Analysis of dynamic light scattering of poly(N-isopropylacrylamide) across the collapse transition

Summary We analyse data from the dynamic light scattering of poly(N-isopropylacrilamide) in water solution as we cross the collapse transition. Experimental data are interpreted by the Gaussian self-consistent Zimm model that takes into account two- and three-body excluded-volume effects, and Oseen hydrodynamic interactions, as well as by the standard cumulant and Contin analyses. By fitting the dynamic structure factor we extract the temperature dependence of the diffusion coefficientD and the first relaxation time τ₁ across the collapse transition for a range of scattering angles. The relaxation time τ₁ possesses a characteristic peak at about 32.4 °C due to slowing of the internal motions of the polymer at the theta-point, and a minimum at 33.4 °C. We interpret this as a combination of collapse closely followed by the growth of critical correlations. At large scattering angles we reach the universalk ³ regime, and observe that this behaviour vanishes at the onset of collapse transition. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph

We study the antiferromagnetic Potts model on the Poissonian Erd?s-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades) and from an entropy positivity argument.     

Core collapse supernovae in the QCD phase diagram

We compare two classes of hybrid equations of state with a hadron-to-quark matter phase transition in their application to core collapse supernova simulations. The first one uses the quark bag model and describes the transition to three-flavor quark matter at low critical densities. The second one employs a Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with parameters describing a phase transition to two-flavor quark matter at higher critical densities. These models possess a distinctly different temperature dependence of their transition densities which turns out to be crucial for the possible appearance of quark matter in supernova cores. During the early post-bounce accretion phase quark matter is found only if the phase transition takes place at sufficiently low densities as in the study based on the bag model. The increase critical density with increasing temperature, as obtained for our PNJL parametrization, prevents the formation of quark matter. The further evolution of the core collapse supernova as obtained applying the quark bag model leads to a structural reconfiguration of the central protoneutron star where, in addition to a massive pure quark matter core, a strong hydrodynamic shock wave forms and a second neutrino burst is released during the shock propagation across the neutrinospheres. We discuss the severe constraints in the freedom of choice of quark matter models and their parametrization due to the recently observed 2M _?? pulsar and their implications for further studies of core collapse supernovae in the QCD phase diagram.     

Bose−Einstein condensates with tunable spin−orbit coupling in the two-dimensional harmonic potential: The ground-state phases,stability phase diagram and collapse dynamics

We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose−Einstein condensates (BECs) with tunable spin−orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross−Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments.     

The two-dimensional coulomb gas in the critical region

We consider the two-dimensional Coulomb gas in the critical region. To avoid the well-known collapse of the system below a certain temperature, the Coulomb interaction is cut inside a core radius. By analysis of the pair correlation function we find that this system exhibits a phase transition with a critical point. Below the critical temperature the ions are unable to shield each other, and they all may be considered as bound in neutral dipolar pairs. The density of dipolar pairs affects the critical temperature. In the critical region we obtain explicit results, and we are able to extract the leading singular behavior of the pair correlation function.     

Strong-coupling properties of the neutral Hubbard model

From a new variational approach to the Hubbard model, communicated previously [1], we derive the magnetic strong-coupling properties for the half filled band case of the Hubbard model in simple cubic lattices. The transition temperature from an AB-antiferromagnetic to a paramagnetic state, the sublattice magnetization and the localization of magnetic moments are investigated in detail. Near the strong coupling limit the results become asymptotically exact in a molecular field sense but they look reasonable even outside this asymptotic region.     

A New Principle to Determine the Variational Parameter for the Variational-Cumulant Expansion

The key point of the variational-cumulant expanhon is the determination of the variational parameter. In this paper, we present the improved mean-field hypothesis (IMFH) which is the bdse to determine the parameter. The new method derived from the IMFH shows advantage over previous methods. The critical temperature and some thermal dynamical functions for the Heisenberg model are calculated with the new method.     

On the existence of free and self-trapped carriers in insulators: an abrupt temperature-dependent conductivity transition

A variational calculation of the eigenstates of the three-dimensional analogue of Holstein's Molecular Crystal Model is utilized as a basis for determining the conditions under which carrier self-trapping does or does not occur in this system. It is found that below a temperature-dependent critical value of the electron-lattice coupling strength self-trapping does not occur; the eigenstates then correspond to an excess electron being only weakly coupled to the vibratory motion. Above a larger temperature-dependent critical value of the electron-lattice coupling strength only self-trapped (small-polaron) eigenstates exist. Between these two (temperature-dependent) critical values of the electron-lattice coupling strength both types of solutions are found.

The condition for the existence of the weakly coupled situation, as well as that for the self-trapped circumstance, is shown to be derivable from arguments which are independent of the detailed variational calculation. These ancillary derivations provide a physical basis for understanding the two existence conditions. In addition, the results of the variational calculation are shown to agree with results obtained by non-variational means in the appropriate limits.

The temperature-dependent appearance or disappearance of states from the energy spectrum of the coupled system manifests itself through an abrupt change in the electrical transport properties of the material. The conductivity, Hall mobility, and thermoelectric power on both sides of such a transition are calculated by an ad hoc application of previously obtained results. The essential feature of the occurrence of this transition is that the carriers on the low-conductivity side of the transition are self-trapped; they possess the low thermally activated mobility that is associated with small-polaron hopping motion. On the high-conductivity side of the transition the mobility of the carriers is considerably higher, it being that which is generally associated with electronic motion in rigid-lattice bands. The possible relevance of the present theory to the so-called insulator-to-metal and insulator-to-insulator transitions is discussed.     

