Simulation and theory of hybrid aligned liquid crystal films

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.

Dynamic transitions in a two dimensional associating lattice gas model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical lambda-line. The high density liquid phase and the fluid phases are separated by a second critical tau-line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong transition when the critical lambda-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the critical tau-line is crossed by decreasing the temperature at a constant chemical potential.

Signature of mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Criticality of colloids with distinct interaction patches: The limits of linear chains, hyperbranched polymers, and dimers

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA)not equal 0, epsilon(AB)=epsilon(BB)=0), hyperbranched polymers (epsilon(AB)not equal 0, epsilon(AA)=epsilon(BB)=0), and dimers (epsilon(BB)not equal 0, epsilon(AA)=epsilon(AB)=0). These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when epsilon(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

Edge excitations and topological order in rotating Bose gas

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.

Edge excitations and topological order in rotating Bose gas

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.

Physik der Elektronen in Nanostrukturen und niedrigdimensionalen Systemen - Studie zweier Beispiele

Als Beispiele für die vielfältigen Phänomene der Physik der Elektronen in niedrigdimensionalen Systemen wurden in dieser Arbeit das Cu(110)(2x1)O-Adsorbatsystem und die violette Li0.9Mo6O17-Bronze untersucht. Das Adsorbatsystem bildet selbstorganisierte quasi-eindimensionale Nanostrukturen auf einer Kupferoberfläche. Die Li-Bronze ist ein Material, das aufgrund seiner Kristallstruktur quasi-eindimensionale elektronische Eigenschaften im Volumen aufweist. Auf der Cu(110)(2x1)O-Oberfläche kann durch Variation der Sauerstoffbedeckung die Größe der streifenartigen CuO-Domänen geändert werden und damit der Übergang von zwei Dimensionen auf eine Dimension untersucht werden. Der Einfluss der Dimensionalität wurde anhand eines unbesetzten elektronischen Oberflächenzustandes studiert. Dessen Energieposition (untere Bandkante) verschiebt mit zunehmender Einschränkung (schmalere CuO-Streifen) zu größeren Energien hin. Dies ist ein bekannter quantenmechanischer Effekt und relativ gut verstanden. Zusätzlich wurde die Lebensdauer des Zustandes auf der voll bedeckten Oberfläche (zwei Dimensionen) ermittelt und deren Veränderung mit der Breite der CuO-Streifen untersucht. Es zeigt sich, dass die Lebensdauer auf schmaleren CuO-Streifen drastisch abnimmt. Dieses Ergebnis ist neu. Es kann im Rahmen eines Fabry-Perot-Modells als Streuung in Zustände außerhalb der CuO-Streifen verstanden werden. Außer den gerade beschriebenen Effekten war es möglich die Ladungsdichte des diskutierten Zustandes orts- und energieabhängig auf den CuO-Streifen zu studieren. Die Li0.9Mo6O17-Bronze wurde im Hinblick auf das Verhalten der elektronischen Zustandsdichte an der Fermikante untersucht. Diese Fragestellung ist besonders wegen der Quasieindimensionalität des Materials interessant. Die Messungen von STS-Spektren in der Nähe der Fermienergie zeigen, dass die Elektronen in der Li0.9Mo6O17-Bronze eine sogenannte Luttingerflüssigkeit ausbilden, die anstatt einer Fermiflüssigkeit in eindimensionalen elektronischen Systemen erwartet wird. Bisher wurde Luttingerflüssigkeitsverhalten erst bei wenigen Materialien und Systemen experimentell nachgewiesen, obschon die theoretischen Voraussagen mehr als 30 Jahre zurückliegen. Ein Charakteristikum einer Luttingerflüssigkeit ist die Abnahme der Zustandsdichte an der Fermienergie mit einem Potenzgesetz. Dieses Verhalten wurde in STS-Spektren dieser Arbeit beobachtet und quantitativ im Rahmen eines Luttingerflüssigkeitsmodells beschrieben. Auch die Temperaturabhängigkeit des Phänomens im Bereich von 5K bis 55K ist konsistent mit der Beschreibung durch eine Luttingerflüssigkeit. Generell zeigen die Untersuchungen dieser Arbeit, dass die Dimensionalität, insbesondere deren Einschränkung, einen deutlichen Einfluss auf die elektronischen Eigenschaften von Systemen und Materialien haben kann.

