Cosine Potential Research Articles

Nonlinear noninertial response of a quantum Brownian particle in a tilted periodic potential to a strong ac force as applied to a point Josephson junction

The quantum Smoluchowski equation for the reduced Wigner function in configuration space pertaining to the quantum Brownian motion of a particle in a tilted cosine potential in the high dissipation or noninertial limit as applied to a model point Josephson junction namely, a resistively shunted junction in the presence of noise and an arbitrarily large microwave ac driving current is considered. The solution of the resulting recurrence relations for the Fourier amplitudes of the statistical moments describing the nonlinear dynamics of the junction ignoring the capacitance is obtained using the matrix continued fractions previously developed for the stationary ac field solution of the corresponding classical problem. Quantum effects in the nonlinear response of the junction to an ac microwave current of arbitrary amplitude nonlinear microwave impedance, frequency dependence of the dc current-voltage characteristic, etc. are estimated.

Conformational Stability from Rare Gas Solutions, r0 Structural Parameters, Barriers to Internal Rotation, and Ab initio Calculations for Vinyl Silyl Fluoride

The Raman (3300-10 cm(-1)) and infrared (3300-40 cm(-1)) spectra of gaseous and solid vinyl silyl fluoride, CH(2)=CHSiH(2)F, have been recorded. Raman spectrum of the liquid has also been recorded and depolarization values obtained. Variable-temperature studies of the infrared spectra of the sample dissolved in liquid krypton (-110 to -150 degrees C) and liquid xenon (-60 to -100 degrees C) have been carried out. From these studies, the enthalpy difference has been determined to be 76 +/- 7 cm(-1) (0.91 +/- 0.08 kJ/mol) from the krypton solutions and 69 +/- 7 cm(-1) (0.82 +/- 0.08 kJ/mol) from the xenon solutions, with the gauche conformer the more stable form. From the far-infrared spectrum of the gas, the asymmetric torsional fundamentals for the cis and gauche conformers have been observed at 102.34 and 86.56 cm(-1), respectively, with each having several "hot bands" falling to lower frequencies. From these frequencies along with the experimentally determined conformational enthalpy difference, as well as the gauche skeletal dihedral angle, the potential function governing the conformational interchange has been determined with the following Fourier cosine potential coefficients: V(1) = -80 +/- 11, V(2) = -42 +/- 15, V(3) = 622 +/- 5, V(4) = 34 +/- 5, and V(6) = -31 +/- 2 cm(-1). The gauche-to-cis and gauche-to-gauche barriers are 664 cm(-1) (7.94 kJ/mol) and 608 cm(-1) (7.27 kJ/mol), respectively. Complete vibrational assignments are provided for both conformers. In addition, equilibrium geometries and electronic energies have been determined for both rotamers from ab initio calculations using restricted Hartree-Fock and Møller-Plesset perturbation method to the second order (MP2), as well as density functional theory by the B3LYP methods, employing a number of basis sets up to 6-311+G(2df,2pd). All levels of calculation predict the gauche conformer to be the more stable form. By systematically adjusting the ab initio predicted structural values to fit the previously reported microwave rotational constants, adjusted r(0) parameters have been obtained for both conformers. These values are compared to those for the corresponding chloride and methyl compounds. The spectroscopic and theoretical results are discussed and compared to the corresponding quantities for some similar molecules.

Extended Model Free Approach To Analyze Correlation Functions of Multidomain Proteins in the Presence of Motional Coupling

Interdomain motion in proteins plays an important role in biomolecular interaction. Its presence also complicates interpretation of many spectroscopy measurements. Nuclear magnetic resonance (NMR) study of domain dynamics relies on knowledge of its rotational correlation function. The extended model free (EMF) approach has been implemented to analyze coupled domain and overall motions for calmodulin, a dual-domain protein; however, the validity of EMF treatment in coupled motion has not been tested. We performed stochastic simulations on a dual-vector system employing two simple restraints to drive hydrodynamics and domain coupling: (1) both unitary vectors diffuse randomly on the surface of a sphere and (2) vectors are correlated through user-defined intervector potential. The resulting correlation curve can be adequately fit with either a single- or double-exponential decay function. The latter is consistent with the EMF treatment. The derived order parameters S (2) range from about 0.4 to 1, while the motion separation, the ratio of overall and domain motion time scales (tau m/tau s), ranges from 1 to 4. A complete overlap between time scales occurs when S (2) is less than 0.4, and the correlation function effectively behaves as a single-exponential. The S (2) values are consistent with theoretical predictions from the given potential function, differing by no more than 0.03, suggesting EMF to be a generally valid approach. In addition, from the dependence of S (2) on tau m/tau s obtained from simulation, we found a cosine potential, favoring extended conformers, as opposed to the normally assumed cone potential, reached a better agreement to experimental data.

