Analytical multisoliton solutions for multicomponent Bose–Einstein condensate systems with time- and space-controlled potentials

We construct explicit multisoliton complex solutions for multicomponent Bose–Einstein condensate systems with time- and spatial-coordinate-dependent atomic potentials and interactions. The exact solutions are used to analyze the important solitary matter wave properties such as the profiles of temporal and spatial multimode beams as well as focusing effects. Results demonstrate that soliton complexes can be controlled nonlinearly during the interaction by modulating the external potentials and nonlinearities.     

A General Approach of Quasi-Exactly Solvable Schrödinger Equations

We construct a general algorithm generating the analytic eigenfunctions as well as eigenvalues of one-dimensional stationary Schrödinger Hamiltonians. Both exact and quasi-exact Hamiltonians enter our formalism but we focus on quasi-exact interactions for which no such general approach has been considered before. In particular we concentrate on a generalized sextic oscillator but also on the Lamé and the screened Coulomb potentials.     

Local simulation algorithms for Coulombic interactions

We consider a problem in dynamically constrained Monte Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the efficiency of the electrostatics algorithm.     

Classical Lattice-Gas Models of Quasicrystals

One of the fundamental problems of quasicrystals is to understand their occurrence in microscopic models of interacting particles. We review here recent attempts to construct stable quasicrystalline phases. In particular, we compare two recently constructed classical lattice-gas models with translation-invariant interactions and without periodic ground-state configurations. The models are based on nonperiodic tilings of the plane by square-like tiles. In the first model, all interactions can be minimized simultaneously. The second model is frustrated; its nonperiodic ground state can arise only by the minimization of the energy of competing interactions. We put forward some hypotheses concerning stabilities of nonperiodic ground states. In particular, we introduce two criteria, the so-called strict boundary conditions, and prove their equivalence to the zero-temperature stability of ground states against small perturbations of potentials of interacting particles. We discuss the relevance of these conditions for the low-temperature stability, i.e., for the existence of thermodynamically stable nonperiodic equilibrium states.     

Reflectionless Potentials via Complex Potentials

We point out that the complex potentials can be used to construct the reflectionless potentials and two new classes of reflectionless potentials are proposed. In particular, the robustness of these reflectionless potentials is thoroughly studied by the analytical transfer matrix method.     

Electrodynamics of Balanced Charges

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.     

Phase Transitions for Uniformly Expanding Maps

Given a uniformly expanding map of two intervals we describe a large class of potentials admitting unique equilibrium measures. This class includes all Hölder continuous potentials but goes far beyond them. We also construct a family of continuous but not Hölder continuous potentials for which we observe phase transitions. This provides a version of the example in (9) for uniformly expanding maps.     

Baryon-Baryon interactions from lattice QCD

We report on new attempt to investigate baryon-baryon interactions in lattice QCD. From the Bethe-Salpeter (BS) wave function, we have successfully extracted the nucleon-nucleon (NN) potentials in quenched QCD simulations, which reproduce qualitative features of modern NN potentials. The method has been extended to obtain the tensor potential as well as the central potential and also applied to the hyperon-nucleon (YN) interactions, in both quenched and full QCD.     

Some Schrödinger Operators with Power-Decaying Potentials and Pure Point Spectrum

We construct (deterministic) potentials such that the Schr?dinger equation on has dense pure point spectrum in for almost all boundary conditions at . As a by-product, we also obtain power-decaying potentials for which the spectrum is purely singular continuous on for all boundary conditions. Received: 8 November 1996 / Accepted: 8 January 1997     

Modified Darboux transformations with foreign auxiliary equations

We construct a new type of first-order Darboux transformations for the stationary Schrödinger equation. In contrast to the conventional case, our Darboux transformations support arbitrary (foreign) auxiliary equations. We show that among other applications, our formalism can be used to systematically construct Darboux transformations for Schrödinger equations with energy-dependent potentials, including a recent result (Lin et al., 2007) [16] as a special case.     

