Abstract: The determination of the layer number ${\cal N}$ in nanoscale thin layered crystals is a challenging problem of technological relevance. In addition to innovative experimental techniques, a thorough knowledge of the underlying lattice dynamics is required. Starting from phenomenological atomic interaction potentials we have carried out an analytical study of the low-frequency optical phonon dispersions in layered crystals. At the gamma point of the two-dimensional Brillouin zone the optical phonon frequencies correspond to rigid-plane shearing and compression modes. We have investigated graphene multilayers (GML) and hexagonal boron-nitride multilayers (BNML). The frequencies show a characteristic dependence on ${\cal N}$. The results which are represented in the form of fan diagrams are very similar for both materials. Due to charge neutrality within layers Coulomb forces play no role, only van der Waals forces between nearest neighbor layers are relevant. The theoretical results agree with recent low-frequency Raman results on rigid-layer modes [Tan et al., Nature Mater. 11, 294 (2012)] in GML and double-resonant Raman scattering data on rigid-layer compression modes [Herziger et al., Phys. Rev. B 85, 235447 (2012)] in GML. (C) 2012 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim

Abstract: By means of replica exchange molecular dynamics simulations we investigate how the length of a silk-like, alternating diblock oligopeptide influences its secondary and quaternary structure. We carry out simulations for two protein sizes consisting of three and five blocks, and study the stability of a single protein, a dimer, a trimer and a tetramer. Initial configurations of our simulations are β-roll and β-sheet structures. We find that for the triblock the secondary and quaternary structures upto and including the tetramer are unstable: the proteins melt into random coil structures and the aggregates disassemble either completely or partially. We attribute this to the competition between conformational entropy of the proteins and the formation of hydrogen bonds and hydrophobic interactions between proteins. This is confirmed by our simulations on the pentablock proteins, where we find that, as the number of monomers in the aggregate increases, individual monomers form more hydrogen bonds whereas their solvent accessible surface area decreases. For the pentablock β-sheet protein, the monomer and the dimer melt as well, although for the β-roll protein only the monomer melts. For both trimers and tetramers remain stable. Apparently, for these the entropy loss of forming β-rolls and β-sheets is compensated for in the free-energy gain due to the hydrogen-bonding and hydrophobic interactions. We also find that the middle monomers in the trimers and tetramers are conformationally much more stable than the ones on the top and the bottom. Interestingly, the latter are more stable on the tetramer than on the trimer, suggesting that as the number of monomers increases protein-protein interactions cooperatively stabilize the assembly.
According to our simulations, the β-roll and β-sheet aggregates must be approximately equally
stable.

Abstract: Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function Z(N) and the Helmholtz free energy F-N as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 – F-N, as illustrated for a two-dimensional fermion gas. (C) 2017 Elsevier B.V. All rights reserved.

Abstract: It is well-known that the Ginzburg-Landau (GL) theory is a reliable and powerful theoretical tool to investigate the magnetic response of a superconducting state. However, in its standard form, this approach is not applicable to atomically uniform nano-thin superconducting films which are effective multiband superconductors. Here we discuss a relevant generalization of the GL theory, focusing on the underlying intraband-pairing approximation. (C) 2014 Elsevier B.V. All rights reserved.

Abstract: We study the coherent dynamics of pairing in a nanoscale superconductor, that is intrinsically multiband, after an external perturbation in the non-adiabatic regime. The description of the dynamics of the pairing order is within the density-matrix approach based on the BCS model and the Bogoliubov-de Gennes equations. We find that for certain resonant wire widths the superconducting order parameter exhibits two oscillatory frequencies which are determined by the long-time asymptotic values of the subgaps. This in turn leads to a pronounced beating phenomenon. (C) 2014 Elsevier B.V. All rights reserved.

Abstract: Using the nonlinear Ginzburg-Landau theory we investigated the dependence of the magnetic coupling between two concentric mesoscopic superconducting rings on their thickness. The size of this magnetic coupling increases with the thickness of the rings. (C) 2001 Elsevier Science B.V. All rights reserved.

Abstract: When a condensate is sheared by imparting a velocity to a part of the condensate, phase singularities must appear at the interface between the region that is still at rest and the region that has acquired a velocity. For helium, Feynman argued that these phase singularies will arrange themselves in the form of a vortex row. BoseEinstein condensates of ultracold atomic gases differ from helium in that the healing length is generally much larger and is, in fact, tunable. Another difference is that multicomponent condensates can be created, where the two components forming the mixture are usually two different hyperfine states of the condensed atoms. These two components can be manipulated separately and can be interconverted. In this contribution, we investigate how these additional degrees of freedom, available in quantum gases, change what happens in sheared condensates. In particular, we consider skyrmion rows as an alternative to vortex rows, and we also consider phase slip lines filled with the second, unmoving component, in a condensate mixture. We show that depending on the ratios of the interaction strengths between the components, and depending on the shear velocity, skyrmion rows and phase slip lines can become lower in energy than vortex rows, and hence should be observable in quantum gases. Moreover, we find that the velocity field affects the stability region of the condensate with respect to phase separation.

Abstract: We study the vortex profiles in two-gap superconductors using the extended Ginzburg-Landau theory. The results shed more light on the disparity between the effective length scales in two bands. We compare the behavior expected from the standard Ginzburg-Landau theory with this new approach, and find good qualitative agreement in the case of LiFeAs. (C) 2011 Elsevier B.V. All rights reserved.

Abstract: The multiband effective-mass model of cylindrical self-assembled quantum dots in a magnetic field normal to the layer of the quantum dots is presented. The strain distribution is computed by the valence force field method. The strain-dependent multiband Hamiltonian is modified into an axially symmetric form, which commutes with the total angular momentum F-2 = fh. where f denotes the total magnetic quantum number. The heavy hole and the light hole parts in the mixed hole state are resolved. It is found that the heavy hole component dominates in the ground states for both f = 1/2 and 3/2. The electronic structure exhibits numerous anticrossings between the hole levels. The Zeeman splitting between the +\f\ and -\f\ states is also computed. (C) 2002 Elsevier Science B.V. All rights reserved.

Abstract: We present an exact diagonalization study of negatively charged excitonic trions in two vertically coupled parabolic quantum dots. The electrons and the hole are confined to different dots. We obtain the energy spectra as a function of inter-dot separation and external magnetic field strength and identify different ground-state angular momentum transitions which are accompanied by abrupt charge redistributions in the dots. (C) 2003 Elsevier B.V. All rights reserved.