Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

Thermodynamics of TmRhO3, Phase Equilibria, and Chemical Potentials in the System Tm-Rh-O

Phase equilibria in the system Tm-Rh-O at 1200 K is established by isothermal equilibration of selected compositions and phase identification after quenching to room temperature. Six intermetallic phases (Tm3Rh, Tm7Rh3, Tm5Rh3, Tm3Rh2, TmRh, TmRh2 +/-delta) and a ternary oxide TmRhO3 are identified. Based on experimentally determined phase relations, a solid-state electrochemical cell is devised to measure the standard free energy of formation of orthorhombic perovskite TmRhO3 from cubic Tm2O3 and beta-Rh2O3 in the temperature range from (900 to 1300) K. The results can be summarized as: Delta G(f,ox)(o) +/- 104/J.mol(-1) = -46474 + 3.925(T/K). Invoking the Neumann-Kopp rule, the standard enthalpy of formation of TmRhO3 from its constituent elements at 298.15 K is estimated as -1193.89 (+/- 2.86) kJ.mol(-1). The standard entropy of TmRhO3 at 298.15 K is evaluated as 103.8 (+/- 1.6) J.mol(-1).K-1. The oxygen potential-composition diagram and three-dimensional chemical potential diagram at 1200 K and temperature-composition diagrams at constant partial pressures of oxygen are computed from thermodynamic data. The compound TmRhO3 decomposes at 1688 (+/- 2) K in pure oxygen and at 1583 (+/- 2) K in air at standard pressure.

Majorana fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials

We present a unified study of the effect of periodic, quasiperiodic, and disordered potentials on topological phases that are characterized by Majorana end modes in one-dimensional p-wave superconducting systems. We define a topological invariant derived from the equations of motion for Majorana modes and, as our first application, employ it to characterize the phase diagram for simple periodic structures. Our general result is a relation between the topological invariant and the normal state localization length. This link allows us to leverage the considerable literature on localization physics and obtain the topological phase diagrams and their salient features for quasiperiodic and disordered systems for the entire region of parameter space. DOI: 10.1103/PhysRevLett.110.146404

Fermions in synthetic non-Abelian gauge potentials: rashbon condensates to novel Hamiltonians

Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin-orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin-orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose-Einstein condensate (RBEC) is a quite intriguing state with the rashbon-rashbon interactions being independent of the fermion-fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin-orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.

Calculation of Chemical Potentials and Occupancies in Clathrate Hydrates through Monte Carlo Molecular Simulations

The flexibility of the water lattice in clathrate hydrates and guest-guest interactions has been shown in previous studies to significantly affect the values of the thermodynamic properties, such as chemical potentials and free energies. Here we describe methods for computing occupancies, chemical potentials, and free energies that account for the flexibility of water lattice and guest-guest interactions in the hydrate phase. The methods are validated for a wide variety of guest molecules, such as methane, ethane, carbon dioxide, and tetrahydrodfuran by comparing the predicted occupancy values of guest molecules with those obtained from isothermal isobaric semigrand Monte Carlo simulations. The proposed methods extend the van der Waals and Platteuw theory for clathrate hydrates, and the Langmuir constant is calculated based on the structure of the empty hydrate lattice. These methods in combination with development of advanced molecular models for water and guest molecules should lead to a more thermodynamically consistent theory for clathrate hydrates.

Electrostatic modulation of periodic potentials in a two-dimensional electron gas: from antidot lattice to quantum dot lattice

We use a dual gated device structure to introduce a gate-tuneable periodic potential in a GaAs/AlGaAs two dimensional electron gas (2DEG). Using only a suitable choice of gate voltages we can controllably alter the potential landscape of the bare 2DEG, inducing either a periodic array of antidots or quantum dots. Antidots are artificial scattering centers, and therefore allow for a study of electron dynamics. In particular, we show that the thermovoltage of an antidot lattice is particularly sensitive to the relative positions of the Fermi level and the antidot potential. A quantum dot lattice, on the other hand, provides the opportunity to study correlated electron physics. We find that its current-voltage characteristics display a voltage threshold, as well as a power law scaling, indicative of collective Coulomb blockade in a disordered background.

Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a `footprint' in the generator potential that obscures incoming signals. These three processes reduce information rates by similar to 50% in generator potentials, to similar to 3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.

