169 research outputs found
Field theoretic description of charge regulation interaction
In order to find the exact form of the electrostatic interaction between two
proteins with dissociable charge groups in aqueous solution, we have studied a
model system composed of two macroscopic surfaces with charge dissociation
sites immersed in a counterion-only ionic solution. Field-theoretic
representation of the grand canonical partition function is derived and
evaluated within the mean-field approximation, giving the Poisson-Boltzmann
theory with the Ninham-Parsegian boundary condition. Gaussian fluctuations
around the mean-field are then analyzed in the lowest order correction that we
calculate analytically and exactly, using the path integral representation for
the partition function of a harmonic oscillator with time-dependent frequency.
The first order (one loop) free energy correction gives the interaction free
energy that reduces to the zero-frequency van der Waals form in the appropriate
limit but in general gives rise to a mono-polar fluctuation term due to charge
fluctuation at the dissociation sites. Our formulation opens up the possibility
to investigate the Kirkwood-Shumaker interaction in more general contexts where
their original derivation fails.Comment: 12 pages, 9 figures, submitted to EPJ
The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles
In this paper, we consider decoherence in continuous-time quantum walks on
long-range interacting cycles (LRICs), which are the extensions of the cycle
graphs. For this purpose, we use Gurvitz's model and assume that every node is
monitored by the corresponding point contact induced the decoherence process.
Then, we focus on large rates of decoherence and calculate the probability
distribution analytically and obtain the lower and upper bounds of the mixing
time. Our results prove that the mixing time is proportional to the rate of
decoherence and the inverse of the distance parameter (\emph{m}) squared.
This shows that the mixing time decreases with increasing the range of
interaction. Also, what we obtain for \emph{m}=0 is in agreement with
Fedichkin, Solenov and Tamon's results \cite{FST} for cycle, and see that the
mixing time of CTQWs on cycle improves with adding interacting edges.Comment: 16 Pages, 2 Figure
Semiclassical Casimir Energies at Finite Temperature
We study the dependence on the temperature T of Casimir effects for a range
of systems, and in particular for a pair of ideal parallel conducting plates,
separated by a vacuum. We study the Helmholtz free energy, combining
Matsubara's formalism, in which the temperature appears as a periodic Euclidean
fourth dimension of circumference 1/T, with the semiclassical periodic orbital
approximation of Gutzwiller. By inspecting the known results for the Casimir
energy at T=0 for a rectangular parallelepiped, one is led to guess at the
expression for the free energy of two ideal parallel conductors without
performing any calculation. The result is a new form for the free energy in
terms of the lengths of periodic classical paths on a two-dimensional cylinder
section. This expression for the free energy is equivalent to others that have
been obtained in the literature. Slightly extending the domain of applicability
of Gutzwiller's semiclassical periodic orbit approach, we evaluate the free
energy at T>0 in terms of periodic classical paths in a four-dimensional cavity
that is the tensor product of the original cavity and a circle. The validity of
this approach is at present restricted to particular systems. We also discuss
the origin of the classical form of the free energy at high temperatures.Comment: 17 pages, no figures, Late
Dynamic exchange-correlation potentials for the electron gas in dimensionality D=3 and D=2
Recent progress in the formulation of a fully dynamical local approximation
to time-dependent Density Functional Theory appeals to the longitudinal and
transverse components of the exchange and correlation kernel in the linear
current-density response of the homogeneous fluid at long wavelength. Both
components are evaluated for the electron gas in dimensionality D=3 and D=2 by
an approximate decoupling in the equation of motion for the current density,
which accounts for processes of excitation of two electron-hole pairs. Each
pair is treated in the random phase approximation, but the role of exchange and
correlation is also examined; in addition, final-state exchange processes are
included phenomenologically so as to satisfy the exactly known high-frequency
behaviours of the kernel. The transverse and longitudinal spectra involve the
same decay channels and are similar in shape. A two-plasmon threshold in the
spectrum for two-pair excitations in D=3 leads to a sharp minimum in the real
part of the exchange and correlation kernel at twice the plasma frequency. In
D=2 the same mechanism leads to a broad spectral peak and to a broad minimum in
the real part of the kernel, as a consequence of the dispersion law of the
plasmon vanishing at long wavelength. The numerical results have been fitted to
simple analytic functions.Comment: 13 pages, 11 figures included. Accepted for publication in Phys. Rev.
Casimir force on amplifying bodies
Based on a unified approach to macroscopic QED that allows for the inclusion
of amplification in a limited space and frequency range, we study the Casimir
force as a Lorentz force on an arbitrary partially amplifying system of
linearly locally responding (isotropic) magnetoelectric bodies. We demonstrate
that the force on a weakly polarisable/magnetisable amplifying object in the
presence of a purely absorbing environment can be expressed as a sum over the
Casimir--Polder forces on the excited atoms inside the body. As an example, the
resonant force between a plate consisting of a dilute gas of excited atoms and
a perfect mirror is calculated
Partially Annealed Disorder and Collapse of Like-Charged Macroions
Charged systems with partially annealed charge disorder are investigated
using field-theoretic and replica methods. Charge disorder is assumed to be
confined to macroion surfaces surrounded by a cloud of mobile neutralizing
counterions in an aqueous solvent. A general formalism is developed by assuming
that the disorder is partially annealed (with purely annealed and purely
quenched disorder included as special cases), i.e., we assume in general that
the disorder undergoes a slow dynamics relative to fast-relaxing counterions
making it possible thus to study the stationary-state properties of the system
using methods similar to those available in equilibrium statistical mechanics.
By focusing on the specific case of two planar surfaces of equal mean surface
charge and disorder variance, it is shown that partial annealing of the
quenched disorder leads to renormalization of the mean surface charge density
and thus a reduction of the inter-plate repulsion on the mean-field or
weak-coupling level. In the strong-coupling limit, charge disorder induces a
long-range attraction resulting in a continuous disorder-driven collapse
transition for the two surfaces as the disorder variance exceeds a threshold
value. Disorder annealing further enhances the attraction and, in the limit of
low screening, leads to a global attractive instability in the system.Comment: 21 pages, 2 figure
Adsorption of mono- and multivalent cat- and anions on DNA molecules
Adsorption of monovalent and multivalent cat- and anions on a deoxyribose
nucleic acid (DNA) molecule from a salt solution is investigated by computer
simulation. The ions are modelled as charged hard spheres, the DNA molecule as
a point charge pattern following the double-helical phosphate strands. The
geometrical shape of the DNA molecules is modelled on different levels ranging
from a simple cylindrical shape to structured models which include the major
and minor grooves between the phosphate strands. The densities of the ions
adsorbed on the phosphate strands, in the major and in the minor grooves are
calculated. First, we find that the adsorption pattern on the DNA surface
depends strongly on its geometrical shape: counterions adsorb preferentially
along the phosphate strands for a cylindrical model shape, but in the minor
groove for a geometrically structured model. Second, we find that an addition
of monovalent salt ions results in an increase of the charge density in the
minor groove while the total charge density of ions adsorbed in the major
groove stays unchanged. The adsorbed ion densities are highly structured along
the minor groove while they are almost smeared along the major groove.
Furthermore, for a fixed amount of added salt, the major groove cationic charge
is independent on the counterion valency. For increasing salt concentration the
major groove is neutralized while the total charge adsorbed in the minor groove
is constant. DNA overcharging is detected for multivalent salt. Simulations for
a larger ion radii, which mimic the effect of the ion hydration, indicate an
increased adsorbtion of cations in the major groove.Comment: 34 pages with 14 figure
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