Liquid crystalline states for two-dimensional electrons in strong magnetic fields

Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma (2DOCP), we investigate the possibility of liquid crystalline states in a single Landau level (LL). We introduce many-body trial wavefunctions that are translationally invariant but posess 2-fold (i.e. {\em nematic}), 4-fold ({\em tetratic}) or 6-fold ({\em hexatic}) broken rotational symmetry at respective filling factors $\nu = 1/3$, 1/5 and 1/7 of the valence LL. We find that the above liquid crystalline states exhibit a soft charge density wave (CDW) which underlies the translationally invariant state but which is destroyed by quantum fluctuations. By means of Monte Carlo (MC) simulations, we determine that, for a considerable variety of interaction potentials, the anisotropic states are energetically unfavorable for the lowest and first excited LL's (with index $L = 0, 1$), whereas the nematic is favorable at the second excited LL ($L = 2$).Comment: 7 figures, submitted to PRB, high-quality figures available upon reques

Financing the Response to AIDS in Low- and Middle-Income Countries: International Assistance From Donor Governments in 2010

Presents 2010 data on international AIDS assistance from donor governments, including trends by donor country and funding channel, aid per $1 million GDP by country, and gaps between needs and resources and between commitments and disbursements

Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations

A variety of recent experiments probing the low-temperature transport properties of quantum Hall systems have suggested an interpretation in terms of liquid crystalline mesophases dubbed {\em quantum Hall liquid crystals}. The single mode approximation (SMA) has been a useful tool for the determination of the excitation spectra of various systems such as phonons in $^4$He and in the fractional quantum Hall effect. In this paper we calculate (via the SMA) the spectrum of collective excitations in a quantum Hall liquid crystal by considering {\em nematic}, {\em tetratic}, and {\em hexatic} generalizations of Laughlin's trial wave function having two-, four- and six-fold broken rotational symmetry, respectively. In the limit of zero wavevector \qq the dispersion of these modes is singular, with a gap that is dependent on the direction along which \qq=0 is approached for {\em nematic} and {\em tetratic} liquid crystalline states, but remains regular in the {\em hexatic} state, as permitted by the fourth order wavevector dependence of the (projected) oscillator strength and static structure factor.Comment: 6 pages, 5 eps figures include

Fermi hypernetted-chain study of half-filled Landau levels with broken rotational symmetry

DOI: 10.1103/PhysRevB.65.205307 http://link.aps.org/doi/10.1103/PhysRevB.65.205307We investigate broken rotational symmetry (BRS) states at half-filling of the valence Landau level (LL). We generalize Rezayi and Read's (RR) trial wave function, a special case of Jain's composite fermion (CF) wave functions, to include anisotropic coupling of the flux quanta to electrons, thus generating a nematic order in the underlying CF liquid. Using the Fermi hypernetted-chain method, which readily gives results in the thermodynamic limit, we determine the properties of these states in detail. By using the anisotropic pair distribution and static structure functions we determine the correlation energy and find that, as expected, RR's state is stable in the lowest LL, whereas BRS states may occur at half- filling of higher LL's, with a possible connection to the recently discovered quantum Hall liquid crystals

Advantages of multi-dimensional biasing in accelerated dynamics: application to the calculation of the acid pKapK_a for acetic acid

The use of accelerated sampling methods such as metadynamics has shown significant advantage in calculations that involve infrequent events, which would otherwise require sampling a prohibitive number of configurations to determine, e.g., difference in free energies between two or more chemically distinct states such as in the calculation of acid dissociation constants $K_a$. In this case, the most common method is to bias the system via a single collective variable (CV) representing the $coordination~number$ of the proton donor group, which yields results in reasonable agreement with experiments. Here we study the deprotonation of acetic acid using the reactive force field ReaxFF and observe a significant dependence of $K_a$ on the simulation box size when biasing only the coordination number CV, which is due to incomplete sampling of the deprotonated state for small simulation systems, and inefficient sampling for larger ones. Incorporating a second CV representing the distance between the H$_3$O$^+$ cation and the acetate anion results in a substantially more efficient sampling both accelerating the dynamics and virtually eliminating the computational box size dependence.Comment: 22 pages, 9 figure

Universality away from critical points in two-dimensional phase transitions

http://arxiv.org/ftp/cond-mat/papers/0511/0511559.pdfThe p-state clock model in two dimensions is a system of discrete rotors with a quasi-liquid phase in a region T1 4. We show that, for p > 4 and above a temperature Teu, all macroscopic thermal averages, such as energy or magnetization, become identical to those of the continuous rotor (p = \infty). This collapse of thermodynamic observables creates a regime of extended universality in the phase diagram and an emergent symmetry, not present in the Hamiltonian. For p \ge 8, the collapse starts in the quasi-liquid phase and makes the transition at T2 identical to the Berezinskii-Kosterlitz-Thouless (BKT) transition of the con-tinuous rotor. For p \le 6, the transition at T2 is below Teu and no longer BKT. The results generate a comprehensive map of the critical properties at T1 and T2, and a range of experimental predictions, such as motion of magnetic domain walls, fabrication of identical devices from different building blocks, and limits on macro-scopic distinguishability of different microscopic interactions.Acknowledgment is made to the University of Missouri Research Board and Council, the Donors of the Petroleum Research Fund, administered by the American Chemical Society, and the National Science Foundation (Grant No. EEC-0438469), for support of this research

Monte Carlo simulation method for Laughlin-like states in a disk geometry

We discuss an alternative accurate Monte Carlo method to calculate the ground-state energy and related quantities for Laughlin states of the fractional quantum Hall effect in a disk geometry. This alternative approach allows us to obtain accurate bulk regime (thermodynamic limit) values for various quantities from Monte Carlo simulations with a small number of particles (much smaller than that needed with standard Monte Carlo approaches).Comment: 13 pages, 6 figures, 2 table

Cross-over mechanism of the melting transition in monolayers of alkanes adsorbed on graphite and the universality of energy scaling

http://arxiv.org/ftp/arxiv/papers/0902/0902.4422.pdfThe interplay between the torsional potential energy and the scaling of the 1-4 van der Waals and Coulomb interactions determines the stiffness of flexible molecules. In molecular simulations often ad-hoc values for the scaling factor (SF) are adopted without adequate justification. In this letter we demonstrate for the first time that the precise value of the SF has direct consequences on the critical properties and mechanisms of systems undergoing a phase transition. By analyzing the melting of n-alkanes (hexane C6, dodecane C12, tetracosane C24) on graphite, we show that the SF is not a universal feature, that it monotonically decreases with the molecular length, and that it drives a cross-over between two distinct mechanisms for melting in such systems.Acknowledgment is made to the donors of The American Chemical Society Petroleum Research Fund (PRF43277-B5) for the support of this research. This material is based upon work supported in part by the Department of Energy under award number DE-FG02-07ER46411. Computational resources were provided by the University of Missouri Bioinformatics Consortium