arXiv subjects
Publications and source records attributed to D. Mukamel.
It is shown that the scaling analysis presented in Phys. Rev. Lett. 85, 4988 (2000) (cond-mat/0007141) is valid for finite chains of lengths relevant to experiments, in contrast to a recent claim made by A. Hanke and R. Metzler in cond-mat/0108323.
Experimental studies of the thermal denaturation of DNA yield a strong indication that the transition is first order. This transition has been theoretically studied since the early sixties, mostly within an approach in which the microscopic configurations of a DNA molecule are given by an alternating sequence of non-interacting bound segments and denaturated loops. Studies of these models neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. In this study we exploit recent results on scaling properties of polymer networks of arbitrary topology in order to take into account the excluded-volume interaction between denaturated loops and the rest of the chain. We thus obtain a first-order phase transition in d=2 dimensions and above, in agreement with experiments. We also consider within our approach the unzipping transition, which takes place when the two DNA strands are pulled apart by an external force acting on one end. We find that the unzipping transition is also first order. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. For instance, the loop size distribution decays algebraically at the transition and the length of the denaturated end segment diverges as the transition is approached. We evaluate these critical properties within our approach.
In this work we study a two species driven diffusive system with open boundaries that exhibits spontaneous symmetry breaking in one dimension. In a symmetry broken state the currents of the two species are not equal, although the dynamics is symmetric. A mean field theory predicts a sequence of two transitions from a strongly symmetry broken state through an intermediate symmetry broken state to a symmetric state. However, a recent numerical study has questioned the existence of the intermediate state and instead suggested a single discontinuous transition. In this work we present an extensive numerical study that supports the existence of the intermediate phase but shows that this phase and the transition to the symmetric phase are qualitatively different from the mean-field predictions.
The evolution of a two-dimensional driven lattice-gas model is studied on an L_x X L_y lattice. Scaling arguments and extensive numerical simulations are used to show that starting from random initial configuration the model evolves via two stages: (a) an early stage in which alternating stripes of particles and vacancies are formed along the direction y of the driving field, and (b) a stripe coarsening stage, in which the number of stripes is reduced and their average width increases. The number of stripes formed at the end of the first stage is shown to be a function of L_x/L_y^ϕ, with ϕ~ 0.2. Thus, depending on this parameter, the resulting state could be either single or multi striped. In the second, stripe coarsening stage, the coarsening time is found to be proportional to L_y, becoming infinitely long in the thermodynamic limit. This implies that the multi striped state is thermodynamically stable. The results put previous studies of the model in a more general framework.
The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a coarsening process in which l(t), the average width of a stripe, grows with time. This is a generalization of the reaction-diffusion process A + A -> A to the case of extended coalescing objects, namely, the interfaces. Scaling arguments which relate the coarsening process to the evolution of a single driven interface are given, yielding growth laws for l(t), for both short and long time. We introduce a simple microscopic model for this process. Numerical simulations of the model confirm the scaling picture and growth laws. The results are compared to the case where the stripes are not driven and different growth laws arise.
A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a non-wet layer having a small deviation from bulk order, and a different non-wet layer with a large deviation from bulk order which decays non-monotonically as distance from the wall increases. In particular the large deviation non-wet layer is a feature of systems at the Lifshitz point and also those having only homogeneous bulk phases.
The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions.
We study the Landau model of the class of incommensurate systems with a scalar order parameter where the modulated phase is driven by a gradient-squared term with negative coefficient. For example, theoretical studies of cholesteric liquid crystals in a field (electric or magnetic) suggest that such an modulated phase should exist at high chirality. The bulk phase diagram in the presence of a bulk external field which couples linearly to the order parameter exhibits a modulated phase inside a loop in the temperature-field plane, and a homogeneous phase outside. On analyzing the same model for a semi-infinite system, we find a surprising result; the system exhibits surface states in a region where the bulk phase is homogeneous (but close to the modulated region). These states are very different from the well-known surface states induced either by a surface field or by enhanced interactions at the surface, for they exist and are energetically favored even when the sole effect of the surface is to terminate the bulk, as expressed by free boundary conditions taken at the surface. Near the surface, the surface-state order parameter is very different from the bulk value (in fact, it has the opposite sign). When the temperature or the bulk field are varied to move away from the modulated state, we find a surface phase transition at which the surface states become energetically unfavorable, though they continue to exist as metastable states. We then study how a surface field changes the surface phase diagram.
A driven system of three species of particle diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational symmetry is given. We show that for the special case where the three densities are equal the model obeys detailed balance and the steady-state distribution is governed by a Hamiltonian with asymmetric long-range interactions. This provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension. The steady state of finite-size systems is studied using a generalized matrix product ansatz. The coarsening process leading to phase separation is studied numerically and in a mean-field model. The system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size. The typical domain size is shown to grow logarithmically in time. Generalizations to a larger number of species are discussed.
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the three densities are equal, it is shown that the model obeys detailed balance. The Hamiltonian governing the steady state distribution in this case is given and is found to have long range asymmetric interactions. The partition sum and bounds on some correlation functions are calculated analytically demonstrating phase separation.
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is manifested by the existence of a phase in which the densities of the two species are not equal. In order to provide a more rigorous basis to these observations we consider the limit of the process when the rate at which particles leave the system goes to zero. In this limit the process reduces to a biased random walk in the positive quarter plane, with specific boundary conditions. The stationary probability measure of the position of the walker in the plane is shown to be concentrated around two symmetrically located points, one on each axis, corresponding to the fact that the system is typically in one of the two states of broken symmetry in the exclusion process. We compute the average time for the walker to traverse the quarter plane from one axis to the other, which corresponds to the average time separating two flips between states of broken symmetry in the exclusion process. This time is shown to diverge exponentially with the size of the chain.