of the self-trapping transition in a one-dimensional Holstein–Hubbard model

The nature of the self-trapping transition in a many-polaron system is investigated within the framework of an extended Holstein–Hubbard model in one dimension using a variational method. The phonon degrees of freedom are first eliminated employing a modified Lang–Firsov transformation and an onsite squeezing transformation and then using a correlated squeezed phonon state to yield an effective Hubbard model which is finally studied using the exact solution of Lieb and Wu and the mean-field Hartree–Fock approximation. It is shown that the exact solution of the effective Hubbard model predicts a smooth crossover from the large polaron to a small polaron state while the mean field treatment leads to a discontinuous transition in the adiabatic regime.

Solid state Pomeranchuk effect in unstable Kondo lattice systems

In this paper we study the first order transitions which occur in Kondo lattice systems accompanied by volume instabilities. In general, in non-magnetic Kondo lattice materials there is a smooth crossover along a coherence line between a Fermi liquid and a local moment regime. We investigate here the conditions that for certain materials this crossover changes into an abrupt transition at which local moment and Fermi liquid phases coexist. The system YbInCu4 is such a material and we point out the similarities of its thermodynamic behavior with that of 3He including the existence of a solid state Pomeranchuk effect. Finally, the possibility of constructing a cooling machine based on unstable Kondo lattice systems is discussed.

Nature of the self-trapping transition in a one-dimensional Holstein?Hubbard model

The nature of the self-trapping transition in a many-polaron system is investigated within the framework of an extended Holstein–Hubbard model in one dimension using a variational method. The phonon degrees of freedom are first eliminated employing a modified Lang–Firsov transformation and an onsite squeezing transformation and then using a correlated squeezed phonon state to yield an effective Hubbard model which is finally studied using the exact solution of Lieb and Wu and the mean-field Hartree–Fock approximation. It is shown that the exact solution of the effective Hubbard model predicts a smooth crossover from the large polaron to a small polaron state while the mean field treatment leads to a discontinuous transition in the adiabatic regime.

Crystal growth and electromagnetic properties of β-vanadium bronzes, β-A 0.33V 2O 5 (A=Ca, Sr and Pb)

Single crystals of β-vanadium bronzes, β-A 0.33V 2O 5 (A=Ca, Sr and Pb) were successfully grown by self-flux method (for A=Ca and Sr) and by a chemical transport reaction method using HCl gas as a transport agent (for A=Pb). By using crystals thus obtained, we measured electrical resistivity along the b-axis in the monoclinic structure. The distinct metal–insulator (M–I) transition was observed at 150 K for β-Ca 0.33V 2O 5 and at 168 K for β-Sr 0.33V 2O 5. The M–I transition is expected to be charge order type as observed in β-Na 0.33V 2O 5. On the other hand, β-Pb 0.33V 2O 5 shows no M–I transition but a smooth crossover from metal to insulator. This crossover seems to be due to the weak localization of very good one-dimensionality.

From Slater to Mott–Heisenberg physics: the antiferromagnetic phase of the Hubbardmodel

We study the optical conductivity of the one-band Hubbard model in the Néel state at half filling atT = 0 using the dynamical mean-field theory. For small values of the Coulomb parameter clearsignatures of a Slater insulator expected from a weak-coupling theory are found, while thestrongly correlated system can be well described in terms of a Mott–Heisenberg picture.However, in contrast to the paramagnet, we do not find any evidence for a transitionbetween these two limiting cases but rather a smooth crossover as a function of theCoulomb interaction.

RNA denaturation: excluded volume, pseudoknots, and transition scenarios.

A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous transition. Otherwise a smooth crossover occurs from the swollen linear polymer behavior to highly ramified, almost compact conformations with secondary structures. In the latter scenario, which is appropriate when these structures are much more stable than pseudoknot links, probability distributions for the lengths of both loops and main branches obey scaling with nonclassical exponents.