Universality classes of self-avoiding fixed-connectivity membranes

We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. We simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we find the membrane to be flat for all temperatures: the size exponent in three dimensions is ν = 0.95(5) (Hausdorff dimension d _H = 2.1(1)). The single flat phase appears, furthermore, to be equivalent to the large bending rigidity phase of non-self-avoiding fixed-connectivity membranes --the roughness exponent in three dimensions is ξ = 0.63(4). This suggests that there is a unique universality class for flat fixed-connectivity membranes without attractive interactions. Finally, we address some theoretical and experimental implications of our work. Received 23 June 2000 and Received in final form 25 October 2000     

On the High Density Behavior of Hamming Codes with Fixed Minimum Distance

We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n→∞, d→∞, d/n = δ. The problem is relevant for coding theory, and the best available bounds state that the maximum density of the system falls in the interval 1 ≤ ρ V _d ≤ exp (n κ(δ)), being κ(δ) > 0 and V _d the volume of a sphere of radius d. We find a solution of the equations describing the liquid up to an exponentially large value of ρ = ρ V _d , but we show that this solution gives a negative entropy for the liquid phase for ρ >rsimn. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. PACS: 05.20.Jj, 64.70.Pf, 61.20.Gy     

The Properties of Strings Formed in the Homochiral Solutions of Trifluoroacetylated Amino Alcohols in Cyclohexane

The strings formed in the solutions of trifluoroacetylated amino alcohols in cyclohexane were studied. It was found that microscopic strings with the diameter d ～ 1 μm were woven from tightly coupled rigid submicroscopic strings with the diameter d ～ 0.1 μm in increments of >100 μm. Therefore, the compound strings are transparent, and they usually look like an unstructured cylinder. Microscopic strings can be tightly combined in strings to 60 μm in diameter. Submicroscopic strings are arranged almost parallel to the axis of a microscopic string. The microscopic string acts as a polarizer: it transmits light polarized across its axis and absorbs light polarized along the axis. The majority of these properties can be explained based on the assumption that a connection between the strings of all hierarchical levels in cyclohexane is stronger than that in solvents with different string morphology.     

Transience, Recurrence and Critical Behavior¶for Long-Range Percolation

We study the behavior of the random walk on the infinite cluster of independent long-range percolation in dimensions d= 1,2, where x and y are connected with probability . We show that if d<s<2d, then the walk is transient, and if s≥ 2d, then the walk is recurrent. The proof of transience is based on a renormalization argument. As a corollary of this renormalization argument, we get that for every dimension d≥ 1, if d>s>2d, then there is no infinite cluster at criticality. This result is extended to the free random cluster model. A second corollary is that when d≥& 2 and d>s>2d we can erase all long enough bonds and still have an infinite cluster. The proof of recurrence in two dimensions is based on general stability results for recurrence in random electrical networks. In particular, we show that i.i.d. conductances on a recurrent graph of bounded degree yield a recurrent electrical network. Received: 27 October 2000 / Accepted: 29 November 2001     

Single-Site Approximation for Reaction-Diffusion Processes

We consider the branching and annihilating random walk and with reaction rates σ and λ, respectively, and hopping rate D, and study the phase diagram in the λ/D,σ/D) plane. According to standard mean-field theory, this system is in an active state for all σ/D≥0, and perturbative renormalization suggests that this mean-field result is valid for d>2; however, nonperturbative renormalization predicts that for all d there is a phase transition line to an absorbing state in the λ/D,σ/D) plane. We show here that a simple single-site approximationreproduces with minimal effort the nonperturbative phase diagram both qualitatively and quantitatively for all dimensions d>2. We expect the approach to be useful for other reaction-diffusion processes involving absorbing state transitions.     

A Dynamical Classification of the Range of Pair Interactions

We formalize a classification of pair interactions based on the convergence properties of the forces acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF) P(F) of the force field F in a particle distribution in the limit that the size of the system is taken to infinity at constant particle density, i.e., in the “usual” thermodynamic limit. For a pair interaction potential V(r) with V(r→∞)∼1/r ^γ defining a bounded pair force, we show that P(F) converges continuously to a well-defined and rapidly decreasing PDF if and only if the pair force is absolutely integrable, i.e., for γ>d−1, where d is the spatial dimension. We refer to this case as dynamically short-range, because the dominant contribution to the force on a typical particle in this limit arises from particles in a finite neighborhood around it. For the dynamically long-range case, i.e., γ≤d−1, on the other hand, the dominant contribution to the force comes from the mean field due to the bulk, which becomes undefined in this limit. We discuss also how, for γ≤d−1 (and notably, for the case of gravity, γ=d−2) P(F) may, in some cases, be defined in a weaker sense. This involves a regularization of the force summation which is generalization of the procedure employed to define gravitational forces in an infinite static homogeneous universe. We explain that the relevant classification in this context is, however, that which divides pair forces with γ>d−2 (or γ<d−2), for which the PDF of the difference in forces is defined (or not defined) in the infinite system limit, without any regularization. In the former case dynamics can, as for the (marginal) case of gravity, be defined consistently in an infinite uniform system.     

