Topologically coupled energy bands in molecules

We propose a concrete application of the Atiyah-Singer index formula in molecular physics, giving the exact number of levels in energy bands, in terms of vector bundles topology. The formation of topologically coupled bands is demonstrated. This phenomenon is expected to be present in many quantum systems.Comment: 16 pages, 3 figure

Doorway states in nuclear reactions as a manifestation of the "super-radiant" mechanism

A mechanism is considered for generating doorway states and intermediate structure in low-energy nuclear reactions as a result of collectivization of widths of unstable intrinsic states coupled to common decay channels. At the limit of strong continuum coupling, the segregation of broad (''super-radiating") and narrow (''trapped") states occurs revealing the separation of direct and compound processes. We discuss the conditions for the appearance of intermediate structure in this process and doorways related to certain decay channels.Comment: 16 page

Adiabatically coupled systems and fractional monodromy

We present a 1-parameter family of systems with fractional monodromy and adiabatic separation of motion. We relate the presence of monodromy to a redistribution of states both in the quantum and semi-quantum spectrum. We show how the fractional monodromy arises from the non diagonal action of the dynamical symmetry of the system and manifests itself as a generic property of an important subclass of adiabatically coupled systems

Helium in superstrong magnetic fields

We investigate the helium atom embedded in a superstrong magnetic field gamma=100-10000 au. All effects due to the finite nuclear mass for vanishing pseudomomentum are taken into account. The influence and the magnitude of the different finite mass effects are analyzed and discussed. Within our full configuration interaction approach calculations are performed for the magnetic quantum numbers M=0,-1,-2,-3, singlet and triplet states, as well as positive and negative z parities. Up to six excited states for each symmetry are studied. With increasing field strength the number of bound states decreases rapidly and we remain with a comparatively small number of bound states for gamma=10^4 au within the symmetries investigated here.Comment: 16 pages, including 14 eps figures, submitted to Phys. Rev.

Resonance trapping and saturation of decay widths

Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a chi_K^2 distribution where K is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.

Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths

A phenomenological schematic model of multipole giant resonances (GR) is considered which treats the external interaction via common decay channels on the same footing as the coherent part of the internal residual interaction. The damping due to the coupling to the sea of complicated states is neglected. As a result, the formation of GR is governed by the interplay and competition of two kinds of collectivity, the internal and the external one. The mixing of the doorway components of a GR due to the external interaction influences significantly their multipole strengths, widths and positions in energy. In particular, a narrow resonance state with an appreciable multipole strength is formed when the doorway components strongly overlap.Comment: 20 pages, LaTeX, 3 ps-figures, to appear in PRC (July 1997

Scaling properties of composite information measures and shape complexity for hydrogenic atoms in parallel magnetic and electric fields

The scaling properties of various composite information-theoretic measures (Shannon and R\'enyi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in position and momentum spaces for the non-relativistic hydrogenic atoms in the presence of parallel magnetic and electric fields. Such measures are found to be invariant at the fixed values of the scaling parameters given by $s_1 = B \hbar^3(4\pi\epsilon_0)^2 / (Z^2m^2e^3)$ and $s_2 = F \hbar^4(4\pi\epsilon_0)^3 / (Z^3e^5m^2)$. Numerical results which support the validity of the scaling properties are shown by choosing the representative example of the position space shape complexity. Physical significance of the resulting scaling behaviour is discussed.Comment: 10 pages, 2 figure

Intramolecular vibrational energy relaxation seen as expansion in phase space. I. Some experimental results for H2O+(X̃ 2B1), C2H4 +(X̃ 2B3), and HCN+(B̃2Σ +)

It has been shown by Heller that a nonstationary wave packet resulting from a Franck-Condon transition evolves on the potential energy surface of the final electronic state and propagates through phase space at a rate which can be determined from the autocorrelation function \C(t)\2 = | 〈∅(0) |∅(t) ) |2. Since C(t) can be obtained by Fourier transformation of an optical spectrum S(E), i.e., from an observable quantity, it is possible to derive from an experimental measurement information concerning the density operator of a so-called dynamical statistical ensemble (DSE). This density operator, denoted ρav, represents a statistical mixture of the eigenstates of the system with weights determined by the dynamics of the system. It becomes diagonal after a so-called break time Script T sign;B. Its measure, according to a definition due to Stechel, can be interpreted as an effective number of states (denoted script N) that significantly contribute to the dynamics. The break time Script T sign;B represents the finite period of time allowed to expand in the phase space and after which no further progress can be made. Therefore, the number script N∞ of phase space cells which are accessed after a very long interval of time (or in practice after the break time) remains limited. Information on the validity of statistical theories of unimolecular reactions is contained in the fraction ℱ of the available phase space which is eventually explored. In order to assess the representativity of the sampling, it is necessary to account for the selection rule which requires all the states counted in script N ∞ to belong to the totally symmetric representation. It is also appropriate to estimate the role played by Fermi resonances and similar vibrational interactions which bring about energy flow into zero-order antisymmetric modes. A method to carry out the necessary partitionings is suggested. The functions script N T and ℛ T, and the quantities Script T signB, script N ∞, t script N, and ℱ have been determined from experimental data in three cases. In each case, the rate ℛT = d script N r/dT starts from an initial value of zero, increases up to a maximum which is reached after a time of the order of 10-14 s, and then exhibits an overall decrease upon which oscillations are superimposed. For state X̃ 2B1 of H2O+, Script T signB ≃a 2.4×10-14 s and Script T sign ≃ 0.3. The wave packet never accesses that part of the phase space that corresponds to the excitation of antisymmetric vibrations. For state X̃ 2B3u of C2 H4 +, Script T signB ≃1.6 × 10-13 s and Script T sign ≃ * 5×10-4. This fraction raises to 6 × 10 -3 if measured with respect to the effectively available phase space. When the spectrum consists of a discrete part followed by a dissociation continuum, the method can be extended to study the behavior of the bound part of the wave packet only. This has been applied to state B̃ 2Σ+ of HCN+ which is characterized by a very irregular spectrum. This case offers an example of complete occupation of phase space after a break time which is of the order of 2 ×10 -13 s. © 1990 American Institute of Physics

Intramolecular vibrational relaxation seen as expansion in phase space. III. The long-time limit

Asymptotic formulas that describe the behavior of the function N(T) measuring the phase space volume sampled by a nonstationary wave packet during its time evolution are derived. It is shown that, in the long-time limit, N(T)∼T-1 when the dynamics is regular, whereas N(T)∼T-2 In T for the chaotic case. © 1997 American Institute of Physics