Table of contents

Double-stranded DNA denaturation induced by an external force is modeled as a pair of complementary self-avoiding polymers with inter-strand binding potential. The resulting force–temperature phase diagram is determined using heuristic arguments, exactly solvable models and 3D Monte Carlo simulations. The results are qualitatively different for the cases where the force is applied to only one strand or to both strands. Crucial ingredients for getting a qualitative agreement with experimental results are the persistence lengths and the monomer sizes of single-stranded and double-stranded DNA. The subtle dependence of the small force behavior on the latter parameters, on the stretching mode and on the presence of denaturation bubbles is analyzed in detail.

We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk thermodynamic pressure to the pair correlation function and we develop the appropriate setting for extending the integral-equation approach of liquid-state theory in order to describe the fluid structure. We apply the formalism and study the influence of negative space curvature on two kinds of systems that have been recently considered: Coulombic systems, such as the one- and two-component plasma models, and fluids interacting through short-range pair potentials, such as the hard-disk and the Lennard-Jones models.

In this paper, we show that spin waves, the elementary excitation of the Heisenberg magnetic system, obey a kind of intermediate statistics with a finite maximum occupation number n. We construct an operator realization for the intermediate statistics obeyed by magnons, the quantized spin waves, and then construct a corresponding intermediate-statistics realization for the angular momentum algebra in terms of the creation and annihilation operators of the magnons. In other words, instead of the Holstein–Primakoff representation, a bosonic representation subject to a constraint on the occupation number, we present an intermediate-statistics representation with no constraints. In this realization, the maximum occupation number is naturally embodied in the commutation relation of creation and annihilation operators, while the Holstein–Primakoff representation is a bosonic operator relation with an additional putting-in-by-hand restriction on the occupation number. We deduce the intermediate-statistics distribution function for magnons from the intermediate-statistics commutation relation of the creation and annihilation operators directly, which is a modified Bose–Einstein distribution. On the basis of these results, we calculate the dispersion relations for ferromagnetic and antiferromagnetic spin waves. The relations between the intermediate statistics that magnons obey and the other two important kinds of intermediate statistics, Haldane–Wu statistics and the fractional statistics of anyons, are discussed. We also compare the spectrum of the intermediate-statistics spin wave with the exact solution of the one-dimensional s = 1/2 Heisenberg model, which is obtained by the Bethe ansatz method. For ferromagnets, we take the contributions from the interaction between magnons (the quartic contribution), the next-to-nearest-neighbor interaction, and the dipolar interaction into account for comparison with the experiment.

The aviation sector is profitable, but sensitive to economic fluctuations, geopolitical constraints and governmental regulations. As for other means of transportation, the relation between origin and destination results in a complex map of routes, which can be complemented with information associated with the routes themselves, for instance, frequency, traffic load and distance. The theory of networks provides a natural framework for investigating the dynamics on the resulting structure. Here, we investigate the structure and evolution of the Brazilian airport network (BAN) as regards several quantities: routes, connections, passengers and cargo. Some structural features are in accordance with previous results for other airport networks. The analysis of the evolution of the BAN shows that its structure is dynamic, with changes in the relative relevance of some airports and routes. The results indicate that the connections converge to specific routes. The network shrinks at the route level but grows in number of passengers and amount of cargo, which more than doubled during the period studied.

Purely self-gravitating systems of point particles have been extensively studied in astrophysics and cosmology, mainly through numerical simulations, but understanding of their dynamics still remains extremely limited. We describe here results of a detailed study of a simple class of cold quasi-uniform initial conditions, for both finite open systems and infinite systems. These examples illustrate well the qualitative features of the quite different dynamics observed in each case, and also clarify the relation between them. In the finite case our study highlights the potential importance of energy and mass ejection prior to virialization, a phenomenon which has been previously overlooked. We discuss for both cases the validity of a mean-field Vlasov–Poisson description of the dynamics observed, and specifically the question of how particle number should be extrapolated to test for it.

We study numerically a model of nonequilibrium networks where nodes and links are added at each time step with ageing of nodes and connectivity-and age-dependent attachment of links. By varying the effects of age in the attachment probability we find, with numerical simulations and scaling arguments, that a giant cluster emerges at a first-order critical point and that the problem is in the universality class of one-dimensional percolation. This transition is followed by a change in the giant cluster's topology from tree-like to quasi-linear, as inferred from measurements of the average shortest-path length, which scales logarithmically with system size in one phase and linearly in the other.

