We derive and discuss the finite-energy sum rules, which form consistency conditions imposed by analyticity on the Regge analysis of a scattering amplitude. Their finite form makes them particularly useful in practical applications. We discuss the various applications, emphasizing a new kind of bootstrap predicting the Regge parameters from low-energy data alone. We apply our methods to xiV charge exchange and are able to derive many interesting features of the high-energy amplitudes at various t. In particular, we establish the existence of zeros of the amplitudes and of additional p poles. On the basis of the finiteenergy sum rules and the analysis of the irN amplitudes, we present theoretical and experimental evidence that double counting is involved in the interference model, which adds direct-channel resonances to the exchanged Regge terms.

The cosmological QCD transition affects primordial density perturbations. If the QCD transition is first order, the sound speed vanishes during the transition and density perturbations fall freely. For scales below the Hubble radius at the transition the primordial Harrison-Zel'dovich spectrum of density fluctuations develops large peaks and dips. These peaks grow with wave number for both the hadron-photon-lepton fluid and for cold dark matter. At the horizon scale the enhancement is small. This by itself does not lead to the formation of black holes at the QCD transition. The peaks in the hadron-photon-lepton fluid are wiped out during neutrino decoupling. For cold dark matter that is kinetically decoupled at the QCD transition ͑e.g., axions or primordial black holes͒ these peaks lead to the formation of CDM clumps of masses 10 Ϫ20 M ᭪ ϽM clump Ͻ10 Ϫ10 M ᭪ . ͓S0556-2821͑99͒05702-1͔PACS number͑s͒: 98.80. Cq, 12.38.Mh, 95.35.ϩd †

Ever since Ernest Rutherford first scattered α-particles from gold foils1, collision experiments have revealed unique insights into atoms, nuclei, and elementary particles2. In solids, many-body correlations also lead to characteristic resonances3, called quasiparticles, such as excitons, dropletons4, polarons, or Cooper pairs. Their structure and dynamics define spectacular macroscopic phenomena, ranging from Mott insulating states via spontaneous spin and charge order to high-temperature superconductivity5. Fundamental research would immensely benefit from quasiparticle colliders, but the notoriously short lifetimes of quasiparticles6 have challenged practical solutions. Here we exploit lightwave-driven charge transport7–24, the backbone of attosecond science9–13, to explore ultrafast quasiparticle collisions directly in the time domain: A femtosecond optical pulse creates excitonic electron–hole pairs in the layered dichalcogenide tungsten diselenide while a strong terahertz field accelerates and collides the electrons with the holes. The underlying wave packet dynamics, including collision, pair annihilation, quantum interference and dephasing, are detected as light emission in high-order spectral sidebands17–19 of the optical excitation. A full quantum theory explains our observations microscopically. This approach opens the door to collision experiments with a broad variety of complex quasiparticles and suggests a promising new way of sub-femtosecond pulse generation.

As conventional electronics is approaching its ultimate limits1, nanoscience has urgently sought for novel fast control concepts of electrons at the fundamental quantum level2. Lightwave electronics3 – the foundation of attosecond science4 – utilizes the oscillating carrier wave of intense light pulses to control the translational motion of the electron’s charge faster than a single cycle of light5–15. Despite being particularly promising information carriers, the internal quantum attributes of spin16 and valley pseudospin17–19 have not been switchable on the subcycle scale20–21. Here we demonstrate lightwave-driven changes of the valley pseudospin and introduce distinct signatures in the optical read out. Photogenerated electron–hole pairs in a monolayer of tungsten diselenide are accelerated and collided by a strong lightwave. The emergence of high odd-order sidebands and anomalous changes in their polarization direction directly attest to the ultrafast pseudospin dynamics. Quantitative computations combining density-functional theory with a non-perturbative quantum many-body approach assign the polarization of the sidebands to a lightwave-induced change of the valley pseudospin and confirm that the process is coherent and adiabatic. Our work opens the door to systematic valleytronic logic at optical clock rates.

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