Bosons in one-dimensional incommensurate superlattices

We investigate numerically the zero-temperature physics of the one-dimensional Bose-Hubbard model in an incommensurate cosine potential, recently realized in experiments with cold bosons in optical superlattices [L. Fallani et al., Phys. Rev. Lett. 98, 130404 (2007)]. An incommensurate cosine potential has intermediate properties between a truly periodic and a fully random potential, displaying a characteristic length scale (the quasiperiod) which is shown to set a finite lower bound to the excitation energy of the system at special incommensurate fillings. This leads to the emergence of gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass (BG) phases for strong quasiperiodic potential for both hard-core and soft-core bosons. Enriching the spatial features of the potential by the addition of a second incommensurate component appears to remove the IBI regions, stabilizing a continuous BG phase over an extended parameter range. Moreover, we discuss the validity of the local-density approximation in the presence of a parabolic trap, clarifying the notion of a local BG phase in a trapped system; we investigate the behavior of first- and second-order coherence upon increasing the strength of the quasiperiodic potential; and we discuss the ab initio derivation of the Bose-Hubbard Hamiltonian with quasiperiodic potential starting from the microscopic Hamiltonian of bosons in an incommensurate superlattice.

Incoherent Quasielastic Neutron Scattering Study on the Polymorphism of Tristearin: Dynamical Properties of Hydrocarbon Chains

Dynamical properties of acyl chains in the three polymorphic phases alpha, beta', and beta of tristearin [C(3)H(5)(OCOC(17)H(35))3] have been studied by means of incoherent quasielastic neutron scattering (IQNS) using selectively deuterated samples. The mean square displacement of hydrogen atoms, <U2>, was estimated from the scattering vector Q dependence of the elastic scattering component under the harmonic approximation. It was shown that the temperature dependence of <U2> was significantly different between the three phases. There was no marked difference in <U2> between these phases up to 193 K, and the <U2> value increased linearly with temperature. Although the beta phase remained linear up to 293 K, the alpha and beta' phases started to show a nonlinear increase around 200 K, suggesting an anharmonic nature of molecular motions. The alpha phase exhibited the most conspicuous temperature dependence. These characteristics were ascribable to the difference in the lateral packing of acyl chains. Compared with the beta phase which has a tightly packed T// subcell, the beta' and alpha phases have looser O perpendicular and H subcells, respectively. The molecular motion in the alpha phase was analyzed using the model of uniaxial rotational diffusion in a onefold cosine potential. It has been clarified that the rotational fluctuation about the chain axis in the alpha phase is rather restricted compared with that in the rotator phase of n-alkanes.

MULTISTABILITY AND MULTI 2π-KINKS IN THE FRENKEL–KONTOROVA MODEL: AN APPLICATION TO ARRAYS OF JOSEPHSON JUNCTIONS

A regular ring of Josephson junctions, connected in parallel, is studied analytically and numerically. We show that, depending on the strength of the r-well cosine potential the energy landscape of the Hamiltonian can have of the order of rN/N locally stable minima separated by large barriers specified by unstable saddle points. The counting problem for the degeneracy of the total energy is equivalent to a wellknown necklace problem in combinatorial mathematics. We also demonstrate that the distribution of the phase differences as well as the energy spectrum is fractal provided that the strength of the cosine potential is sufficiently strong.

