318 research outputs found
The influence of droplet size on line tension
Within the effective interfacial Hamiltonian approach we evaluate the excess
line free energy associated with cylinder-shaped droplets sessile on a
stripe-like chemical inhomogeneity of a planar substrate. In the case of
short-range intermolecular forces the droplet morphology and the corresponding
expression for the line tension - which includes the inhomogeneity finite width
effects - are derived and discussed as functions of temperature and increasing
width. The width-dependent contributions to the line tension change their
structure at the stripe wetting temperature T_W1: for T<T_W1 they decay
exponentially while for T>T_W1 the decay is algebraic. In addition, a geometric
construction of the corresponding contact angle is carried out and its
implications are discussed
Bogoliubov correction to the mean-field dynamics of interacting bosons
We consider the dynamics of a large quantum system of identical bosons in
3D interacting via a two-body potential of the form . For fixed and large , we obtain a norm
approximation to the many-body evolution in the -particle Hilbert space. The
leading order behaviour of the dynamics is determined by Hartree theory while
the second order is given by Bogoliubov theory.Comment: Final version, to appear in ATM
Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls
We analyze the lateral critical Casimir force acting between two planar,
chemically inhomogeneous walls confining an infinite 2D Ising strip of width
. The inhomogeneity of each of the walls has size ; they are shifted by
the distance along the strip. Using the exact diagonalization of the
transfer matrix, we calculate the lateral critical Casimir force and discuss
its properties, in particular its scaling close to the 2D bulk critical point,
as a function of temperature, surface magnetic field, and the geometric
parameters , , . We determine the magnetization profiles which
display the formation of the bridge joining the inhomogeneities on the walls
and establish the relation between the characteristic properties of the lateral
Casimir force and magnetization morphologies. We check numerically that
breaking of the bridge is related to the inflection point of the lateral force.Comment: 5 pages, 6 figure
Lateral critical Casimir force in two-dimensional inhomogeneous Ising strip. Exact results
We consider two-dimensional Ising strip bounded by two planar, inhomogeneous
walls. The inhomogeneity of each wall is modeled by a magnetic field acting on
surface spins. It is equal to except for a group of sites where it
is equal to . The inhomogeneities of the upper and lower wall are shifted
with respect to each other by a lateral distance . Using exact
diagonalization of the transfer matrix, we study both the lateral and normal
critical Casimir forces as well as magnetization profiles for a wide range of
temperatures and system parameters. The lateral critical Casimir force tends to
reduce the shift between the inhomogeneities, and the excess normal force is
attractive. Upon increasing the shift we observe, depending on the
temperature, three different scenarios of breaking of the capillary bridge of
negative magnetization connecting the inhomogeneities of the walls across the
strip. As long as there exists a capillary bridge in the system, the magnitude
of the excess total critical Casimir force is almost constant, with its
direction depending on . By investigating the bridge morphologies we have
found a relation between the point at which the bridge breaks and the
inflection point of the force. We provide a simple argument that some of the
properties reported here should also hold for a whole range of different models
of the strip with the same type of inhomogeneity
Formation of capillary bridges in AFM-like geometry
We discuss the phase diagram of fluid confined in AFM-like geometry. It
combines the properties of capillary condensation and complete filling of a
wedge.Comment: 9 pages, 7 figure
Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation
Following an earlier calculation in 3D, we calculate the 2D critical
temperature of a dilute, translation-invariant Bose gas using a variational
formulation of the Bogoliubov approximation introduced by Critchley and Solomon
in 1976. This provides the first analytical calculation of the
Kosterlitz-Thouless transition temperature that includes the constant in the
logarithm.Comment: Published version, 7 pages, 2 figure
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
We provide general conditions for which bosonic quadratic Hamiltonians on
Fock spaces can be diagonalized by Bogoliubov transformations. Our results
cover the case when quantum systems have infinite degrees of freedom and the
associated one-body kinetic and paring operators are unbounded. Our sufficient
conditions are optimal in the sense that they become necessary when the
relevant one-body operators commute.Comment: Revised version to appear in Journal of Functional Analysi
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