Quantum Dispersion Research Articles

Ab initio path-integral molecular dynamics

A path-integral molecular dynamics technique for strongly interacting atoms using ab initio potentials derived from density functional theory is implemented. This allows the efficient inclusion of nuclear quantum dispersion in ab initio simulations at finite temperatures. We present an application to the quantum cluster H 5 + .

Quantum state diffusion, localization and quantum dispersion entropy

The quantum state diffusion model introduced in an earlier paper represents the evolution of an individual open quantum system by an Ito diffusion equation for its quantum state. The diffusion and drift terms in this equation are derived from interaction with the environment. In this paper two localization theorems are proved. The dispersion entropy theorem shows that under special conditions, which are commonly satisfied to a good approximation, the mean quantum dispersion entropy, which measures the mean dispersion or delocalization of the quantum states, decreases at a rate equal to a weighted sum of effective interaction rates, so that the localization always increases in the mean, except when the effective interaction with the environment is zero. The general localization theorem provides a formula for more general conditions.

Classical and quantum dispersion in Robertson–Walker cosmologies

The instability of world lines in Robertson–Walker universes of negative spatial curvature is investigated. A probabilistic description of this instability, similar to the Liouville equation, is developed, but in a manifestly covariant, non-Hamiltonian form. To achieve this the concept of a horospherical geodesic flow of expanding bundles of parallel world lines is introduced. An invariant measure and a covariant evolution equation for the probability density on which this flow acts is constructed. The orthogonal surfaces to these bundles of trajectories are horospheres, closed surfaces in three-space, touching the boundary at infinity of hyperbolic space, where the flow lines emerge. These horospheres are just the wave fronts of spherical waves, which constitute a complete set of eigenfunctions of the Klein–Gordon equation. This fact suggests that the evolution of the quantum mechanical density with the classical one be compared, and asymptotic identity in the asymptotically flat region is found. This leads, furthermore, to the study of the time behavior of the dispersion of the energy and the coordinates and the energy-time uncertainty relation, and identity in the late stage of the cosmic evolution is again found. In an example it is finally demonstrated that this identity can persist in the early phase of the expansion with a rapidly varying scale factor, provided the fields are conformally coupled to the curvature.

A discrete theory of the induced polarization of adsorbed atoms and molecules on an ionic crystal

The potential response of a non-planar dielectric crystal surface to a fluctuating electronic charge density of admolecules is characterized using a discrete approach and quasi-static approximation. In this method, the multipolar response function of the ionic crystal is introduced from a general propagator of potential and the electric properties of the adsorbed molecules are described as the electric susceptibility. This allows us to obtain an iterative self-consistent determination of the long-range van der Waals interaction potential. The discrete description of the crystal matter takes into account the influence of the face specificity and adsorption sites of the substrate. The multipolar (electrostatic + induction) contribution and the quantum (dispersion) terms are determined for the dipolar and the quadrupolar moments of the molecule. A numerical application of each contribution is given for a xenon atom adsorbed on an MgO surface.

Femtosecond time domain measurements of group velocity dispersion in diode lasers at 1.5 mu m

The authors have measured the group velocity dispersion of bulk V-groove semiconductor lasers and multiple quantum well lasers operating at a wavelength near 1.5 mu m. The data yield group velocity dispersions in the range from -0.63 to -0.95 mu m/sup -1/ and indicate that material dispersion is the dominant factor in the diodes. Cross-correlation traces of transmitted femtosecond pulses confirm the measured values of dispersion. >

Localization in a Lennard-Jones fluid: The path-integral approach

The equilibrium properties of a light particle (LP) in a dense fluid are investigated analytically and numerically. It is assumed that the fluid molecules interact via a Lennard-Jones 6,12 potential and that the LP is a rigid sphere. The path-integral RISM model of the LP developed by Chandler et al. is employed, extended to include the smooth intermolecular interaction, to investigate the quantum dispersion of the position of the LP and the LP-fluid radial distribution function, g(r). It is found that important changes in g(r) occur in a region of the liquid-vapor critical point of the fluid that are qualitatively similar to the properties of the ‘‘self-trapped’’ states that arise in the earlier density functional theories. It is demonstrated that the thermodynamic pressure and compressibility exert a competing influence on g(r), and evidence is presented that the usual understanding of localization in fluids has to be extended.

