Complex Condensed Matter Systems Research Articles

Two-Dimensional Short-Range Disordered Crystalline Networks from Flexible Molecular Modules

Studies of complex condensed matter systems have led to the discovery of materials of unexpected spatial organization as glasses, glassy crystals, quasicrystals, and protein and virus crystals. Here, we present two-dimensional (2D) short-range disordered molecular crystalline networks, which, regarding spatial organization, can be considered as surface analogues of 3D glassy crystals. In particular, the deposition of a flexible molecular module on Cu(111) gives rise to distinct phases whose characteristics have been examined in real space by scanning tunneling microscopy: a 2D short-range distortional disordered crystalline network and a 2D short-range orientational disordered crystalline network, respectively. Both phases exhibit a random arrangement of nanopores that are stabilized by the simultaneous presence of metal-organic and pyridyl-pyridyl interactions. The 2D short-range distortional disordered crystalline network displayed intriguing flexibility, as probed by the STM tip that modifies the pore shape, a prerequisite for adaptive behavior in host-guest processes.

Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices

Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-T$_c$ superconductivity and unconventional magnetism. In contrast, phenomena in superfluids -- especially in ultracold quantum gases -- are commonly well described by the lowest orbital and a real order parameter. Here, we report on the observation of a novel multi-orbital superfluid phase with a {\it complex} order parameter in binary spin mixtures. In this unconventional superfluid, the local phase angle of the complex order parameter is continuously twisted between neighboring lattice sites. The nature of this twisted superfluid quantum phase is an interaction-induced admixture of the p-orbital favored by the graphene-like band structure of the hexagonal optical lattice used in the experiment. We observe a second-order quantum phase transition between the normal superfluid (NSF) and the twisted superfluid phase (TSF) which is accompanied by a symmetry breaking in momentum space. The experimental results are consistent with calculated phase diagrams and reveal fundamentally new aspects of orbital superfluidity in quantum gas mixtures. Our studies might bridge the gap between conventional superfluidity and complex phenomena of orbital physics.

Directionally negative friction: A method for enhanced sampling of rare event kinetics

A method exploiting the properties of an artificial (nonphysical) Langevin dynamics with a negative frictional coefficient along a suitable manifold and positive friction in the perpendicular directions is presented for the enhanced calculation of time-correlation functions for rare event problems. Exact time-correlation functions that describe the kinetics of the transitions for the all-positive, physical system can be calculated by reweighting the generated trajectories according to stochastic path integral treatment involving a functional weight based on an Onsager-Machlup action functional. The method is tested on a prototypical multidimensional model system featuring the main elements of conformational space characteristic of complex condensed matter systems. Using the present method, accurate estimates of rate constants require at least three order of magnitudes fewer trajectories than regular Langevin dynamics. The method is particularly useful in calculating kinetic properties in the context of multidimensional energy landscapes that are characteristic of complex systems such as proteins and nucleic acids.

Monte Carlo study of the two-dimensional Bose-Hubbard model

One of the most promising applications of ultracold gases in optical lattices is the possibility to use them as quantum emulators of more complex condensed matter systems. We provide benchmark calculations, based on exact quantum Monte Carlo simulations, for the emulator to be tested against. We report results for the ground state phase diagram of the two-dimensional Bose-Hubbard model at unity filling factor. We precisely trace out the critical behavior of the system and resolve the region of small insulating gaps, $\ensuremath{\Delta}⪡J$. The critical point is found to be ${(J/U)}_{c}=0.05974(3)$, in perfect agreement with the high-order strong-coupling expansion method of Elstner and Monien [Phys. Rev. B 59, 12184 (1999)]. In addition, we present data for the effective mass of particle and hole excitations inside the insulating phase and obtain the critical temperature for the superfluid-normal transition at unity filling factor.

Large-scale grid-enabled lattice Boltzmann simulations of complex fluid flow in porous media and under shear.

Well-designed lattice Boltzmann codes exploit the essentially embarrassingly parallel features of the algorithm and so can be run with considerable efficiency on modern supercomputers. Such scalable codes permit us to simulate the behaviour of increasingly large quantities of complex condensed matter systems. In the present paper, we present some preliminary results on the large-scale three-dimensional lattice Boltzmann simulation of binary immiscible fluid flows through a porous medium, derived from digitized X-ray micro-tomographic data of Bentheimer sandstone, and from the study of the same fluids under shear. Simulations on such scales can benefit considerably from the use of computational steering, and we describe our implementation of steering within the lattice Boltzmann code, called LB3D, making use of the RealityGrid steering library. Our large-scale simulations benefit from the new concept of capability computing, designed to prioritize the execution of big jobs on major supercomputing resources. The advent of persistent computational grids promises to provide an optimal environment in which to deploy these mesoscale simulation methods, which can exploit the distributed nature of computer, visualization and storage resources to reach scientific results rapidly; we discuss our work on the grid-enablement of lattice Boltzmann methods in this context.

Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems.

A method is presented that can find the global minimum of very complex condensed matter systems. It is based on the simple principle of exploring the configurational space as fast as possible and of avoiding revisiting known parts of this space. Even though it is not a genetic algorithm, it is not based on thermodynamics. The efficiency of the method depends strongly on the type of moves that are used to hop into new local minima. Moves that find low-barrier escape-paths out of the present minimum generally lead into low energy minima.

Origin of stretched exponential relaxation for hopping-transport models.

We propose a novel geometric approach to the description of the relaxation phenomena in complex condensed-matter systems. It is shown within a fairly general random site hopping model that the stretched exponential decay law, exp([-(t/tau)(beta)], originates from the simple and general geometric features of a random distribution of transport and trapping sites in the 3D space. The value of the variable stretching index beta is determined by the localization radius of hopping electrons. The possibilities for generalization of the obtained results and interpretation of the relevant experimental data are discussed.

The decay of OSL signals as stretched-exponential functions

Optically stimulated luminescence (OSL) and pulsed OSL have been utilized broadly for luminescence dosimetry as well as archaelogical and geological dating. It has been pointed out that in many cases, the decay of the OSL during continuous stimulating light (cw-OSL) and that of pulsed OSL following a pulse of stimulating light, do not generally behave according to a simple exponential function. In the present work, it is shown by the use of numerical simulation, that with the simplest model of a single trapping state and a single kind of recombination center, a decay curve significantly slower than a “normal” exponential can emerge. These results could be fitted to a stretched-exponential law, exp[−( t/ τ) β ] with 0< β<1 with surprisingly good agreement for the decay of OSL following a stimulating light pulse. As for the decay of OSL during the exposure to stimulating light, a typical behavior found in the simulation is an initial nearly exponential decay, followed by stretched-exponential decay at longer times. In particular, the cases where β is significantly smaller than unity (e.g., β∼0.5) are of interest. It is to be pointed out that several relaxation phenomena in complex condensed-matter systems have been found to follow the mentioned stretched-exponential decay law. This includes some reports in the literature of stretched-exponential decay of luminescence, usually in the very short time range. It has been suggested, however, that this behavior is always associated with some kind of disorder in the sample, e.g. the disorder occurring in porous silicon. The main new points in the present work are that this kind of relaxation can be expected to occur in the two kinds of OSL mentioned above and that they result from a single crystal with only one trapping state and one kind of recombination center. The concept of half-life of the decay in these cases is considered in view of the present results.

Application of the Wolf method for the evaluation of Coulombic interactions to complex condensed matter systems: Aluminosilicates and water

The application of the method recently proposed by Wolf et al. [J. Chem. Phys. 110, 8254 (1999)] for the evaluation of Coulombic energy in condensed state systems by spherically truncated, pairwise r−1 summation is verified for liquid water and anhydrous and hydrated aluminosilicates. Criteria for the estimation of the optimum values for the truncation radius and the damping parameter are discussed. By several examples it is verified that the new method is computationally more efficient than the traditional Ewald summations. For the considered systems the performances of the new method are good, provided that the truncation radius and the damping parameter are carefully chosen.

Low-temperature quasi-classical approximation for quantum macroscopic phenomena

Quantum systems with two distinct time scales for “fast” (quantum) and “slow” (quasi-classical) degrees of freedom with the respective frequencies Ω and ω≪Ω are considered. A general path-integral representation for a partition function involves ordinary coherent states for Bose and Fermi degrees of freedom as well as generalized coherent states for a nontrivial algebra of variables. Path-integral averaging over “fast” variables results in a nonlocal (in imaginary time) effective action for a “slow” (quasi-classical) variable, which becomes local in the low-temperature approximation. This low-temperature adiabatic path-integral approach, expressed by the inequality βΩ≫1≫ω/Ω, yields an appropriate basis for a subsequent quasi-classical description. Theories of three complex condensed matter systems are developed with the “slow” and “fast” subsystems represented by localized and band electrons in the lattice Anderson model, by condensate and noncondensate bosons in the Bogoliubov model (with broken translational symmetry), and by soft-mode phonons and electrons induced in large molecules by an electron-phonon optical transition. The corresponding quantum macroscopic phenomena are the Kondo-type reorganization of the spectrum of correlated electrons, Bose condensation in nonuniform media, and chaotization of the phonon spectrum in molecules.