The Phase Diagram of the Quantum Curie-Weiss Model

This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the model in the parameters of inverse temperature and transverse field strength. Further analysis computes the critical exponent for the vanishing of the order parameter in the approach to the critical curve and gives useful stability properties for a variational problem associated with the representation.     

Ground State and Single Vortex for Bose-Einstein Condensates in Anisotropic Traps

For Bose-Einstein condensation of neutral atoms in anisotropic traps at zero temperature, we present simple analytical methods for computing the properties of ground state and single vortex of Bose-Einstein condensates, and compare those results to extensive numerical simulations. The critical angular velocity for production of vortices is calculated for both positive and negative scattering lengths a, and find an analytical expression for the large-N limit of the vortex critical angular velocity for a 〉0, and the critical number for condensate population approaches the point of collapse for a 〈 0, by using approximate variational method.     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Critical scaling of shear viscosity at the jamming transition

We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity eta is computed as a function of particle volume density rho and applied shear stress sigma, for diffusively moving particles with a soft core interaction. We find an excellent scaling collapse of our data as a function of the scaling variable sigma/|rho(c)-rho|(Delta), where rho(c) is the critical density at sigma=0 ("point J"), and Delta is the crossover scaling critical exponent. We define a correlation length xi from velocity correlations in the driven steady state and show that it diverges at point J. Our results support the assertion that jamming is a true second-order critical phenomenon.     

A note on localized transition in the spin-boson model by variational calculation

We present mathematical analyses of the evolution of solutions of the self-consistent equation derived from variational calculations based on the displaced-oscillator-state and the displaced-squeezed-state in spin-boson model at a zero temperature and a finite temperature. It is shown that, for a given spectral function defined as J（w） = π∑k Ck^2 = π/2αw^8w^1-s, there exists a universal sc for both kinds of variational schemes, the localized transition happens only for 2 s ≤ sc, moreover, the localized transition is discontinuous for s 〈 sc while a continuous transition always occurs when s = sc. At T = 0, we have sc = 1, while for T ≠ 0, sc = 2 which indicates that the localized transition in super-Ohmic case still exists, manifesting that the result is in discrepancy with the existing result.     

Finite-temperature density-dependent HF calculation of nuclear matter with gogny interaction

A finite-temperature density-dependent Hartree-Fock method is formulated starting from a variational principle for the thermodynamic potential. Based on this method, we have carried out a nuclear-matter calculation using the Gogny D1 finite-range effective interaction. The equation of state and several other thermal properties of nuclear matter so obtained are found to be rather similar to those given by the Skyrme SkM¹ interaction. The critical temperature and density for the liquid-gas phase transition of nuclear matter are found to be 15.1 MeV and 0.05 fm⁻³, respectively. The effect of the finite-temperature rearrangement potential is discussed     

Finite-temperature behavior of the lattice abelian Higgs model

We study phase transitions in the lattice version of the abelian Higgs model, a model which can exhibit both spontaneous symmetry breaking and confinement. When the Higgs charge is the basic U(1) unit, we find that the Higgs and confinement regions are not separated by a phase transition and form a single homogenous phase which we call the total screening phase. The model does not undergo a symmetry restoring phase transition at finite temperature.If the Higgs charge is some multiple of the basic unit the model follows the conventional wisdom: there are 3 phases (normal, Higgs and confinement) at zero temperature, two of which disappear above some critical point. We apply the lessons learned from the lattice Higgs model to understand the behavior of the weak interactions at high temperature.In a long appendix we give an intuitive physical picture for the Polyakov-Susskind quark liberating phase transition and show that it is related to the Hagedorn spectrum of a confining model. We end with a collection of effective field theory approximations to various lattice theories.     

Fractal Aggregation Near the Threshold

In this papel, we present two fractal aggregation models, line pattern seed model (model 1) and point pattern seed model (model 2), which are particle-cluster models. Using the current models, we investigate the critical transition in fractal aggregation processes in two dimensions, and suggest a method for finding the critical transition point. The computer simulation results show that the critical concentration is P_ca=0.69±0.02 for model 1 and P_ca=0.72±0.01 for model 2, critical fractal dimension. D_c= 1.71±0.06 for model 1 and D_c=1.66±0.07 for model 2, which are in good agreement with those of DLA model (D=5/3) and experimental data. The results also show that the critical transition point in two dimensions seems to be inilependent of the size of lattices and the initial seed patterns. The results seem to belong to the same universality class.     

Thermal signatures of the Kondo volume collapse in cerium

X-ray diffraction measurements of cerium in the vicinity of the isostructural gamma-alpha transition have been performed with high precision and accuracy from room temperature to almost 800 K. The disputed location of the critical point has been found to occur at 1.5+/-0.1 GPa and 480+/-10 K. The data are well fit by the Kondo volume collapse model plus a quasiharmonic representation of the phonons. The resultant free energy is validated against data for the thermodynamic Grüneisen parameter and, beyond the dominant spin-fluctuation contribution, indicates a dramatic change in the lattice Grüneisen parameter across the transition.     

Variational method in hamiltonian lattice gauge theories

A general expression for the expectation value of the hamiltonian of a d + 1 dimensional lattice gauge theory as a function of the norm of the variational state (that itself has the form of a partition function of a d-dimensional lattice gauge theory) is given. Applications include U(1), SU(2), U(2) and U(N) gauge theories for large N in d = 2 + 1 dimensions. It is also demonstrated that the deconfining phase transition is of first order in every dimension above the critical one, provided it is of first or second order at the critical dimension.