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

Short time evolved wave functions for solving quantum many-body problems

The exact ground state of a strongly interacting quantum many-body system can be obtained by evolving a trial state with finite overlap with the ground state to infinite imaginary time. In this work, we use a newly discovered fourth order positive factorization scheme which requires knowing both the potential and its gradients. We show that the resultaing fourth order wave function alone, without further iterations, gives an excellent description of strongly interacting quantum systems such as liquid 4He, comparable to the best variational results in the literature.Comment: 5 pages, 3 figures, 1 tabl

Hypernetted-chain study of broken rotational symmetry states for the ν\bm{\nu} = 1/3 fractional quantum Hall effect and other fractionally filled Landau levels

We investigate broken rotational symmetry (BRS) states for the fractional quantum Hall effect (FQHE) at 1/3-filling of the valence Landau level (LL). Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens.\ Matter {\bf 8}, L105 (1996)] suggest that Laughlin's state becomes unstable to a BRS state for some critical finite thickness value. We study in detail the properties of such state by performing a hypernetted-chain calculation that gives results in the thermodynamic limit, complementing other methods which are limited to a finite number of particles. Our results indicate that while Laughlin's state is stable in the lowest LL, in higher LLs a BRS instability occurs, perhaps indicating the absence of FQHE at partial fillings of higher LLs. Possible connections to the newly discovered liquid crystalline phases in higher LLs are also discussed.Comment: 7 pages including 3 eps figure

Monte Carlo study of Bose Laughlin wave function for filling factors 1/2, 1/4 and 1/6

Strongly correlated two-dimensional electronic systems subject to a perpendicular magnetic field at lowest Landau level (LLL) filling factors: 1/2, 1/4 and 1/6 are believed to be composite fermion (CF) Fermi liquid phases. Even though a Bose Laughlin wave function cannot describe these filling factors we investigate whether such a wave function provides a lower energy bound to the true CF Fermi liquid energies. By using Monte Carlo simulations in disk geometry we compute the Bose Laughlin energies and compare them to corresponding results for the spin-polarized LLL CF Fermi liquid state and avalable data from literature.We find the unexpected result that, for filling factors 1/4 and 1/6, the Bose Laughlin ground state energy is practically identical to the true CF liquid energy while this is not the case at 1/2 where the Bose Laughlin ground state energy is sizeably lower than the energy of the CF Fermi liquid state.Comment: 7 pages, 2 figures, 2 table

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

Anyon Wave Function for the Fractional Quantum Hall Effect

An anyon wave function (characterized by the statistical factor $n$) projected onto the lowest Landau level is derived for the fractional quantum Hall effect states at filling factor $\nu = n/(2pn+1)$ ($p$ and $n$ are integers). We study the properties of the anyon wave function by using detailed Monte Carlo simulations in disk geometry and show that the anyon ground-state energy is a lower bound to the composite fermion one.Comment: Reference adde

Combinatorial Identities for Incomplete Tribonacci Polynomials

The incomplete tribonacci polynomials, denoted by T_n^{(s)}(x), generalize the usual tribonacci polynomials T_n(x) and were introduced in [10], where several algebraic identities were shown. In this paper, we provide a combinatorial interpretation for T_n^{(s)}(x) in terms of weighted linear tilings involving three types of tiles. This allows one not only to supply combinatorial proofs of the identities for T_n^{(s)}(x) appearing in [10] but also to derive additional identities. In the final section, we provide a formula for the ordinary generating function of the sequence T_n^{(s)}(x) for a fixed s, which was requested in [10]. Our derivation is combinatorial in nature and makes use of an identity relating T_n^{(s)}(x) to T_n(x)

From Wires to Cables: Attempted Synthesis of 1,3,5-Trifluorenylcyclohexane as a Platform for Molecular Cables

Multiple molecular wires braided together in a single assembly, termed as molecular cable, are promising next-generation materials for effective long-range charge transport. As an example of the platform for constructing molecular cables, 1,3,5-trifluorenylcyclohexane (TFC) and its difluorenyl analogues (DFCs) were systematically investigated both experimentally (X-ray crystallography) and theoretically (DFT calculations). Although the syntheses of DFCs were successfully achieved, the synthesis of TFC, which involved a similar intramolecular Friedel–Crafts cyclization as the last step, was unsuccessful. An exhaustive study of the conformational landscape of cyclohexane ring of TFC and DFCs revealed that TFC is a moderately strained molecule (∼17 kcal/mol), and computational studies of the reaction profile show that this steric strain, present in the transition state, is responsible for the unusually high (∼5 years) reaction half-life. A successful synthesis of TFC will require that the steric strain is introduced in multiple steps, and such alternative strategies are being currently explored

Fabrication and characterization of chitosan coated and uncoated pcl/ha/ppy composite scaffoldsusing freeze drying technique

Chitosan is an abundantly common, naturally occurring, polysaccharide biopolymer. In this study, chitosan was used to coat previously fabricated conductive Polycaprolactone/Hydroxyapatite/Polypyrrole (PCL/HA/PPY) composite scaffold and the properties of the coated and non-coated scaffolds were investigated and compared. The morphology of the chitosan coated and non-coated scaffolds were characterized using a scanning electron microscope (SEM). The wettability was determined using a water contact angle measuring system. Furthermore, water uptake was determined by measuring the water absorption of each sample before and after coated with chitosan. Water contact angle result revealed an increase in wettability of the scaffolds ranging from 108° ± 4.2 down to 59.4° ± 0.7. On the other hand, the coated sample showed a higher water uptake than the non-coated sample. The results indicated that coating with chitosan was important to increase water absorption of composite scaffold, rendering it more hydrophilic

PEDOT:PSS-containing nanohydroxyapatite/chitosan conductive bionanocomposite scaffold: fabrication and evaluation

Conductive poly(3,4-ethylenedioxythiophene)-poly(4-styrene sulfonate) (PEDOT:PSS) was incorporated into nanohydroxyapatite/chitosan (nHA/CS) composite scaffolds through a freezing and lyophilization technique. The bionanocomposite conductive scaffold was then characterized using several techniques. A scanning electron microscope image showed that the nHA and PEDOT:PSS were dispersed homogeneously in the chitosan matrix, which was also confirmed by energy-dispersive X-ray (EDX) analysis. The conductive properties were measured using a digital multimeter. The weight loss and water-uptake properties of the bionanocomposite scaffolds were studied in vitro. An in vitro cell cytotoxicity test was carried out using mouse fibroblast (L929) cells cultured onto the scaffolds. Using a freezing and lyophilization technique, it was possible to fabricate three-dimensional, highly porous, and interconnected PEDOT:PSS/nHA/CS scaffolds with good handling properties. The porosity was 74% and the scaffold's conductivity was 9.72 ± 0.78 μS. The surface roughness was increased with the incorporation of nHA and PEDOT:PSS into the CS scaffold. The compressive mechanical properties increased significantly with the incorporation of nHA but did not change significantly with the incorporation of PEDOT:PSS. The PEDOT:PSS-containing nHA/CS scaffold exhibited significantly higher cell attachment. The PEDOT:PSS/nHA/CS scaffold could be a potential bionanocomposite conductive scaffold for tissue engineering