The ionic correlation contribution to the free energy of spherical double layers

An estimate of the ion fluctuation contribution to the free energy for a dispersion of spherical macroions, without additional salt, is made using the cell model. The Poisson–Boltzmann approximation is used to estimate the linear response in a given cell, which together with second order perturbation theory allow us to calculate the free energy of interaction between a pair of cells. As well, an infinite order theory is developed. We find excellent agreement with simulations for monovalent counterions, the comparison becoming poorer for more strongly coupled systems. A cubic lattice of cells is studied, modeling a macroionic dispersion. The fluctuation contribution is shown to be several orders of magnitude larger than the usual quantum dispersion forces. However, it plays a minor role in the thermodynamics of the lattice.

High-frequency sum rules for the quasi-one-dimensional quantum plasma dielectric tensor

A high-frequency sum-rule expansion is derived for all elements of the spinless quasi-one-dimensional quantum plasma response tensor atT=0 K. As in the magnetized classical plasmas, we find that Ω 4 13 is the only coefficient of ω−4 that has no correlational term. Further, we find that the correlations either enhance or reduce the negative quantum dispersion, depending on the direction of propagation. It is also noted that the quantum effect does not exist for the ordinary and the extraordinary modes for perpendicular and parallel propagation, respectively.

Valence band dispersion in finite quantum wells with uniform electric field

Valence band dispersion of GaAs-Ga 1-xAl xAs single finite quantum well in presence of an external electric field is computed by means of the perturbed Luttinger Hamiltonian, when the field is perpendicular to the semiconductor layers. We use an iterative process to solve the set of coupled differential equations, taking into account only the mixing of the deepest bounded valence states. This situation is important for the second and third valence band levels in the k-space.

Self-consistent interaction potential for a molecule adsorbed on a dielectric surface: A symmetric top molecule on an ionic crystal

An iterative self-consistent determination of the long range interaction energy between an admolecule and a ionic crystal is performed within the scheme of local and response potentials and the definition of the generalized electric susceptibilities of the two partners. The multipolar (electrostatic+induction) contributions and the quantum (dispersion+empirical short range) terms are determined as a sum of interactions between the molecule and the atomic planes parallel to the surface, constituting the crystal. The discrete structure of each plane is described with an increasing accuracy by increasing the order of the Fourier expansion in the reciprocal planar lattice. A semianalytical expression of each contribution is given for a symmetric top molecule adsorbed on a NaCl surface as a function of the location of the center of mass and of the orientation of the molecule.

Gap and Bethe-Salpeter equations in Hamiltonian lattice QCD with Wilson fermions.

The dynamical breaking of symmetries in strong-coupling large-${N}_{c}$ Hamiltonian lattice QCD with Dirac fermions, thoroughly studied by Smit, is reconsidered and clarified here in another language. We use the Bogoliubov-Valatin variational method to formulate the gap equation and obtain the 〈\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\psi}〉 condensate, the dynamical mass, and the shift in energy density between the invariant and the broken vacua. We also solve the Bethe-Salpeter equation and get the quantum numbers, dispersion laws, and Dirac wave functions of the meson spectra in the whole Brillouin zone. The eightfold fermion multiplicity reflects in the meson spectrum through 8${N}_{f}$${}^{2}$ Goldstone bosons by the breaking U(4${N}_{f}$)->U(2${N}_{f}$)\ifmmode\times\else\texttimes\fi{}U(2${N}_{f}$ ) (${N}_{f}$=number of flavors). We repeat the program in the presence of a current mass and a Wilson term; we study the stability of the vacuum and see how the high degeneracy of Goldstone bosons is lifted. Although a massless pseudoscalar can be obtained by adjusting the current mass and the Wilson coupling, we find that the vacuum is not chiral degenerate and therefore this massless pseudoscalar is not a Goldstone boson. Although not chiral degenerate, the vacuum satisfies nevertheless the weaker condition of being a flat minimum: a finite number of derivatives vanish in the chiral direction. We conjecture that higher derivatives will converge to zero as the coupling decreases, chiral degeneracy being recovered only in the continuum weak-coupling limit. For any value of the Wilson term, the mass of a local baryon is just equal to ${N}_{c}$${M}_{\mathrm{dyn}}$ where ${M}_{\mathrm{dyn}}$ is the solution of the gap equation.

