We study an interacting system of N classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repel each other via pairwise interaction potential that ...behaves as a power law ∝∑i≠jN|xi−xj|−k (with k>−2) of their mutual distance. This is a generalization of the well-known cases of the one-component plasma (k=−1), Dyson's log gas (k→0+), and the Calogero-Moser model (k=2). Because of the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all k>−2. We compute exactly the average density profile for large N for all k>−2 and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on k with distinct behavior for −2<k<1, k>1 and k=1.
We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the ...membrane behind or ahead of the interface, are not symmetrically related. On the basis of numerical results and an exact calculation, we argue that these two arrangements represent two distinct universality classes for interfacial growth: while the well-established Kardar-Parisi-Zhang (KPZ) growth is obtained in the "ahead" arrangement, we find an arrested KPZ growth with a smaller roughness exponent in the "behind" arrangement. This suggests that the surface properties of growing cell membranes and expanding bacterial colonies, for example, are fundamentally distinct.
The thermodynamic and dynamical properties of an Ising model with both short-range and long-range, mean-field-like, interactions are studied within the microcanonical ensemble. It is found that the ...relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short-range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long-range interactions and are expected to be valid even when the interaction is slowly decaying with distance.
The effect of particle-nonconserving processes on the steady state of driven diffusive systems is studied within the context of a generalized ABC model. It is shown that in the limit of slow ...nonconserving processes, the large deviation function of the overall particle density can be computed by making use of the steady-state density profile of the conserving model. In this limit one can define a chemical potential and identify first order transitions via Maxwell's construction, similarly to what is done in equilibrium systems. This method may be applied to other driven models subjected to slow nonconserving dynamics.
A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) ...density-conserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with long-range interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (density-conserving) and grand canonical (density nonconserving) ensembles, as expected in long-range interacting systems. The implications of this result to nonequilibrium steady states, such as those of the ABC model with unequal average densities, are briefly discussed.
Steady-state properties of a driven tracer moving in a narrow two-dimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and ...pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a one-dimensional (1D) SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of mean-field theory and exact solution in the limit where no exchange is allowed gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.
Loop dynamics in DNA denaturation Bar, A; Kafri, Y; Mukamel, D
Physical review letters,
01/2007, Letnik:
98, Številka:
3
Journal Article
Recenzirano
Odprti dostop
The dynamics of a loop in DNA molecules at the denaturation transition is studied by scaling arguments and numerical simulations. The autocorrelation function of the state of complementary bases ...(either closed or open) is calculated. The long-time decay of the autocorrelation function is expressed in terms of the loop exponent c both for homopolymers and heteropolymers. This suggests an experimental method for measuring the exponent c using florescence correlation spectroscopy.
PDF
