Non-adiabatic Perturbations Research Articles

Fluctuating annihilation cross sections and the generation of density perturbations

Fluctuations in the mass and decay rate of a heavy particle which for some period dominates the energy density of the Universe are known to lead to adiabatic density perturbations. We show that generically the annihilation cross section of the same particle also receives fluctuations, which leads to entropy perturbations at freeze-out. If the particle comes to dominate the energy density of the Universe and subsequently decays, this leads to an additional source of adiabatic density perturbations. On the other hand, nonadiabatic density perturbations result when the particle does not decay but contributes to the observed dark matter.

Matter power spectrum for convex quartessence

The possibility of unifying dark matter and dark energy has recently attracted considerable interest. In this so called quartessence scenario, a single component is responsible for both the clustering of matter and the accelerated expansion of the universe. A model archetype for such scenario is provided by the Chaplygin gas. Although this model is in agreement with the data on the expansion history, problems arise in the power spectrum of density fluctuations for adiabatic perturbations. In this contribution we consider other quartessence models and confirm that instabilities and oscillations in the matter power spectrum are a characteristic of more generic quartessence models, namely those with a convex equation of state. We show that, as in the Chaplygin case, this kind of problem can be solved by considering intrinsic non-adiabatic perturbations such that, as an initial condition, the perturbed fluid is gradient pressure free. We also discuss how the problems of adiabatic quartessence can be circumvented by other types of equations of state.

Must cosmological perturbations remain nonadiabatic after multifield inflation?

Even if nonadiabatic perturbations are generated in multifield inflation, the perturbations will become adiabatic if the Universe after inflation enters an era of local thermal equilibrium, with no nonzero conserved quantities, and will remain adiabatic as long as the wavelength is outside the horizon, even when local thermal equilibrium no longer applies. Small initial nonadiabatic perturbations associated with imperfect local thermal equilibrium remain small when baryons are created from out-of-equilibrium decay of massive particles, or when dark matter particles go out of local thermal equilibrium.

Can nonadiabatic perturbations arise after single-field inflation?

It is shown that non-adiabatic cosmological perturbations cannot arise during the period of reheating following inflation with a single scalar inflaton field.

Initial conditions of the universe: how much isocurvature is allowed?

We investigate the constraints imposed by current data on correlated mixtures of adiabatic and nonadiabatic primordial perturbations. We discover subtle flat directions in parameter space that tolerate large (approximately 60%) fractions of nonadiabatic fluctuations. In particular, larger values of the baryon density and a spectral tilt are allowed. The cancellations in the degenerate directions are explored and the role of priors is elucidated.

Double tunneling in dipole bound anions: A model study

The applicability of the Born-Oppenheimer approximation for the description of the coupled nuclear and electronic tunneling dynamics in anionic dimers of hydrogen fluoride and water is studied. These complex molecules are modeled by a simpler system, with only one nuclear coordinate, which can be solved easily with arbitrary accuracy. Although the Born-Oppenheimer approximation is not applicable in a strict sense in the tunneling region where the electron becomes unbound, quite accurate values for the binding energy can be obtained when working with a discrete electronic basis. Employing a basis which is diabatic with respect to the angular coordinates, but adiabatic with respect to the radial coordinate, the convergence of a nonadiabatic perturbation expansion is also studied. Inclusion of the lowest-order nonadiabatic corrections reduces the error in the binding energy already by a factor of 10-20, while for the correct prediction of the tunneling splitting, it proves necessary to take into account higher-order corrections. With increasing number of diffuse functions included in the electronic basis, the nonadiabatic effects increase and the perturbation series converges more slowly.

Separate universe approach and the evolution of nonlinear superhorizon cosmological perturbations

In this paper we review the separate universe approach for cosmological perturbations and point out that it is essentially the lowest order approximation to a gradient expansion. Using this approach, one can study the nonlinear evolution of inhomogeneous spacetimes and find the conditions under which the long wavelength curvature perturbation can vary with time. When there is one degree of freedom or a well-defined equation of state the nonlinear long wavelength curvature perturbation remains constant. With more degrees of freedom it can vary and this variation is determined by the nonadiabatic pressure perturbation, exactly as in linear theory. We identify combinations of spatial vectors characterizing the curvature perturbation which are invariant under a change of time hypersurfaces.