Asymptotic [formula omitted] in classic particle limit of non-relativistic quantum mechanics

The unitary group describing the evolution of the quantum fluctuation around any classic phase orbit has a perturbative strongly asymptotic expansion in the small parameter h z.shtsls; 1 2 . Likewise, the mean values of the observables position and momentum in suitable time-dependent states have an asymptotic expansion in h z.shtsls; 1 2 , whose zeroth-order term satisfies the classic canonical equations. Similar expansions are found for the squared quantum dispersions.

Theoretical foundations of the chronometric cosmology

The derivation of the redshift (z)-distance (r) relation in the chronometric theory of the Cosmos is amplified. The basic physical quantities are represented by precisely defined self-adjoint operators in global Hilbert spaces. Computations yielding explicit bounds for the deviation of the theoretical prediction from the relation z = tan(2)(r/2R) (where R denotes the radius of the universe), earlier derived employing less formal procedures, are carried out for: (a) a cut-off plane wave in two dimensions; (b) a scalar spherical wave in four dimensions; (c) the same as (b) with appropriate incorporation of the photon spin. Both this deviation and the (quantum) dispersion in redshift are shown to be unobservably small. A parallel classical treatment is possible and leads to similar results.

Derivation of the Quantum Vlasov Equation and Dispersion Relation of a Relativistic Electron Gas

The selfconsistent field equation (VLASOV equation) is derived for the one-particle WIGNER function of a relativistic electron-positron gas. From the linearized form we obtain the dispersion relation for any quasi-equilibrium state, which for the special case of thermal equilibrium has already been derived by TSYTOVICH 1.

Anomalous Dispersion of ϐ-Carotene Solutions*

Refractive indices of liquids were determined by measuring reflectance at a glass-liquid interface, measuring transmittance of the liquids, and calculating their relative refractive indices from a Fresnel reflection equation of Simon. The refractive index of the glass was measured independently and used to calculate n values of the liquids relative to vacuum. The spectral region investigated, 400–589 mμ, includes four absorption bands of β-carotene. Dispersion curves of two solution-solvent pairs were measured. The differences, Δnsolute=nsolution−nsolvent=f(λ), were compared with the predictions of quantum dispersion equations of Davydov.

Quantum Effects in the Interaction between Free Electrons and Electromagnetic Fields

An electron beam shot through a transverse rf field may suffer a directional spread. If experimental conditions are suitably chosen, the directional spread may be due only to the quantum dispersion of energy exchange between free electrons and rf field. A simple collector electrode system might allow not only the detection of the directional spread of the electrons, but the presence of a quantum effect might be checked by plotting the collector current versus rf field amplitude, the plot for the quantum effect being different from those for classical effects. The results of various theoretical treatments of the effect are briefly compared, both from the point of view of their principal foundations and of the possibility of their experimental verification.

Quantum effects in the interaction between free electrons and electromagnetic fields

An electron beam shot through a transverse r. f. field suffers a direction spread. If experimental conditions are suitably chosen, the direction spread seems to be due only to the quantum dispersion of energy exchange between free electrons and r. f. field. A simple collector electrode system might allow not only the detection of the direction spread of the electrons, but the presence of a quantum effect might be chequed by plotting the collector current versus r. f. field amplitude, the plot for the quantum effect being different from those for classical effects.

The ‘Common Third Level’ in the Raman Effect

IN recent communications to NATURE, Langer and Dieke have pointed out that generally the shifts observed in the Raman spectra correspond not directly to the absorption frequencies of the scattering substance but to differences between its absorption frequencies, and that this is in accordance with the dispersion theory of Kramers, Heisenberg and Schrodinger. As a consequence of the quantum dispersion theory, the probability that we should observe a shift of Raman lines corresponding to the transition El→Ek is dependent on the probabilities of the transitions from El→En and from Ek→En where En is any third common level. The purpose of this note is to point out the significance of the common level from a physical point of view.