Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp(n,R) of the symplectic model, in particular for the cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. The relationship to the collective dynamics is formulated as a theorem that associates the mapping with an exact solution of the time-dependent Hartree approximation. This solution determines a decoupled classical symplectic manifold, thus satisfying the criteria that define an exactly solvable model in the theory of large amplitude collective motion. The models thus obtained also provide a test of methods for constructing an approximately decoupled manifold in fully realistic cases. We show that an algorithm developed in one of our earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.

Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles

We consider free lattice fermions subjected to a static bounded potential and a time- and space-dependent electric field. For any bounded convex region $\mathcal{R}\subset \mathbb{R}^{d}$ ($d\geq 1$) of space, electric fields $\mathcal{E}$ within $\mathcal{R}$ drive currents. At leading order, uniformly with respect to the volume $\left| \mathcal{R}\right|$ of $\mathcal{R}$ and the particular choice of the static potential, the dependency on $\mathcal{E}$ of the current is linear and described by a conductivity distribution. Because of the positivity of the heat production, the real part of its Fourier transform is a positive measure, named here (microscopic) conductivity measure of $\mathcal{R}$, in accordance with Ohm's law in Fourier space. This finite measure is the Fourier transform of a time-correlation function of current fluctuations, i.e., the conductivity distribution satisfies Green-Kubo relations. We additionally show that this measure can also be seen as the boundary value of the Laplace-Fourier transform of a so-called quantum current viscosity. The real and imaginary parts of conductivity distributions satisfy Kramers-Kronig relations. At leading order, uniformly with respect to parameters, the heat production is the classical work performed by electric fields on the system in presence of currents. The conductivity measure is uniformly bounded with respect to parameters of the system and it is never the trivial measure $0\,\mathrm{d}\nu$. Therefore, electric fields generally produce heat in such systems. In fact, the conductivity measure defines a quadratic form in the space of Schwartz functions, the Legendre-Fenchel transform of which describes the resistivity of the system. This leads to Joule's law, i.e., the heat produced by currents is proportional to the resistivity and the square of currents

A very brief introduction to quantum computing and quantum information theory for mathematicians

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references

On Dimensional Degression in AdS(d)

We analyze the pattern of fields in d+1 dimensional anti-de Sitter space in terms of those in d dimensional anti-de Sitter space. The procedure, which is neither dimensional reduction nor dimensional compactification, is called dimensional degression. The analysis is performed group-theoretically for all totally symmetric bosonic and fermionic representations of the anti-de Sitter algebra. The field-theoretical analysis is done for a massive scalar field in AdS(d+d$^\prime$) and massless spin one-half, spin one, and spin two fields in AdS(d+1). The mass spectra of the resulting towers of fields in AdS(d) are found. For the scalar field case, the obtained results extend to the shadow sector those obtained by Metsaev in [1] by a different method.Comment: 30 page

Transient Nucleation near the Mean-Field Spinodal

Nucleation is considered near the pseudospinodal in a one-dimensional $\phi^4$ model with a non-conserved order parameter and long-range interactions. For a sufficiently large system or a system with slow relaxation to metastable equilibrium, there is a non-negligible probability of nucleation occurring before reaching metastable equilibrium. This process is referred to as transient nucleation. The critical droplet is defined to be the configuration of maximum likelihood that is dynamically balanced between the metastable and stable wells. Time-dependent droplet profiles and nucleation rates are derived, and theoretical results are compared to computer simulation. The analysis reveals a distribution of nucleation times with a distinct peak characteristic of a nonstationary nucleation rate. Under the quench conditions employed, transient critical droplets are more compact than the droplets found in metastable equilibrium simulations and theoretical predictions.Comment: 7 Pages, 5 Figure

Massive color-octet bosons and the charge asymmetries of top quarks at hadron colliders

Several models predict the existence of heavy colored resonances decaying to top quarks in the TeV energy range that might be discovered at the LHC. In some of those models, moreover, a sizable charge asymmetry of top versus antitop quarks might be generated. The detection of these exotic resonances, however, requires selecting data samples where the top and the antitop quarks are highly boosted, which is experimentally very challenging. We asses that the measurement of the top quark charge asymmetry at the LHC is very sensitive to the existence of excited states of the gluon with axial-vector couplings to quarks. We use a toy model with general flavour independent couplings, and show that a signal can be detected with relatively not too energetic top and antitop quarks. We also compare the results with the asymmetry predicted by QCD, and show that its highest statistical significance is achieved with data samples of top-antitop quark pairs of low invariant masses.Comment: 20 page

High-temperature signatures of quantum criticality in heavy fermion systems

We propose a new criterion for distinguishing the Hertz-Millis (HM) and the local quantum critical (LQC) mechanism in heavy fermion systems with a magnetic quantum phase transition (QPT). The criterion is based on our finding that the spin screening of Kondo ions can be completely suppressed by the RKKY coupling to the surrounding magnetic ions even without magnetic ordering and that, consequently, the signature of this suppression can be observed in spectroscopic measurements above the magnetic ordering temperature. We apply the criterion to high-resolution photoemission (UPS) measurements on CeCu$_{6-x}$Au$_{x}$ and conclude that the QPT in this system is dominated by the LQC scenario.Comment: Inveted paper, International Conference on Magnetism, ICM 2009, Karlsruhe. Published version, added discussions of the relevance of Fermi-surface fluctuations and of a structural transition near the QC

Fractal extra dimension in Kaluza-Klein theory

Kaluza-Klein theory in which the geometry of an additional dimension is fractal has been considered. In such a theory the mass of an elementary electric charge appears to be many orders of magnitude smaller than the Planck mass, and the "tower" of masses which correspond to higher integer charges becomes aperiodic.Comment: 3 pages, accepted for publication in Phys.Rev.D (submitted on 3.28.2001

First Order Calculation of the Inclusive Cross Section pp to ZZ by Graviton Exchange in Large Extra Dimensions

We calculate the inclusive cross section of double Z-boson production within large extra dimensions at the Large Hadron Collider (LHC). Using perturbatively quantized gravity in the ADD model we perform a first order calculation of the graviton mediated contribution to the pp to ZZ cross section. At low energies (e.g. Tevatron) this additional contribution is very small, making it virtually unobservable, for a fundamental mass scale above 2500 GeV. At LHC energies however, the calculation indicates that the ZZ-production rate within the ADD model should differ significantly from the Standard Model if the new fundamental mass scale would be below 15000 GeV. A comparison with the observed production rate at the LHC might therefore provide direct hints on the number and structure of the extra dimensions.Comment: 7 pages, 7 figures, accepted for publication in Phys. Rev.