5,691 research outputs found
Universality and non-universality of mobility in heterogeneous single-file systems and Rouse chains
We study analytically the tracer particle mobility in single-file systems
with distributed friction constants. Our system serves as a prototype for
non-equilibrium, heterogeneous, strongly interacting Brownian systems. The long
time dynamics for such a single-file setup belongs to the same universality
class as the Rouse model with dissimilar beads. The friction constants are
drawn from a density and we derive an asymptotically exact
solution for the mobility distribution , where is the
Laplace-space mobility. If is light-tailed (first moment exists) we
find a self-averaging behaviour: with
. When is heavy-tailed,
for large we obtain
moments where
and no self-averaging. The results are corroborated by
simulations.Comment: 8 pages, 4 figures, REVTeX, to appear in Physical Review
Entanglement, quantum phase transitions, and density matrix renormalization
We investigate the role of entanglement in quantum phase transitions, and
show that the success of the density matrix renormalization group (DMRG) in
understanding such phase transitions is due to the way it preserves
entanglement under renormalization. We provide a reinterpretation of the DMRG
in terms of the language and tools of quantum information science which allows
us to rederive the DMRG in a physically transparent way. Motivated by our
reinterpretation we suggest a modification of the DMRG which manifestly takes
account of the entanglement in a quantum system. This modified renormalization
scheme is shown,in certain special cases, to preserve more entanglement in a
quantum system than traditional numerical renormalization methods.Comment: 5 pages, 1 eps figure, revtex4; added reference and qualifying
remark
Applying a potential across a biomembrane: electrostatic contribution to the bending rigidity and membrane instability
We investigate the effect on biomembrane mechanical properties due to the
presence an external potential for a non-conductive non-compressible membrane
surrounded by different electrolytes. By solving the Debye-Huckel and Laplace
equations for the electrostatic potential and using the relevant stress-tensor
we find: in (1.) the small screening length limit, where the Debye screening
length is smaller than the distance between the electrodes, the screening
certifies that all electrostatic interactions are short-range and the major
effect of the applied potential is to decrease the membrane tension and
increase the bending rigidity; explicit expressions for electrostatic
contribution to the tension and bending rigidity are derived as a function of
the applied potential, the Debye screening lengths and the dielectric constants
of the membrane and the solvents. For sufficiently large voltages the negative
contribution to the tension is expected to cause a membrane stretching
instability. For (2.) the dielectric limit, i.e. no salt (and small wavevectors
compared to the distance between the electrodes), when the dielectric constant
on the two sides are different the applied potential induces an effective
(unscreened) membrane charge density, whose long-range interaction is expected
to lead to a membrane undulation instability.Comment: 16 pages, 3 figures, some revisio
Fitting a function to time-dependent ensemble averaged data
Time-dependent ensemble averages, i.e., trajectory-based averages of some
observable, are of importance in many fields of science. A crucial objective
when interpreting such data is to fit these averages (for instance, squared
displacements) with a function and extract parameters (such as diffusion
constants). A commonly overlooked challenge in such function fitting procedures
is that fluctuations around mean values, by construction, exhibit temporal
correlations. We show that the only available general purpose function fitting
methods, correlated chi-square method and the weighted least squares method
(which neglects correlation), fail at either robust parameter estimation or
accurate error estimation. We remedy this by deriving a new closed-form error
estimation formula for weighted least square fitting. The new formula uses the
full covariance matrix, i.e., rigorously includes temporal correlations, but is
free of the robustness issues, inherent to the correlated chi-square method. We
demonstrate its accuracy in four examples of importance in many fields:
Brownian motion, damped harmonic oscillation, fractional Brownian motion and
continuous time random walks. We also successfully apply our method, weighted
least squares including correlation in error estimation (WLS-ICE), to particle
tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and
we provide a publically available WLS-ICE software.Comment: 47 pages (main text: 15 pages, supplementary: 32 pages
Dissimilar bouncy walkers
We consider the dynamics of a one-dimensional system consisting of dissimilar
hardcore interacting (bouncy) random walkers. The walkers' (diffusing
particles') friction constants xi_n, where n labels different bouncy walkers,
are drawn from a distribution rho(xi_n). We provide an approximate analytic
solution to this recent single-file problem by combining harmonization and
effective medium techniques. Two classes of systems are identified: when
rho(xi_n) is heavy-tailed, rho(xi_n)=A xi_n^(-1-\alpha) (0<alpha<1) for large
xi_n, we identify a new universality class in which density relaxations,
characterized by the dynamic structure factor S(Q,t), follows a Mittag-Leffler
relaxation, and the the mean square displacement of a tracer particle (MSD)
grows as t^delta with time t, where delta=alpha/(1+\alpha). If instead rho is
light-tailedsuch that the mean friction constant exist, S(Q,t) decays
exponentially and the MSD scales as t^(1/2). We also derive tracer particle
force response relations. All results are corroborated by simulations and
explained in a simplified model.Comment: 11 pages, to appear in Journal of Chemical Physic
Optimal target search on a fast folding polymer chain with volume exchange
We study the search process of a target on a rapidly folding polymer (`DNA')
by an ensemble of particles (`proteins'), whose search combines 1D diffusion
along the chain, Levy type diffusion mediated by chain looping, and volume
exchange. A rich behavior of the search process is obtained with respect to the
physical parameters, in particular, for the optimal search.Comment: 4 pages, 3 figures, REVTe
Aging dynamics in interacting many-body systems
Low-dimensional, complex systems are often characterized by logarithmically
slow dynamics. We study the generic motion of a labeled particle in an ensemble
of identical diffusing particles with hardcore interactions in a strongly
disordered, one-dimensional environment. Each particle in this single file is
trapped for a random waiting time with power law distribution
, such that the values are
independent, local quantities for all particles. From scaling arguments and
simulations, we find that for the scale-free waiting time case ,
the tracer particle dynamics is ultra-slow with a logarithmic mean square
displacement (MSD) . This extreme
slowing down compared to regular single file motion is due to the high likelihood that the labeled
particle keeps encountering strongly immobilized neighbors. For the case
we observe the MSD scaling , where we recover Harris law
.Comment: 5 pages, 4 figure
Quantum states far from the energy eigenstates of any local Hamiltonian
What quantum states are possible energy eigenstates of a many-body
Hamiltonian? Suppose the Hamiltonian is non-trivial, i.e., not a multiple of
the identity, and L-local, in the sense of containing interaction terms
involving at most L bodies, for some fixed L. We construct quantum states \psi
which are ``far away'' from all the eigenstates E of any non-trivial L-local
Hamiltonian, in the sense that |\psi-E| is greater than some constant lower
bound, independent of the form of the Hamiltonian.Comment: 4 page
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