23,297 research outputs found
The homotopy theory of dg-categories and derived Morita theory
The main purpose of this work is the study of the homotopy theory of
dg-categories up to quasi-equivalences. Our main result provides a natural
description of the mapping spaces between two dg-categories and in
terms of the nerve of a certain category of -bimodules. We also prove
that the homotopy category is cartesian closed (i.e. possesses
internal Hom's relative to the tensor product). We use these two results in
order to prove a derived version of Morita theory, describing the morphisms
between dg-categories of modules over two dg-categories and as the
dg-category of -bi-modules. Finally, we give three applications of our
results. The first one expresses Hochschild cohomology as endomorphisms of the
identity functor, as well as higher homotopy groups of the \emph{classifying
space of dg-categories} (i.e. the nerve of the category of dg-categories and
quasi-equivalences between them). The second application is the existence of a
good theory of localization for dg-categories, defined in terms of a natural
universal property. Our last application states that the dg-category of
(continuous) morphisms between the dg-categories of quasi-coherent (resp.
perfect) complexes on two schemes (resp. smooth and proper schemes) is
quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect)
on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm.
8.15 is new. Minor corrections. Final version, to appear in Inventione
Nonequilibrium effects due to charge fluctuations in intrinsic Josephson systems
Nonequilibrium effects in layered superconductors forming a stack of
intrinsic Josephson junctions are investigated. We discuss two basic
nonequilibrium effects caused by charge fluctuations on the superconducting
layers: a) the shift of the chemical potential of the condensate and b) charge
imbalance of quasi-particles, and study their influence on IV-curves and the
position of Shapiro steps.Comment: 17 pages, 2 figures, revised version slightly shortene
The Invisible Thin Red Line
The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)’s non-standard tense realism, according to which reality is divided up into maximally coherent collections of tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world
Symmetry Breaking in Linearly Coupled Dynamical Lattices
We examine one- and two-dimensional (1D and 2D) models of linearly coupled
lattices of the discrete-nonlinear-Schr{\"{o}}dinger type. Analyzing ground
states of the systems with equal powers in the two components, we find a
symmetry-breaking phenomenon beyond a critical value of the squared -norm.
Asymmetric states, with unequal powers in their components, emerge through a
subcritical pitchfork bifurcation, which, for very weakly coupled lattices,
changes into a supercritical one. We identify the stability of various solution
branches. Dynamical manifestations of the symmetry breaking are studied by
simulating the evolution of the unstable branches. The results present the
first example of spontaneous symmetry breaking in 2D lattice solitons. This
feature has no counterpart in the continuum limit, because of the collapse
instability in the latter case.Comment: 9 pages, 9 figures, submitted to Phys. Rev. E, Apr, 200
Revisiting Clifford algebras and spinors III: conformal structures and twistors in the paravector model of spacetime
This paper is the third of a series of three, and it is the continuation of
math-ph/0412074 and math-ph/0412075. After reviewing the conformal spacetime
structure, conformal maps are described in Minkowski spacetime as the twisted
adjoint representation of the group Spin_+(2,4), acting on paravectors.
Twistors are then presented via the paravector model of Clifford algebras and
related to conformal maps in the Clifford algebra over the lorentzian R{4,1}$
spacetime. We construct twistors in Minkowski spacetime as algebraic spinors
associated with the Dirac-Clifford algebra Cl(1,3)(C) using one lower spacetime
dimension than standard Clifford algebra formulations, since for this purpose
the Clifford algebra over R{4,1} is also used to describe conformal maps,
instead of R{2,4}. Although some papers have already described twistors using
the algebra Cl(1,3)(C), isomorphic to Cl(4,1), the present formulation sheds
some new light on the use of the paravector model and generalizations.Comment: 17 page
Semi-classical spectrum of integrable systems in a magnetic field
The quantum dynamics of an electron in a uniform magnetic field is studied
for geometries corresponding to integrable cases. We obtain the uniform
asymptotic approximation of the WKB energies and wavefunctions for the
semi-infinite plane and the disc. These analytical solutions are shown to be in
excellent agreement with the numerical results obtained from the Schrodinger
equations even for the lowest energy states. The classically exact notions of
bulk and edge states are followed to their semi-classical limit, when the
uniform approximation provides the connection between bulk and edge.Comment: 17 pages, Revtex, 6 figure
Spectral signature of short attosecond pulse trains
We report experimental measurements of high-order harmonic spectra generated
in Ar using a carrier-envelope-offset (CEO) stabilized 12 fs, 800nm laser field
and a fraction (less than 10%) of its second harmonic. Additional spectral
peaks are observed between the harmonic peaks, which are due to interferences
between multiple pulses in the train. The position of these peaks varies with
the CEO and their number is directly related to the number of pulses in the
train. An analytical model, as well as numerical simulations, support our
interpretation
Semiclassical Quantisation Using Diffractive Orbits
Diffraction, in the context of semiclassical mechanics, describes the manner
in which quantum mechanics smooths over discontinuities in the classical
mechanics. An important example is a billiard with sharp corners; its
semiclassical quantisation requires the inclusion of diffractive periodic
orbits in addition to classical periodic orbits. In this paper we construct the
corresponding zeta function and apply it to a scattering problem which has only
diffractive periodic orbits. We find that the resonances are accurately given
by the zeros of the diffractive zeta function.Comment: Revtex document. Submitted to PRL. Figures available on reques
Neutron scattering study of the magnetic phase diagram of underdoped YBa(2)Cu(3)O(6+x)
We present a neutron triple-axis and resonant spin-echo spectroscopy study of
the spin correlations in untwinned YBCO crystals with x= 0.3, 0.35, and 0.45 as
a function of temperature and magnetic field. As the temperature T approaches
0, all samples exhibit static incommensurate magnetic order with propagation
vector along the a-direction in the CuO2 planes. The incommensurability delta
increases monotonically with hole concentration, as it does in LSCO. However,
delta is generally smaller than in LSCO at the same doping level. The intensity
of the incommensurate Bragg reflections increases with magnetic field for
YBCO(6.45) (superconducting Tc = 35 K), whereas it is field-independent for
YBCO(6.35) (Tc = 10 K). These results suggest that YBCO samples with x ~ 0.5
exhibit incommensurate magnetic order in the high fields used for the recent
quantum oscillation experiments on this system, which likely induces a
reconstruction of the Fermi surface. We present neutron spin-echo measurements
(with energy resolution ~ 1 micro-eV) for T > 0 that demonstrate a continuous
thermal broadening of the incommensurate magnetic Bragg reflections into a
quasielastic peak centered at excitation energy E = 0, consistent with the
zero-temperature transition expected for a two-dimensional spin system with
full spin-rotation symmetry. Measurements on YBCO(6.45) with a triple-axis
spectrometer (with energy resolution ~ 100 micro-eV) yield a crossover
temperature T_SDW ~ 30 K for the onset of quasi-static magnetic order. Upon
further heating, the wavevector characterizing low-energy spin excitations
approaches the commensurate antiferromagnetic wave vector, and the
incommensurability vanishes in an order-parameter-like fashion at an
"electronic liquid-crystal" onset temperature T_ELC ~ 150 K. Both T_SDW and
T_ELC increase continuously as the Mott-insulating phase is approached with
decreasing doping level.Comment: to appear in a special issue on "Fermiology of Cuprates" of the New
Journal of Physic
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