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

We consider directed walk models of a polymer that is adsorbing at a surface due to polymer–surface interactions, and is also pulled away from the surface by an elongational force. We obtain force–temperature, force–extension, and density–extension curves for the Dyck path and partially directed walk models for the situation where the polymer is pulled from one end, and for Dyck paths when the polymer is pulled from a central location in the polymer. We obtain force–extension and density–extension curves for these models, and their dependence on the length of the polymer.

We consider spin-polarized electrons in a single Landau level on a cylinder as the circumference of the cylinder goes to infinity. This gives a model of interacting electrons on a circle where the momenta of the particles are restricted and there is no kinetic energy. Quantum Hall states are exact ground states for appropriate short range interactions, and there is a gap to excitations. These states develop adiabatically from this one-dimensional quantum Hall circle to the bulk quantum Hall states and further on into the Tao–Thouless states as the circumference goes to zero. For low filling fractions a gapless state is formed which we suggest is connected to the Wigner crystal expected in the bulk.

We propose a general framework that leads to one-dimensional XX and Hubbard models in full generality, based on the decomposition of an arbitrary vector space (possibly infinite dimensional) into a direct sum of two subspaces, the two corresponding orthogonal projectors allowing one to define an R-matrix of a universal XX model, and then of a Hubbard model using a Shastry type construction. The QISM approach ensures integrability of the models, the properties of the R-matrices obtained leading to local Hubbard-like Hamiltonians.

In all cases, the energies, the symmetry algebras and the scattering matrices are explicitly determined. The computation of the Bethe ansatz equations for some subsectors of the universal Hubbard theories is carried out, while they are fully computed in the XX case. A perturbative calculation in the large coupling regime is also carried out for the universal Hubbard models.

We present measurements of the fractal dimensions associated with the spin clusters for Z₄ and Z₅ spin models. We also attempted to measure similar fractal dimensions for the generalized Fortuin–Kastelyn clusters in these models, but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in behavior of these non-local objects as compared to the Ising model or the three-state Potts model, which correspond to the simplest cases of Z_N spin models with N = 2 and N = 3 respectively. We compare these fractal dimensions with the ones obtained for SLE interfaces.

We address the issue of the validity of the fluctuation dissipation theorem and the time evolution of viscoelastic properties during ageing of aqueous suspensions of a clay (Laponite RD) in a colloidal glass phase. Given the conflicting results reported in the literature for different experimental techniques, our goal is to check and reconcile them using simultaneously passive and active microrheology techniques. For this purpose we measure the thermal fluctuations of microsized Brownian particles immersed in the colloidal glass and trapped by optical tweezers. We find that several methods based on both microrheology techniques lead to consistent and complementary results and no violation of the FDT is convincingly observed either for any frequency as low as 0.25 Hz or as an increase of the effective temperature during the formation of the viscoelastic glass. Our results are supported by the study of the probability density functions of heat fluctuations between the probe particles and the suspension transferred at different timescales. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition.

We derive an exact formula for the covariance of Cartesian distances in two simple polymer models: the freely jointed chain and a discrete flexible model with nearest-neighbor interaction. We show that even in the interaction-free case, correlations exist as long as the two distances at least partially share the same segments. For the interacting case, we demonstrate that the naive expectation of increasing correlations with increasing interaction strength only holds for a finite range of values. Some suggestions for future single-molecule experiments are made.

We explicitly describe certain components of the finite size ground state of the inhomogeneous transfer matrix of the O(n = 1) loop model on a strip with non-trivial boundaries on both sides. In addition we compute explicitly the ground state normalization which is given as a product of four symplectic characters.

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalizes the preferential attachment model and Ford's α-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from 1 to ∞, depending on the parameters of the model.

Taking the Bohm potential approach, equations can be derived possessing QM information but classical form. Following this approach, an infinite set of equations for the infinite moments of the distribution function was derived, from which a P_L approximation can be drawn at any order L. From the P₁ approximation, Onsager-type equations are derived. They are QM equations insofar as: (1) they contain the Bohm potential; (2) collisional processes are described by the BUU kernel; (3) the equilibrium distribution functions are either FD or BE.

We discuss possible connections between the thermostatistical properties of a gas of the two-parameter deformed bosonic particles called Fibonacci oscillators and the properties of the Tsallis thermostatistics. In this framework, we particularly focus on a comparison of the non-extensive entropy functions expressed by these two generalized theories. We also show that the thermostatistics of the two-parameter deformed bosons can be studied using the formalism of Fibonacci calculus, which generalizes the recently proposed formalism of Lavagno and Narayana Swamy of q-calculus for the one-parameter deformed boson gas. As an application, we briefly summarize some of the recent results on the Bose–Einstein condensation phenomenon for the present two-parameter generalized boson gas.