Unforced translocation of a polymer chain through a nanopore: The solvent effect

The authors have performed the Langevin dynamics simulation to investigate the unforced polymer translocation through a narrow nanopore in an impermeable membrane. The effects of solvent quality controlled by the attraction strength lambda of the Lennard-Jones cosine potential between polymer beads and beads on two sides of the membrane on the translocation processes are extensively examined. For polymer translocation under the same solvent quality on both sides of the membrane, the two-dimensional and three-dimensional simulations confirm the scaling law of tautrans approximately N1+2upsilon for the translocation in the good solvent, where tautrans is the translocation time, N is the chain length, and upsilon is the Flory exponent. For the three-dimensional polymer translocation under different solvent qualities on two sides of the membrane, the translocation efficiency may be notably improved. The scaling law between tautrans and N varies from tautrans approximately N1+2upsilon to tautrans approximately N with the increase of the difference of solvent qualities, and the crossover occurs at the theta temperature point, where a scaling law of tautrans approximately N1.27 is found. The simulation results here also show that the translocation time changes from a wide and asymmetric distribution with a long tail to a narrow and symmetric distribution with the increase of the difference of the solvent qualities.

Exact manipulations to Bloch states of a particle in a double cosine potential

For a single particle held in a double cosine potential with suitable parameters it is demonstrated that the Schrödinger equation has two sets of exact and simple Bloch solutions which are associated with the different boundary conditions. The corresponding eigenenergies can be positive or negative that depend on the amplitude and wave-vector of the laser potential. The results supply possibility for exactly manipulating the quantum motional states of the particle by using the laser beams.

Cavity Ring-Down Spectroscopy of the Torsional Motions of 1,4-Bis(phenylethynyl)benzene

The torsional motions of jet-cooled 1,4-bis(phenylethynyl)benzene (BPEB), a prototype molecular wire, were studied using cavity ring-down spectroscopy in the first UV absorption band (316-321 nm). The torsional spectrum of 1,4-bis(phenylethynyl)-2,3,5,6-tetradeuteriobenzene was also recorded in the gas phase. Both spectra were successfully simulated using simple cosine potentials to describe the torsional motions. The ground-state barrier to rotation was estimated to be 220-235 cm(-1), which is similar to that of diphenylacetylene (tolane). Complementary DFT calculations were found to overestimate the torsional barrier.

Geometrical tachyon kinks andNS5 branes

We further investigate the $NS$5 ring background using the tachyon map. Mapping the radion fields to the rolling tachyon helps to explain the motion of a probe $Dp$-brane in this background. It turns out that the radion field becomes tachyonic when the brane is confined to one dimensional motion inside the ring. We find explicit solutions for the geometrical tachyon field that describe stable kink solutions which are similar to those of the open string tachyon. Interestingly in the case of the geometric tachyon, the dynamics is controlled by a cosine potential. In addition, we couple a constant electric field to the probe-brane, but find that the only stable kink solutions occur when there is zero electric field or a critical field value. We also investigate the behaviour of Non-BPS branes in this background, and find that the end state of any probe brane is that of tachyonic matter 'trapped' around the interior of the ring. We conclude by considering compactification of the ring solution in one of the transverse directions.

Quasi-elastic neutron scattering study on polymorphism of tristearin: relationship between dynamical properties and subcell structures

Dynamical properties of the three polymorphic phases α, β′ and β of tristearin [C 3H 5(OCOC 17H 35) 3] have been studied by incoherent quasi-elastic neutron scattering and X-ray diffraction. At 293 K the difference in the lateral packing density of hydrocarbon chains significantly affected the mean square displacement 〈 U 2 〉 . As compared with β, an increase by 4% in the cross-sectional area for β′ resulted in a twofold increase in 〈 U 2 〉 . In case of α, an increase by 7% led to a threefold increase in 〈 U 2 〉 . The molecular motion in the α phase was analyzed using the model of the uniaxial rotational diffusion in a onefold cosine potential. It has been clarified that the rotational fluctuation about the chain axis in the α phase is rather restricted compared with that in the rotator phase of n-alkanes. The 〈 U 2 〉 in the α phase decreased significantly with the temperature, and reached the level of the 〈 U 2 〉 in the β phase at 193 K.