Phase separation between phospholipids and grafted polymer chains onto a fluctuating membrane

We re-examine here the theoretical study of the phase separation between phospholipids and grafted long polymer chains onto a fluid membrane. The polymer chains are assumed to be anchored to the membrane by one extremity (anchor). The anchors are big amphiphile lipid molecules. The anchors and phospholipids forming the bilayer phase separate under the variation of a suitable parameter (temperature, pressure, membrane environment, ...). To investigate the demixtion transition, we elaborate a new approach that takes into account the membrane undulations. We show that these undulations have the tendency to induce additional attractive forces between anchors, and consequently, the separation transition is accentuated and occurs at high temperature. Quantitatively, we show that the membrane undulations contribute with an extra positive segregation parameter χ_m > 0 , which scales as χ_m κ^-2 , where κ is the bending rigidity constant. Therefore, the attraction phenomenon between species of the same kind is significant only for those membranes of small bending rigidity constant. Finally, the study is extended to the case where the lengths of the anchored polymer chains are randomly distributed. To achieve calculations, we choose a length distribution of fractal form. The essential conclusion is that the polydispersity increases the size of domains alternatively rich in phospholipids and anchors.     

Controlling the noise enhanced stability effect via noise recycling in a metastable system

We analyze the role of the delay time τ _d and the fraction ε of recycled noise on the enhancement of the mean first-passage time (MFPT) in a metastable system with recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay. The results indicate that MFPT as a function of the noise intensity D shows either a non-monotonic behavior with a maximum or a divergent behavior, which is the identifying characteristic of the noise enhanced stability (NES) phenomenon. The increasing of τ _d or ε strengthens the NES effect for ε > 0. However, for ε < 0, there is a critical value of τ _d , below which we observe an increase of MFPT whose maximum goes to infinity, and above which the divergent behavior tends to disappear and MFPT versus D shows a transition from one peak to two peaks and eventually one peak as τ _d or |ε| increases. Moreover, we also discuss the effect of different initial conditions. These observations illustrate that the noise recycling may be used as an effective scheme for controlling the NES effect.     

First-Order Phase Transition in Potts Models with Finite-Range Interactions

We consider the Q-state Potts model on Z ^d , Q≥ 3, d≥ 2, with Kac ferromagnetic interactions and scaling parameter γ. We prove the existence of a first order phase transition for large but finite potential ranges. More precisely we prove that for γ small enough there is a value of the temperature at which coexist Q+1 Gibbs states. The proof is obtained by a perturbation around mean-field using Pirogov-Sinai theory. The result is valid in particular for d = 2, Q = 3, in contrast with the case of nearest-neighbor interactions for which available results indicate a second order phase transition. Putting both results together provides an example of a system which undergoes a transition from second to first order phase transition by changing only the finite range of the interaction.     

Spectral Analysis of Weakly Coupled Stochastic Lattice Ginzburg–Landau Models

We consider the relaxation to equilibrium of solutions , t>0, , of stochastic dynamical Langevin equations with white noise and weakly coupled Ginzburg–Landau interactions. Using a Feynman–Kac formula, which relates stochastic expectations to correlation functions of a spatially non-local imaginary time quantum field theory, we obtain results on the joint spectrum of H, , where H is the self-adjoint, positive, generator of the semi-group associated with the dynamics, and P ^j , j= 1, …, d are the self-adjoint generators of the group of lattice spatial translations. We show that the low-lying energy-momentum spectrum consists of an isolated one-particle dispersion curve and, for the mass spectrum (energy-momentum at zero-momentum), besides this isolated one-particle mass, we show, using a Bethe–Salpeter equation, the existence of an isolated two-particle bound state if the coefficient of the quartic term in the polynomial of the Ginzburg–Landau interaction is negative and d= 1, 2; otherwise, there is no two-particle bound state. Asymptotic values for the masses are obtained. Received: 27 September 2000 / Accepted: 16 January 2001     

Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions

Systems of particles interacting with long range interactions present generically ”quasi-stationary states” (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) ∼ 1/r ^γ with γ > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > d − 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a ”dynamical” classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not.     

Fields with continuously distributed mass

We describe local field theories with continuously distributed mass. Such models can be realized as models in d > 4 space-time with Poincare invariance only in four-dimensional space-time. We also discuss some possible phenomenological consequences. Namely, we show that the Higgs boson phenomenology in the SM extension with continuously distributed Higgs boson mass can differ in a drastic way from the standard Higgs boson phenomenology.     