Nuclear forces from chiral Lagrangians using the method of unitary transformation (I): Formalism

We construct the two- and three-nucleon potential based on the most general chiral effective pion-nucleon Lagrangian using the method of unitary transformations. For that, we develop a power counting scheme consistent with this projection formalism. In contrast to previous results obtained in old-fashioned time-ordered perturbation theory, the method employed leads to energy-independent potentials. We discuss in detail the similarities and differences to the existing chiral nucleon-nucleon potentials. We also show that to leading order in the power counting, the three-nucleon forces vanish lending credit to the result obtained by Weinberg using old-fashioned time-ordered perturbation theory.     

Localized nonlinear waves in combined time-dependent magnetic–optical potentials with spatiotemporally modulated nonlinearities

We construct explicit novel solutions of the nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and potentials. By using a modified similarity transformation we explore some localized nonlinearities and combined time-dependent magnetic–optical potentials in the form of linear-lattice ones and harmonic-lattice ones. Several families of exact localized nonlinear wave solutions in terms of Mathieu and elliptic functions corresponding to these potentials are then studied, such as snakelike solitons and breathing solitons. The stability of the obtained localized nonlinear wave solutions is investigated numerically such that some stable solutions are found.     

On the development of a general force field for the molecular simulation of perfluoroethers

We report the development of a transferable force field for the accurate modelling of perfluoroethers. The potential model takes the general form in which separate bond bending and torsional terms describe the intramolecular interactions, with the addition of van der Waals and electrostatic terms to describe the non-bonded interactions. Ab initio quantum mechanical calculations were carried out to obtain the partial charges and intramolecular torsional and bending potentials. The van der Waals interactions are described by Lennard-Jones potentials, the parameters of which are optimized to reproduce the available experimental vapour-liquid equilibrium data. An extension of the Gibbs-Duhem method was used to speed up the optimization.     

Supersymmetry and Darboux transformations for the generalized Schrödinger equation

We construct Darboux transformations for a generalized Schrödinger equation by means of the intertwining operator method. We establish a relation between first-order Darboux transformations, supersymmetry, and factorization of the Hamiltonians that are associated with our generalized Schrödinger equation. Furthermore, our methods allow for the generation of isospectral potentials, where one of the potentials has additional or less bound states than its partner. In the particular case of a conventional Schrödinger equation our generalized Darboux transformations reduce correctly to the well-known expressions.     

Lie point symmetries,conservation laws and exact solutions of ($$1+ n$$)-dimensional modified Zakharov–Kuznetsov equation describing the waves in plasma physics

An approximate solution for the nuclear Hulthén plus atomic Hulthén potentials is constructed by solving the associated Volterra integral equation by series substitution method. Within the framework of supersymmetry-inspired factorisation method, this solution is exploited to construct higher partial wave interactions. The merit of our approach is examined by computing elastic scattering phases of the \(\alpha {-}\alpha \) system by the judicious use of phase function method. Reasonable agreements in phase shifts are obtained with standard data.     

Isospectrality of conventional and new extended potentials,second-order supersymmetry and role of $$ \mathcal{P}\mathcal{T} $$ symmetry

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry may facilitate reconciling our approach to the requirement that the rationally extended potentials be singularity free. Some examples are shown.     

Selective-pivot sampling of radial distribution functions in asymmetric liquid mixtures

We present a new method for selectively sampling radial distribution functions and effective interaction potentials in asymmetric liquid mixtures using a Monte Carlo simulation. We demonstrate its efficiency for hard-sphere mixtures, and for model systems with more general interactions, and compare our simulations with several analytical approximations. For interaction potentials containing a hard-sphere contribution, the algorithm yields the contact value of the radial distribution function.     

Exact solution of an integrable quantum spin chain with competing interactions

We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky-Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T-Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.     

Direct measurement of entropic forces induced by rigid rods

We present the first direct depletion potential measurements for a single colloidal sphere close to a wall in a suspension of rigid colloidal rods. Since all particle interactions are as good as hard-core-like, the depletion potentials are of entirely entropic origin. We developed a density functional theory approach that accurately accounts for this experimental situation. The depletion potentials calculated for different rod number densities are in very good quantitative agreement with the experimental results.     

Monte Carlo Hamiltonian

We construct an effective Hamiltonian via Monte Carlo from a given action. This Hamiltonian describes physics in the low energy regime. We test it by computing spectrum, wave functions and thermodynamical observables (average energy and specific heat) for the free system and the harmonic oscillator. The method is shown to work also for other local potentials.