Rough interfaces, accurate predictions: The necessity of capillary modes in a minimal model of nanoscale hydrophobic solvation

Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing in particular the importance of interfaces that emerge in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of such nanoscale interfaces requires careful attention to the statistics of capillary waves, with significant quantitative implications for the calculation of solvation thermodynamics. Here we show that a coarse-grained lattice model in the spirit of those pioneered by Chandler and coworkers, when informed by this understanding, can capture a broad range of hydrophobic behaviors with striking accuracy. Specifically, we calculate probability distributions for microscopic density fluctuations that agree very well with results of atomistic simulations, even many standard deviations from the mean, and even for probe volumes in highly heterogeneous environments. This accuracy is achieved without adjustment of free parameters, as the model is fully specified by well-known properties of liquid water. As illustrative examples of its utility, we characterize the free energy profile for a solute crossing the air-water interface, and compute the thermodynamic cost of evacuating the space between extended nanoscale surfaces. Together, these calculations suggest that a highly reduced model for aqueous solvation can serve as the basis for efficient multiscale modeling of spatial organization driven by hydrophobic and interfacial forces.Comment: 14 pages, 7 figure

Ansatz of Hans Bethe for a two-dimensional Bose gas

The method of q-oscillator lattices, proposed recently in [hep-th/0509181], provides the tool for a construction of various integrable models of quantum mechanics in 2+1 dimensional space-time. In contrast to any one dimensional quantum chain, its two dimensional generalizations -- quantum lattices -- admit different geometrical structures. In this paper we consider the q-oscillator model on a special lattice. The model may be interpreted as a two-dimensional Bose gas. The most remarkable feature of the model is that it allows the coordinate Bethe Ansatz: the p-particles' wave function is the sum of plane waves. Consistency conditions is the set of 2p equations for p one-particle wave vectors. These "Bethe Ansatz" equations are the main result of this paper.Comment: LaTex2e, 12 page

Lattice Gas Automata for Reactive Systems

Reactive lattice gas automata provide a microscopic approachto the dynamics of spatially-distributed reacting systems. After introducing the subject within the wider framework of lattice gas automata (LGA) as a microscopic approach to the phenomenology of macroscopic systems, we describe the reactive LGA in terms of a simple physical picture to show how an automaton can be constructed to capture the essentials of a reactive molecular dynamics scheme. The statistical mechanical theory of the automaton is then developed for diffusive transport and for reactive processes, and a general algorithm is presented for reactive LGA. The method is illustrated by considering applications to bistable and excitable media, oscillatory behavior in reactive systems, chemical chaos and pattern formation triggered by Turing bifurcations. The reactive lattice gas scheme is contrasted with related cellular automaton methods and the paper concludes with a discussion of future perspectives.Comment: to appear in PHYSICS REPORTS, 81 revtex pages; uuencoded gziped postscript file; figures available from [email protected] or [email protected]

The cold atom Hubbard toolbox

We review recent theoretical advances in cold atom physics concentrating on strongly correlated cold atoms in optical lattices. We discuss recently developed quantum optical tools for manipulating atoms and show how they can be used to realize a wide range of many body Hamiltonians. Then we describe connections and differences to condensed matter physics and present applications in the fields of quantum computing and quantum simulations. Finally we explain how defects and atomic quantum dots can be introduced in a controlled way in optical lattice systems.Comment: Review article, 31 pages, 14 figures, to be published in Annals of Physic

Quantum algorithm for Bose-Einstein condensate quantum fluid dynamics

The dynamics of vortex solitons in a BEC superfluid is studied. A quantum lattice-gas algorithm (localization-based quantum computation) is employed to examine the dynamical behavior of vortex soliton solutions of the Gross-Pitaevskii equation (phi^4 interaction nonlinear Schroedinger equation). Quantum turbulence is studied in large grid numerical simulations: Kolmogorov spectrum associated with a Richardson energy cascade occurs on large flow scales. At intermediate scales a k^{-6} power law emerges, in a classical-quantum transition from vortex filament reconnections to Kelvin wave-acoustic wave coupling. The spontaneous exchange of intermediate vortex rings is observed. Finally, at very small spatial scales a k^{-3} power law emerges, characterizing fluid dynamics occurring within the scale size of the vortex cores themselves, a characteristic Kelvin wave cascade region. Poincare recurrence is studied: in the free non-interacting system, a fast Poincare recurrence occurs for regular arrays of line vortices. The recurrence period is used to demarcate dynamics driving the nonlinear quantum fluid towards turbulence, since fast recurrence is an approximate symmetry of the nonlinear quantum fluid at early times. This class of quantum algorithms is useful for studying BEC superfluid dynamics over a broad range of wave numbers, from quantum flow to a pseudo-classical inviscid flow regime to a Kolmogorov inertial subrange.Comment: 10 pages, 6 figure

Quartic Parameters for Acoustic Applications of Lattice Boltzmann Scheme

Using the Taylor expansion method, we show that it is possible to improve the lattice Boltzmann method for acoustic applications. We derive a formal expansion of the eigenvalues of the discrete approximation and fit the parameters of the scheme to enforce fourth order accuracy. The corresponding discrete equations are solved with the help of symbolic manipulation. The solutions are explicited in the case of D3Q27 lattice Boltzmann scheme. Various numerical tests support the coherence of this approach.Comment: 23 page

Topological Phases: An Expedition off Lattice

Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a fluctuating geometry can remove the separation between the system size and the range of local interactions, which is important for topological protection and ultimately the stability of a topological phase. In particular, it can open the door to a pathology, which has been studied in the context of quantum gravity and goes by the name of `baby universe', Here we discuss three distinct approaches to suppressing these pathological fluctuations. We complement this discussion by applying Cheeger's theory relating the geometry of manifolds to their vibrational modes to study the spectra of Hamiltonians. In particular, we present a detailed study of the statistical properties of loop gas and string net models on fluctuating lattices, both analytically and numerically.Comment: 38 pages, 22 figure