Global strings in extra dimensions: The full map of solutions,matter trapping,and the hierarchy problem

We consider (d ₀ + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d ₀ dimensions, endowed with a warp factor e ^2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l _c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough distances l _c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane, where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading to matter particle mass spectra that seem promising from the standpoint of hierarchy problems. The text was submitted by the authors in English.     

Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

We study some aspects of Maldacena's large-N correspondence between superconformal gauge theory on the D3-brane and maximal supergravity on AdS by introducing macroscopic strings as heavy (anti-) quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on a D3-brane world-volume. We first study deformation and fluctuation of D3-branes when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for the macroscopic string in anti-de Sitter supergravity. As a by-product we clarify how Polchinski's Dirichlet and Neumann open string boundary conditions arise dynamically. We then study the non-BPS macroscopic string–anti-string pair configuration as a physical realization of a heavy quark Wilson loop. We obtain the static potential from the supergravity side and find that the potential exhibits non-analyticity of the square-root branch cut in the 't Hooft coupling parameter. We put forward non-analyticity as a prediction for large-N gauge theory in the strong 't Hooft coupling limit. By turning on the Ramond–Ramond zero-form potential, we also study the vacuum angle dependence of the static potential. We finally discuss the possible dynamical realization of the heavy N-prong string junction and of the large-N loop equation via a local electric field and string recoil thereof. Throughout comparisons of the AdS–CFT correspondence, we find that a crucial role is played by “geometric duality” between the UV and IR scales in directions perpendicular to the D3-brane and parallel ones, explaining how the AdS spacetime geometry emerges out of four-dimensional gauge theory at strong coupling. Received: 21 September 2001 / Published online: 12 November 2001     

Neutron-neutron scattering length from the reaction γd → πnn employing chiral perturbation theory

We discuss the possibility to extract the neutron-neutron scattering length a_nn from experimental spectra on the reaction γd → π⁺ nn . The transition operator is calculated to high accuracy from chiral perturbation theory. We argue that for properly chosen kinematics, the theoretical uncertainty of the method can be as low as 0.1 fm.     

On the Distinguishability of Random Quantum States

We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter, and results from random matrix theory, to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p > 0.72. An application to distinguishing Boolean functions (the “oracle identification problem”) in quantum computation is given.     

Discrete symmetries in Kaluza-Klein theories

We investigate discrete symmetries in theories of higher-dimensional (d > 4) gravity and their consequences for the reduced four-dimensional theory, obtained for a ground state which is a direct product of four-dimensional Minkowski space and a compact d ? 4 dimensional internal space. If the action of pure d-dimensional gravity coupled to spinors is invariant under time reversal or reflection of an odd number of spacelike co-ordinates, the reduced four-dimensional theory has a non-trivial parity or CT symmetry not consistent with observation. A non-trivial d-dimensional charge conjugation results in an unwanted doubling of the four-dimensional fermion spectrum. As a consequence, realistic theories can only be obtained for Majorana-Weyl spinors in d = 2 mod 8 dimensions. The constraints are less stringent if supplementary fields are introduced in d dimensions. For d = 11 supergravity, for example, parity and CT invariance can be broken by a non-vanishing field strength of the totally antisymmetric three-index tensor.A ground state invariant under reflections of “internal” co-ordinates often gives rise to a non-trivial charge conjugation in four dimensions. We find that the ground state of a realistic Kaluza-Klein theory should not be invariant under any non-trivial internal co-ordinate reflection (which cannot be obtained by a gauge transformation). We finally comment on a possible solution of the strong-CP problem from Kaluza-Klein theories and discuss prospectives for finding internal spaces admitting chiral fermions.     

String theories and millisecond pulsars

We discuss the two ways of connecting string theories (cosmic, fundamental and the connection between them) to the observational reality: (i) radioastronomy observations (millisecond pulsar timing), and (ii) elementary particle phenomenology (compactification schemes). We study the limits imposed on the string parameter Gμ by recent millisecond pulsar timings. Cosmic strings derived from GUTs agree with (i). For cosmic strings derived from fundamental strings themselves there is contradiction between (i) and (ii). One of these scenarios connecting string theory to reality must be revised (or the transition from fundamental into cosmic strings rejected). Meanwhile, millisecond pulsar can select one scenario, or reject both of them.     

On the stability of AdS black strings

We explore via linearized perturbation theory the Gregory–Laflamme instability of the black string solutions of Einstein's equations with negative cosmological constant recently discussed in literature. Our results indicate that the black strings whose conformal infinity is the product of time and Sd−3×S¹$S^{d-3}\times S^1$ are stable for large enough values of the event horizon radius. All topological black strings are also classically stable. We argue that this provides an explicit realization of the Gubser–Mitra conjecture.