Adiabatic-following criterion, estimation of the nonadiabatic excitation fraction, and quantum jumps

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimated quantitatively. It is shown that the limiting value to which the amplitude of the nonadiabatic part tends is equal to the Fourier component of the nonadiabatic perturbation parameter taken at the Rabi frequency of the Raman excitation. The time scale of the variation of both parts is found. While the adiabatic part of the solution varies slowly and follows the change of the nonadiabatic perturbation parameter, the nonadiabatic part appears almost instantly, revealing a jumpwise transition between the dark and bright states. This jump happens when the nonadiabatic perturbation parameter takes its maximum value.

Ion induced kinetic electron emission from highly oriented pyrolytic graphite by impact of H +, C +, N +, and O +

Total electron yields from highly oriented pyrolytic graphite (HOPG) have been measured for perpendicular impact of H +, C +, N +, and O + projectile ions with kinetic energies from a few hundred eV up to 30 keV. The data are interpreted within a model for kinetic electron emission based on non-adiabatic time-dependent perturbation of valence-band electrons by the moving particle. The microscopical parameters of this excitation processes describe well the qualitative trends in the experimental data when changing the target from HOPG to polycrystalline gold.

High order nonadiabatic perturbation theory on different adiabatic bases

A new partitioning of the nonadiabatic terms of a Hamiltonian consisting of a “slow” and a “fast” subsystem is introduced for high order numerical calculations of perturbation series. The Hamiltonian H(ν,λ) depends on two parameters, λ and ν. While the momentum dependent part of the perturbation is taken to be a linear function of the perturbation parameter λ, the other nonadiabatic terms are either assumed to be independent of λ, or depend quadratically on it. Especially the diagonal correction is partitioned into a constant and a quadratic function of λ. This partitioning will be controlled by the parameter ν. In zeroth order, the Hamiltonian will therefore be either the Born–Oppenheimer Hamiltonian, when ν=1, or the Born–Huang Hamiltonian, when ν=0. For other values of ν, more general adiabatic bases result. The new partitioning, in combination with the Hutson and Howard approach, forms a new method for the calculation of nonadiabatic perturbation series which is tested on a set of four model Hamiltonians. These have been studied already by Špirko et al. in a similar context. It is shown that the new method, as compared to traditional approaches, strongly enhances the rate of convergence and the accuracy of summability of the perturbation series, especially in the case of nearly avoided intersections or of near degeneracies.

New approach to the evolution of cosmological perturbations on large scales

We discuss the evolution of linear perturbations about a Friedmann-Robertson-Walker background metric, using only the local conservation of energy momentum. We show that on sufficiently large scales the curvature perturbation on spatial hypersurfaces of uniform density is conserved when the non-adiabatic pressure perturbation is negligible. This is the first time that this result has been demonstrated independently of the gravitational field equations. A physical picture of long-wavelength perturbations as being composed of separate Robertson-Walker universes gives a simple understanding of the possible evolution of the curvature perturbation, in particular clarifying the conditions under which super-horizon curvature perturbations may vary.

Non-adiabatic electron excitation in ion-induced kinetic electron emission from metal surfaces

Both high-energy features and the major low-energy peak of ion-induced kinetic electron emission spectra are often being explained by level promotion processes and by various related electron energy loss mechanisms. There are, however, many experiments, especially with very low-energy ions (hundreds of eV), where the electron promotion mechanisms cannot explain the kinetic electron emission and where the particle velocity is too low to produce electrons by classical particle-electron collisions. An additional mechanism for kinetic electron emission is suggested and discussed in this paper. This mechanism is based on the non-adiabatic perturbation of the Fermi gas due to the rapid passage of the particle through the surface. The first quantitative comparisons with experiments (e.g. Ne on Au) yield reasonable values for the critical microscopic parameters of the theory.

