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

Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

Interfacial morphology and correlations in adsorption at a chemically structured substrate - exact results in d=2

Adsorption at a 1-dimensional planar substrate equipped with a localized chemical inhomogeneity is studied within the framework of a continuum interfacial model from the point of view of interfacial morphology and correlation function properties. Exact expressions for the one-point and two-point probability distribution functions $P_\Gamma (l_\Gamma)$ and $P_{\Gamma_1, \Gamma_2}(l_{\Gamma_1},l_{\Gamma_2})$, $l_\Gamma$ being the interface position above a fixed point $\Gamma$ of the substrate, are derived for temperature corresponding to the inhomogeneity's wetting transition. It is demonstrated that in the limit of macroscopic inhomogeneity's size the net effect of the remaining homogeneous parts of the substrate on the interfacial morphology above the inhomogeneity is exactly equivalent to appropriate pinning of the interface at its boundaries. The structure of the average interfacial morphology and correlation function in this limit are discussed and compared to earlier results obtained for systems with homogeneous substrate

An alternative approach to the construction of Schur-Weyl transform

We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to the system, results in a change of degrees of freedom, uncovering the information hidden in non-local degrees of freedom. This information can be used, inter alia, to study the structure of entangled states, their classification and may be useful for construction of quantum algorithms.Comment: 6 page

Quantum interface unbinding transitions

We consider interfacial phenomena accompanying bulk quantum phase transitions in presence of surface fields. On general grounds we argue that the surface contribution to the system free energy involves a line of singularities characteristic of an interfacial phase transition, occurring below the bulk transition temperature T_c down to T=0. This implies the occurrence of an interfacial quantum critical regime extending into finite temperatures and located within the portion of the phase diagram where the bulk is ordered. Even in situations, where the bulk order sets in discontinuously at T=0, the system's behavior at the boundary may be controlled by a divergent length scale if the tricritical temperature is sufficiently low. Relying on an effective interfacial model we compute the surface phase diagram in bulk spatial dimensionality $d\geq 2$ and extract the values of the exponents describing the interfacial singularities in $d\geq 3$