Confining Dirac electrons on a topological insulator surface using potentials and a magnetic field

We study the effects of extended and localized potentials and a magnetic field on the Dirac electrons residing at the surface of a three-dimensional topological insulator like Bi2Se3. We use a lattice model to numerically study the various states; we show how the potentials can be chosen in a way which effectively avoids the problem of fermion doubling on a lattice. We show that extended potentials of different shapes can give rise to states which propagate freely along the potential but decay exponentially away from it. For an infinitely long potential barrier, the dispersion and spin structure of these states are unusual and these can be varied continuously by changing the barrier strength. In the presence of a magnetic field applied perpendicular to the surface, these states become separated from the gapless surface states by a gap, thereby giving rise to a quasi-one-dimensional system. Similarly, a magnetic field along with a localized potential can give rise to exponentially localized states which are separated from the surface states by a gap and thereby form a zero-dimensional system. Finally, we show that a long barrier and an impurity potential can produce bound states which are localized at the impurity, and an ``L''-shaped potential can have both bound states at the corner of the L and extended states which travel along the arms of the potential. Our work opens the way to constructing wave guides for Dirac electrons.

Role of applied potentials on bioleaching of chalcopyrite concentrate and growth of Acidithiobacillus ferrooxidans

The effect of applied DC potentials on the bioleaching of a chalcopyrite concentrate in the presence of Acidithiobacillus ferrooxidans is discussed. Copper dissolution was the highest at an applied potential of +600mV (SCE), while all the dissolved copper got cathodically deposited at a negative potential of -600mV (SCE). Electrobioleaching at an applied potential of +600mV (SCE) was established at different pulp densities as a function of time. The effect of applied potentials and electrolytic currents on the activity and growth of bacterial cells was assessed Preadaptation of bacterial cells to the concentrate slurry and electrolytic growth conditions significantly enhanced copper dissolution. Electrochemical and biochemical mechanisms involved in electrobioleaching are illustrated with respect to oxidative dissolution and biocatalysis of anodic oxidation.

Oxygen potentials and phase equilibria in the system Ca-Co-O and thermodynamic properties of Ca3Co2O6 and Ca3Co4O9.163

Oxygen potentials established by the equilibrium between three condensed phases, CaOss+CoOss+ Ca3Co2O6 and CoOss+Ca3Co2O6+Ca3CO3.93+O-alpha(9.36-delta), are measured as a function of temperature using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte and pure oxygen as the reference electrode. Cation non-stoichiometry and oxygen non-stoichiometry in Ca3Co3.93+alpha O9.36-delta are determined using different techniques under defined conditions. Decomposition temperatures and thermodynamic properties of Ca3Co2O6 and Ca3Co4O9.163 are calculated from the results. The standard entropy and enthalpy of formation of Ca3Co2O6 at 298.15 K are evaluated. Using thermodynamic data from this study and auxiliary information from the literature, phase diagram for the ternary system Ca-Co-O is computed. Isothermal sections at representative temperatures are displayed to demonstrate the evolution of phase relations with temperature. (C) 2014 Elsevier Inc. All rights reserved.

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Ab initio pair potentials at metal-ceramic interfaces

A systematic approach is proposed to obtain the interfacial interatomic potentials. By inverting ab initio adhesive energy curves for the metal-MgO ceramic interfaces, We derive interfacial potentials between Ag and O2-, Ag and Mg2+, Al and O2-, Al and Mg2+. The interfacial potentials, obtained from this method, demonstrate general features of bondings between metal atoms and ceramic ions.

Quantum and variational monte-carlo interaction potentials for li2 (x1-sigma-g+)

Optimized trial functions are used in quantum Monte Carlo and variational Monte Carlo calculations of the Li₂(X ¹Σ⁺_g) potential curve. The trial functions used are a product of a Slater determinant of molecular orbitals multiplied by correlation functions of electron—nuclear and electron—electron separation. The parameters of the determinant and correlation functions are optimized simultaneously by reducing the deviations of the local energy E_L (E_L  Ψ⁻¹_THΨ_T, where Ψ_T denotes a trial function) over a fixed sample. At the equilibrium separation, the variational Monte Carlo and quantum Monte Carlo methods recover 68% and 98% of the correlation energy, respectively. At other points on the curves, these methods yield similar accuracies.