The Caldeira–Leggett quantum master equation in Wigner phase space: continued-fraction solution and application to Brownian motion in periodic potentials

The continued-fraction method to solve classical Fokker--Planck equations has been adapted to tackle quantum master equations of the Caldeira--Leggett type. This can be done taking advantage of the phase-space (Wigner) representation of the quantum density matrix. The approach differs from those in which some continued-fraction expression is found for a certain quantity, in that the full solution of the master equation is obtained by continued-fraction methods. This allows to study in detail the effects of the environment (fluctuations and dissipation) on several classes of nonlinear quantum systems. We apply the method to the canonical problem of quantum Brownian motion in periodic potentials both for cosine and ratchet potentials (lacking inversion symmetry).

Multi-instantons and exact results II: specific cases, higher-order effects, and numerical calculations

In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton contributions to the partition function, using the formalism introduced in the first part of the treatise [Ann. Phys. (N. Y.) (previous issue) (2004)]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker–Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is non-zero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited.

Thermally activated escape rate for the Brownian motion of a fixed axis rotator in a double well potential for all values of the dissipation.

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel'nikov and Meshkov [J. Chem, Phys. 85, 1018 (1986)] is applied to the rotational Brownian motion of fixed axis rotators in a double well cosine potential. The procedure yields an expression for the Kramers escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes. This equation provides a good asymptotic estimate of the correlation time tau per pendicular of the longitudinal dipole moment correlation function calculated by solving the underlying Langevin equation using the matrix-continued fraction method. Moreover, for low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for tau in the VLD and VHD limits are derived and a simple extrapolating equation that is valid for all values of the damping is proposed.

Some properties of the integrable noncommutative sine–Gordon system

In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in order to guarantee classical integrability. We show that the system of constraint plus dynamical equation of motion can be obtained by a suitable reduction of a noncommutative version of 4d self-dual Yang-Mills theory. The field equations can be derived from an action which is the sum of two WZNW actions with cosine potentials corresponding to a complexified noncommutative U(1) gauge group. A brief discussion of the relation with the bosonized noncommutative Thirring model is given. In spite of integrability we show that the S-matrix is acasual and particle production takes place.

Studies of translational diffusion in the smectic A phase of a Gay-Berne mesogen using molecular dynamics computer simulation.

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.

Quantum states of a mesoscopic SQUID measured using a small Josephson junction

We have experimentally studied the energy levels of a mesoscopic superconducting quantum interference device (SQUID) using inelastic Cooper-pair tunneling. The tunneling in a small Josephson junction depends strongly on its electromagnetic environment. We use this fact to do energy-level spectroscopy of a SQUID loop by coupling it to a small junction. Our samples with strong quasiparticle dissipation are well described by a model of a particle localized in one of the dips in a cosine potential, while in the samples with weak dissipation we can see formation of energy bands.

The Asymptotics of Spectral Gaps of a 1D Dirac Operator with Cosine Potential

The Asymptotics of Spectral Gaps of a 1D Dirac Operator with Cosine Potential

Search for tracker potentials in quintessence theory

We report a significant finding in quintessence theory that scalar fields with tracker potentials have a model-independent scaling behaviour in the expanding universe. So far, widely discussed exponential, power law or hyperbolic potentials can simply mimic the tracking behaviour over a limited range of redshift. A new version of the tracker field theory is proposed and it is shown that in the small redshift range where the variation of the tracking parameter ϵ may be taken to be negligible, the differential equation of generic potentials leads to hyperbolic sine and hyperbolic cosine potentials which may approximate a tracker field in the present-day universe. We have plotted the variation of the tracker potential and the equation of state of the tracker field as a function of the redshift z for the model-independent relation derived from tracker field theory; we have also plotted the variation of V(Φ) in terms of the scalar field Φ for the chosen hyperbolic cosine function and have compared it with the curves obtained by the reconstruction of V(Φ) from real observational data from the supernovae.

Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential.

In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear Schrödinger equation with a periodic potential is equivalent to a vector lattice with long-range interactions. For the case-example of the cosine potential we study the validity of the so-called tight-binding approximation, i.e., the approximation when nearest neighbor interactions are dominant. The results are relevant to the Bose-Einstein condensate theory as well as to other physical systems, such as, for example, electromagnetic wave propagation in nonlinear photonic crystals.