Fine structure of the 4f complexes of ArH and KrH revisited: Quantum defect theory used as a spectroscopic tool

The 4f,v=0 manifolds of levels of ArH, ArD, and KrD observed by Dabrowski et al. [J. Mol. Spectrosc. 189, 110 (1998)] and Dabrowski and Sadovskii [J. Chem. Phys. 107, 8874 (1997)] have been reanalyzed using multichannel quantum defect theory. The nondiagonal (l-mixing) quantum defect matrices are partially extracted from the experimental data and are found to be in reasonable agreement with the quantum defects calculated theoretically by Jungen et al. [Phil. Trans. R. Soc. Lond. A 355, 1481 (1997)]. The quantum defect calculations reproduce the observed level fine structure in great detail including nonadiabatic rotational l-uncoupling and electronic l-mixing perturbations.

Raman dispersion spectroscopy on the highly saddled nickel(II)-octaethyltetraphenylporphyrin reveals the symmetry of nonplanar distortions and the vibronic coupling strength of normal modes

We have measured the polarized Raman cross sections and depolarization ratios of 16 fundamental modes of nickel octaethyltetraphenylporphyrin in a CS2 solution for 16 fundamental modes, i.e., the A1g-type vibrations ν1, ν2, ν3, ν4, ν5, and φ8, the B1g vibrations ν11 and ν14, the B2g vibrations ν28, ν29, and ν30 and the antisymmetric A2g modes ν19, ν20, ν22, and ν23 as function of the excitation wavelength. The data cover the entire resonant regions of the Q- and B-bands. They were analyzed by use of a theory which describes intra- and intermolecular coupling in terms of a time-independent nonadiabatic perturbation theory [E. Unger, U. Bobinger, W. Dreybrodt, and R. Schweitzer-Stenner, J. Phys. Chem. 97, 9956 (1993)]. This approach explicitly accounts in a self-consistent way for multimode mixing with all Raman modes investigated. The vibronic coupling parameters obtained from this procedure were then used to successfully fit the vibronic side bands of the absorption spectrum and to calculate the resonance excitation profiles in absolute units. Our results show that the porphyrin macrocycle is subject to B2u-(saddling) and B1u-(ruffling) distortions which lower its symmetry to S4. Thus, evidence is provided that the porphyrin molecule maintains the nonplanar structure of its crystal phase in an organic solvent. The vibronic coupling parameters indicate a breakdown of the four-orbital model. This notion is corroborated by (ZINDO/S) calculations which reveal that significant configurational interaction occurs between the electronic transitions into |Q〉- and |1B〉-states and various porphyrin→porphyrin, metal→porphyrin, and porphyrin→metal transitions. The intrastate coupling parameters are used to estimate the excited electronic states’ displacements along the normal coordinates with respect to the ground state and their contributions to the reorganization energy. It turns out that the |B〉-state is predominantly affected by symmetric A1g-displacements, whereas the |Q〉-state is subject to A2g, B1g, and B2g displacements of its equilibrium configuration. While the former is induced by the combined effect of ruffling and saddling, the latter arises from Jahn–Teller coupling within the degenerate states.

The rotator model in excited collective bands of even deformed nuclei

The rotator model is used for separately fitting the - and -bands of even rare earth and actinide collective nuclei. It is shown that in the excited bands the violation of the exact SU(2) rotational symmetry is generally stronger than in the ground-state bands, indicating the presence of non-adiabatic perturbations. The physical content of the parameter q as well as the implications on classification schemes for spectra of deformed nuclei are discussed. Predictions of the model for B(E2) intraband transitions in excited bands are presented and the need for

Bulk viscous cosmology.

We propose a scenario in which the dark components of the Universe are manifestations of a single bulk viscous fluid. Using dynamical system methods, a qualitative study of the homogeneous, isotropic background scenario is performed in order to determine the phase space of all possible solutions. The specific model which we investigate shares similarities with a generalized Chaplygin gas in the background but is characterized by nonadiabatic pressure perturbations. This model is tested against supernova type Ia and matter power spectrum data. Different from other unified descriptions of dark matter and dark energy, the matter power spectrum is well behaved, i.e., there are no instabilities or oscillations on small perturbation scales. The model is competitive in comparison with the currently most popular proposals for the description of the cosmological dark sector.