Although classical density functional theory provides reliable predictions for the static properties of simple equilibrium fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence that knowledge of how confinement modifies static behavior can aid in forecasting dynamics. Specifically, recent molecular simulation studies have shown that the relationship between excess entropy and self-diffusivity of a bulk equilibrium fluid changes only modestly when the fluid is isothermally confined, indicating that knowledge of the former might allow semi-quantitative predictions of the latter. Do other static measures, such as those that characterize free or available volume, also strongly correlate with single-particle dynamics of confined fluids? Here, we investigate this question for both the single-component hard-sphere fluid and hard-sphere mixtures. Specifically, we use molecular simulations and fundamental measure theory to study these systems at approximately 10³ equilibrium state points. We examine three different confining geometries (slit pore, square channel, and cylindrical pore) and the effects of particle packing fraction and particle–boundary interactions. Although average density fails to predict some key qualitative trends for the self-diffusivity of confined fluids, we provide strong empirical evidence that a new generalized measure of available volume for inhomogeneous fluids correlates excellently with self-diffusivity across a wide parameter space in these systems, approximately independently of the degree of confinement. An important consequence, which we demonstrate here, is that density functional theory predictions of this static property can be used together with knowledge of bulk fluid behavior to semi-quantitatively estimate the self-diffusion coefficient of confined fluids under equilibrium conditions.

We propose a classification of the solutions of the graded reflection equations for the U_q[spo(2n|2m)] vertex model. We find twelve distinct classes of reflection matrices such that four of them are diagonal. In the non-diagonal matrices the number of free parameters depends on the number of bosonic (2n) and fermionic (2m) degrees of freedom while in the diagonal ones we find solutions with at most one free parameter.

As generalizations of results of Christandl et al (2004 Phys. Rev. Lett. 92 187902; 2005 Phys. Rev. A 71 032312) and Facer et al (2008 Phys. Rev. A 77 012334), Bernasconi et al (2008 0808.0510 [quant-ph]; 2008 0806.2074 [math.CO]) studied perfect state transfer (PST) between two particles in quantum networks modeled by a large class of cubelike graphs (e.g. the hypercube) which are the Cayley graphs of the elementary Abelian group Z₂ⁿ. In Jafarizadeh and Sufiani (2008 Phys. Rev. A 77 022315) Jafarizadeh et al (2008 J. Phys. A: Math. Theor. 41 475302) respectively, PST of a qubit over distance regular spin networks and optimal state transfer (ST) of a d-level quantum state (qudit) over pseudo-distance regular networks were discussed, where the networks considered there were not, in general, related to a certain finite group. In this paper, PST of a qudit over antipodes of more general networks, called underlying networks of association schemes, is investigated. In particular, we consider the underlying networks of group association schemes in order to employ the group properties (such as irreducible characters) and use the algebraic structure of these networks (such as Bose–Mesner algebra) in order to give an explicit analytical formula for coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will perfectly evolve to the opposite site without any dynamical control. It is shown that the only necessary condition in order for PST over these networks to be achieved is that the centers of the corresponding groups be non-trivial. Therefore, PST over the underlying networks of the group association schemes over all the groups with non-trivial centers such as the Abelian groups, the dihedral group D_2n with even n, the Clifford group CL(n) and all of the p-groups can be achieved.

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin–spin correlation function of the XXZ Heisenberg spin- 1/2 chain (with magnetic field) in the disordered regime as well as to the density–density correlation function of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.

We study the current–density diagram for when a slow vehicle is introduced in multi-lane traffic flow. We extend the conventional optimal velocity model to the multi-lane traffic by taking into account the lane changing. The dynamical state of the traffic changes with increasing density. The dynamical phase transitions occur at certain densities. It is found that there are four distinct states for the two-lane traffic flow including a slow vehicle: (1) the free traffic at a low density, (2) the jammed traffic at an intermediate density, (3) the homogeneous traffic with different occupancies on the first and second lanes, at increasing density furthermore, and (4) the congested traffic with the same occupancy on the first and second lanes at a high density. Traffic state (2) is divided into two dynamic states for the three-lane and four-lane traffic. In addition, traffic state (3) is divided into two dynamic states for the four-lane traffic. The dependence of the current on the velocity of a slow vehicle is derived numerically and analytically.

The subrecoil laser cooling process is considered in the framework of a model with two states (trapping and recycling), with instantaneous transitions between them. The key point of the work is the use of a fractional exponential function for waiting time distributions. This allows us to derive a general master equation covering both important cases: those with exponential and power type tails. Their solutions are expressed through fractionally stable distributions. The pdfs of the total trapping time of an atom and the proportion of trapped atoms are found. Analytical relationships show a good agreement with numerical results from Monte Carlo simulation.