Atomistic-continuum modeling of ultrafast laser-induced melting of silicon targets

In this work, we present an atomistic-continuum model for simulations of ultrafast laser-induced melting processes in semiconductors on the example of silicon. The kinetics of transient non-equilibrium phase transition mechanisms is addressed with MD method on the atomic level, whereas the laser light absorption, strong generated electron-phonon nonequilibrium, fast heat conduction, and photo-excited free carrier diffusion are accounted for with a continuum TTM-like model (called nTTM). First, we independently consider the applications of nTTM and MD for the description of silicon, and then construct the combined MD-nTTM model. Its development and thorough testing is followed by a comprehensive computational study of fast nonequilibrium processes induced in silicon by an ultrashort laser irradiation. The new model allowed to investigate the effect of laser-induced pressure and temperature of the lattice on the melting kinetics. Two competing melting mechanisms, heterogeneous and homogeneous, were identified in our big-scale simulations. Apart from the classical heterogeneous melting mechanism, the nucleation of the liquid phase homogeneously inside the material significantly contributes to the melting process. The simulations showed, that due to the open diamond structure of the crystal, the laser-generated internal compressive stresses reduce the crystal stability against the homogeneous melting. Consequently, the latter can take a massive character within several picoseconds upon the laser heating. Due to the large negative volume of melting of silicon, the material contracts upon the phase transition, relaxes the compressive stresses, and the subsequent melting proceeds heterogeneously until the excess of thermal energy is consumed. A series of simulations for a range of absorbed fluences allowed us to find the threshold fluence value at which homogeneous liquid nucleation starts contributing to the classical heterogeneous propagation of the solid-liquid interface. A series of simulations for a range of the material thicknesses showed that the sample width we chosen in our simulations (800 nm) corresponds to a thick sample. Additionally, in order to support the main conclusions, the results were verified for a different interatomic potential. Possible improvements of the model to account for nonthermal effects are discussed and certain restrictions on the suitable interatomic potentials are found. As a first step towards the inclusion of these effects into MD-nTTM, we performed nanometer-scale MD simulations with a new interatomic potential, designed to reproduce ab initio calculations at the laser-induced electronic temperature of 18946 K. The simulations demonstrated that, similarly to thermal melting, nonthermal phase transition occurs through nucleation. A series of simulations showed that higher (lower) initial pressure reinforces (hinders) the creation and the growth of nonthermal liquid nuclei. For the example of Si, the laser melting kinetics of semiconductors was found to be noticeably different from that of metals with a face-centered cubic crystal structure. The results of this study, therefore, have important implications for interpretation of experimental data on the kinetics of melting process of semiconductors.

LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS

An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga-Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density-density correlation due to umklapp scattering in lattice models.

Strukturfaktoren, Modenkopplungsgleichungen und Glasübergang molekularer Kristalle

In dieser Arbeit wird der Orientierungsglasübergang ungeordneter, molekularer Kristalle untersucht. Die theoretische Behandlung ist durch die Anisotropie der Einteilchen-Verteilungsfunktion und der Paarfunktionen erschwert. Nimmt man ein starres Gitter, wird der reziproke Raum im Gegenzug auf die 1. Brillouin-Zone eingeschränkt. Der Orientierungsglasübergang wird im Rahmen der Modenkopplungsgleichungen studiert, die dazu hergeleitet werden. Als Modell dienen harte Rotationsellipsoide auf einem starren sc Gitter. Zur Berechnung der statischen tensoriellen Strukturfaktoren wird die Ornstein-Zernike(OZ)-Gleichung molekularer Kristalle abgeleitet und selbstkonsistent zusammen mit der von molekularen Flüssigkeiten übernommenen Percus-Yevick(PY)-Näherung gelöst. Parallel dazu werden die Strukturfaktoren durch MC-Simulationen ermittelt. Die OZ-Gleichung molekularer Kristalle ähnelt der von Flüssigkeiten, direkte und totale Korrelationsfunktion kommen jedoch wegen des starren Gitters nur ohne Konstantanteile in den Winkelvariablen vor, im Gegensatz zur PY-Näherung. Die Anisotropie bringt außerdem einen nichttrivialen Zusatzfaktor. OZ/PY-Strukturfaktoren und MC-Ergebnisse stimmen gut überein. Bei den Matrixelementen der Dichte-Dichte-Korrelationsfunktion gibt es drei Hauptverläufe: oszillatorisch, monoton und unregelmäßig abfallend. Oszillationen gehören zu alternierenden Dichtefluktuationen, führen zu Maxima der Strukturfaktoren am Zonenrand und kommen bei oblaten und genügend breiten prolaten, schwächer auch bei dünnen, nicht zu langen prolaten Ellipsoiden vor. Der exponentielle monotone Abfall kommt bei allen Ellipsoiden vor und führt zu Maxima der Strukturfaktoren in der Zonenmitte, was die Tendenz zu nematischer Ordnung zeigt. Die OZ/PY-Theorie ist durch divergierende Maxima der Strukturfaktoren begrenzt. Bei den Modenkopplungsgleichungen molekularer Kristalle zeigt sich eine große Ähnlichkeit mit denen molekularer Flüssigkeiten, jedoch spielen auf einem starrem Gitter nur die Matrixelemente mit l,l' > 0 eine Rolle und es finden Umklapps von reziproken Vektoren statt. Die Anisotropie bringt auch hier nichtkonstante Zusatzfaktoren ins Spiel. Bis auf flache oblate Ellipsoide wird die Modenkopplungs-Glaslinie von der Divergenz der Strukturfaktoren bestimmt. Für sehr lange Ellipsoide müssen die Strukturfaktoren zur Divergenz hin extrapoliert werden. Daher treibt nicht der Orientierungskäfigeffekt den Glasübergang, sondern Fluktuationen an einer Phasengrenze. Nahe der Kugelform ist keine zuverlässige Glasline festlegbar. Die eingefrorenen kritischen Dichte-Dichte-Korrelatoren haben nur in wenigen Fällen die Oszillationen der statischen Korrelatoren. Der monotone Abfall bleibt dagegen für lange Zeiten meist erhalten. Folglich haben die kritischen Modenkopplungs-Nichtergodizitätsparameter abgeschwächte Maxima in der Zonenmitte, während die Maxima am Zonenrand meist verschwunden sind. Die normierten Nichtergodizitätsparameter zeigen eine Fülle von Verläufen, besonders tiefer im Glas.