Constraints from inflation on scalar-tensor gravity theories.

We show how observations of the perturbation spectra produced during inflation may be used to constrain the parameters of general scalar-tensor theories of gravity, which include both an inflaton and dilaton field. An interesting feature of these models is the possibility that the curvature perturbations on super-horizon scales may not be constant due to non-adiabatic perturbations of the two fields. Within a given model, the tilt and relative amplitude of the scalar and tensor perturbation spectra gives constraints on the parameters of the gravity theory, which may be comparable with those from primordial nucleosynthesis and post-Newtonian experiments.

Nonadiabatic perturbations and fine structure splittings in the 1,2 3Πg states of B2: An analysis based on adiabatic and rigorous diabatic states

Nonadiabatic effects and fine structure splittings in the 1,2 3Πg states of B2 were studied. Adiabatic electronic wave functions Ψa(J 3Πg) were computed at the multireference configuration interaction level. The interstate derivative couplings 〈Ψa(1 3Πg)‖(d/dR)Ψa(2 3Πg)〉 were computed and used to construct ‘‘rigorous’’ diabatic electronic states. The spin–orbit interactions responsible for the fine structure splitting in the 1,2 3Πg states were determined, as were the 1,2 3Πg∼1 1Πg spin–orbit interactions. These electronic structure data were used to determine the vibrational structure of the 1,2 3Πg states in both coupled adiabatic and coupled diabatic states bases. As a result of an avoided crossing of the 1,2 3Πg states the fine structure splitting constants exhibit a marked geometry dependence. The fine structure splitting constants for the (1 3Πg, v=0–4) levels were found to be −4.2(−4.4), −3.7, −2.8, −1.8, and −0.83 cm−1, respectively. The (1 3Πg, v=0) value is in good agreement with a recent experimental determination given parenthetically. While the diabatic basis provides illuminating qualitative insights into the electronic structure of the states in question the adiabatic basis is preferred computationally.

Extragalactic light fluctuations in the decaying dark matter hypothesis

Sciama has attributed the ionization of diffuse interstellar gas and intergalactic clouds to a UV background arising from the decay of ∼ 30-eV primordial neutrinos on a time-scale of ∼10 23 s. Cosmological structure forms as in any hot dark matter model, and the existence of non-linear structure at redshifts of ∼5 then requires the presence of non-adiabatic or non-Gaussian perturbations on galactic scales. This hypothesis is testable through the emission of photons of a well-defined energy from the dark matter, which may be detectable wherever structure has developed. Non-detections from clusters of galaxies argue strongly against the decaying dark matter model, but debate about the distribution of dark matter within clusters makes the interpretation of the data inconclusive

Cyclic states, Berry phases and the Schrodinger operator

The evolution of a quantum mechanical system under a nonadiabatic external perturbation at a time interval (0,T) is considered. It is shown that all the cyclic states of the system, mod Psi (T))=ei phi mod Psi (0)), are determined by the eigenvalues in (quasi-energies) and associated eigenvectors mod phi in (t)) of the Schrodinger operator Sq(t)=H(t)-i( delta / delta t) acting on some Hilbert space. The set of linearly independent cyclic (quasi-energy) states possess some properties similar to the properties of the stationary states of a closed system. The Berry phases of the states associated with eigenvectors of the discrete spectrum of Sq(t), which are single-valued functions of omega =2 pi /T, are supplied by the partial derivatives of the corresponding eigenvalues (quasi-energies) with respect to omega . The approach developed is illustrated by several applications to time-dependent systems: the system under an adiabatic perturbation, the forced harmonic oscillator, and the two-level system. Even in the case of a system with a time-independent Hamiltonian there exist nonstationary quasi-energy states that have nontrivial Berry phases ( beta /2 pi not an integer). The criterion of existence of such states is formulated in terms of the energies of the system, and the corresponding expression for the Berry phases is obtained. Some examples of nonstationary cyclic states of closed systems, including the coherent states of a force-free oscillator and the Wannier states of electrons in the parabolic band, are considered.