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Register a new userInput and output in damped quantum systems III: Formulation of damped systems driven by Fermion fields
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Authors
C. W. Gardiner
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A comprehensive input-output theory is developed for Fermionic input fields. Quantum stochastic differential equations are developed in both the Ito and Stratonovich forms. The major technical issue is the development of a formalism which takes account of anticommutation relations between the Fermionic driving field and those system operators which can change the number of Fermions within the system.
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This research was stimulated by the recent studies of damping solutions in dynamically stable spherical stellar systems. Using the simplest model of the homogeneous stellar medium, we discuss nontrivial features of stellar systems. Taking them into account will make it possible to correctly interpret the results obtained earlier and will help to set up decisive numerical experiments in the future. In particular, we compare the initial value problem versus the eigenvalue problem. It turns out that in the unstable regime, the Landau-damped waves can be represented as a superposition of van Kampen modes {it plus} a discrete damped mode, usually ignored in the stability study. This mode is a solution complex conjugate to the unstable Jeans mode. In contrast, the Landau-damped waves are not genuine modes: in modes, eigenfunctions depend on time as $exp (-{rm i} omega t)$, while the waves do not have eigenfunctions on the real $v$-axis at all. However, `eigenfunctions on the complex $v$-contours do exist. Deviations from the Landau damping are common and can be due to singularities or cut-off of the initial perturbation above some fixed value in the velocity space.
We report evidence for a bimodality in damped Ly systems (DLAs). Using [C II] 158 mu cooling rates, lc, we find a distribution with peaks at lc=10^-27.4 and 10^-26.6 ergs s^-1 H^-1 separated by a trough at lc^crit ~= lc < 10^-27.0 ergs s^-1 H^-1. We divide the sample into low cool DLAs with lc < lc^crit and high cool DLAs with lc > lc^crit and find the Kolmogorv-Smirnov probabilities that velocity width, metallicity, dust-to-gas ratio, and Si II equivalent width in the two subsamples are drawn from the same parent population are small. All these quantities are significantly larger in the high cool population, while the H I column densities are indistinguishable in the two populations. We find that heating by X-ray and FUV background radiation is insufficient to balance the cooling rates of either population. Rather, the DLA gas is heated by local radiation fields. The rare appearance of faint, extended objects in the Hubble Ultra Deep Field rules out in situ star formation as the dominant star-formation mode for the high cool population, but is compatible with in situ star formation as the dominant mode for the low cool population. Star formation in the high cool DLAs likely arises in Lyman Break galaxies. We investigate whether these properties of DLAs are analogous to the bimodal properties of nearby galaxies. Using Si II equivalent width as a mass indicator, we construct bivariate distributions of metallicity, lc, and areal SFR versus the mass indicators. Tentative evidence is found for correlations and parallel sequences, which suggest similarities between DLAs and nearby galaxies. We suggest that the transition-mass model provides a plausible scenario for the bimodality we have found. As a result, the bimodality in current galaxies may have originated in DLAs.
We propose and analyse analogs of optical cavities for atoms using three-well Bose-Hubbard models with pumping and losses. We consider triangular configurations. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, preserving good coherence between the wells in the steady-state. We find quadrature squeezing and mode entanglement for some parameter regimes and demonstrate that the trimer with pumping and damping at the same well is the stronger option for producing non-classical states. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict.
In this paper, we develop a theory of learning nonlinear input-output maps with fading memory by dissipative quantum systems, as a quantum counterpart of the theory of approximating such maps using classical dynamical systems. The theory identifies the properties required for a class of dissipative quantum systems to be {em universal}, in that any input-output map with fading memory can be approximated arbitrarily closely by an element of this class. We then introduce an example class of dissipative quantum systems that is provably universal. Numerical experiments illustrate that with a small number of qubits, this class can achieve comparable performance to classical learning schemes with a large number of tunable parameters. Further numerical analysis suggests that the exponentially increasing Hilbert space presents a potential resource for dissipative quantum systems to surpass classical learning schemes for input-output maps.
Recent observations have revealed that damped Ly$alpha$ clouds (DLAs) host star formation activity. In order to examine if such star formation activity can be triggered by ionization fronts, we perform high-resolution hydrodynamics and radiative transfer simulations of the effect of radiative feedback from propagating ionization fronts on high-density clumps. We examine two sources of ultraviolet (UV) radiation field to which high-redshift (z ~ 3) galaxies could be exposed: one corresponding to the UV radiation originating from stars within the DLA, itself, and the other corresponding to the UV background radiation. We find that, for larger clouds, the propagating I-fronts created by local stellar sources can trigger cooling instability and collapse of significant part, up to 85%, of the cloud, creating conditions for star formation in a timescale of a few Myr. The passage of the I-front also triggers collapse of smaller clumps (with radii below ~4 pc), but in these cases the resulting cold and dense gas does not reach conditions conducive to star formation. Assuming that 85% of the gas initially in the clump is converted into stars, we obtain a star formation rate of $sim 0.25 M_odot {yr}^{-1} {kpc}^{-2}$. This is somewhat higher than the value derived from recent observations. On the other hand, the background UV radiation which has harder spectrum fails to trigger cooling and collapse. Instead, the hard photons which have long mean-free-path heat the dense clumps, which as a result expand and essentially dissolve in the ambient medium. Therefore, the star formation activity in DLAs is strongly regulated by the radiative feedback, both from the external UV background and internal stellar sources and we predict quiescent evolution of DLAs (not starburst-like evolution).
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