New physics of metals: fermi surfaces without Fermi liquids.

I relate the historic successes, and present difficulties, of the renormalized quasiparticle theory of metals ("AGD" or Fermi liquid theory). I then describe the best-understood example of a non-Fermi liquid, the normal metallic state of the cuprate superconductors.

Many-body approach to the BCS-BEC crossover for an imbalanced ultra-cold Fermi gas

The aim of this thesis is the study of the normal phase of a mass imbalanced and polarized ultra-cold Fermi gas in the context of the BCS-BEC crossover, using a diagrammatic approach known as t-matrix approximation. More specifically, the calculations are implemented using the fully self-consistent t-matrix (or Luttinger- Ward) approach, which is already experimentally and numerically validated for the balanced case. An imbalance (polarization) between the two spin populations works against pairing and superfluidity. For sufficiently large polarization (and not too strong attraction) the system remains in the normal phase even at zero temperature. This phase is expected to be well described by the Landau’s Fermi liquid theory. By reducing the spin polarization, a critical imbalance is reached where a quantum phase transition towards a superfluid phase occurs and the Fermi liquid description breaks down. Depending on the strength of the interaction, the exotic superfluid phase at the quantum critical point (QCP) can be either a FFLO phase (Fulde-Ferrell-Larkin-Ovchinnikov) or a Sarma phase. In this regard, the presence of mass imbalance can strongly influence the nature of the QCP, by favouring one of these two exotic types of pairing over the other, depending on whether the majority of the two species is heavier or lighter than the minority. The analysis of the system is made by focusing on the temperature-coupling-polarization phase diagram for different mass ratios of the two components and on the study of different thermodynamic quantities at finite temperature. The evolution towards a non-Fermi liquid behavior at the QCP is investigated by calculating the fermionic quasi-particle residues, the effective masses and the self-energies at zero temperature.

Theory of small-signal ac response of a dielectric liquid containing two groups of ions

The analysis of Macdonald for electrolytes is generalized to the case in which two groups of ions are present. We assume that the electrolyte can be considered as a dispersion of ions in a dielectric liquid, and that the ionic recombination can be neglected. We present the differential equations governing the ionic redistribution when the liquid is subjected to an external electric field, describing the simultaneous diffusion of the two groups of ions in the presence of their own space charge fields. We investigate the influence of the ions on the impedance spectroscopy of an electrolytic cell. In the analysis, we assume that each group of ions have equal mobility, the electrodes perfectly block and that the adsorption phenomena can be neglected. In this framework, it is shown that the real part of the electrical impedance of the cell has a frequency dependence presenting two plateaux, related to a type of ambipolar and free diffusion coefficients. The importance of the considered problem on the ionic characterization performed by means of the impedance spectroscopy technique was discussed. (c) 2008 American Institute of Physics.