77 research outputs found
Notes on Wick's theorem in many-body theory
In these pedagogical notes I introduce the operator form of Wick's theorem,
i.e. a procedure to bring to normal order a product of 1-particle creation and
destruction operators, with respect to some reference many-body state. Both the
static and the time- ordered cases are presented.Comment: 6 page
Simple conformally recurrent space-times are conformally recurrent PP-waves
We show that in dimension n>3 the class of simple conformally recurrent
space-times coincides with the class of conformally recurrent pp-waves.Comment: Dedicated to the memory of professor Witold Rote
Extended Derdzinski-Shen theorem for the Riemann tensor
We extend a classical result by Derdzinski and Shen, on the restrictions
imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor.
The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms)
as well as tensors with gauged Codazzi condition (i.e. "recurrent 1-forms"),
typical of some well known differential structures.Comment: 5 page
Twisted Lorentzian manifolds, a characterization with torse-forming time-like unit vectors
Robertson-Walker and Generalized Robertson-Walker spacetimes may be
characterized by the existence of a time-like unit torse-forming vector field,
with other constrains. We show that Twisted manifolds may still be
characterized by the existence of such (unique) vector field, with no other
constrain. Twisted manifolds generalize RW and GRW spacetimes by admitting a
scale function that depends both on time and space. We obtain the Ricci tensor,
corresponding to the stress-energy tensor of an imperfect fluid.Comment: 6 pages, marginal errors corrected, reference update
Non-Hermitian spectra and Anderson localization
The spectrum of exponents of the transfer matrix provides the localization
lengths of Anderson's model for a particle in a lattice with disordered
potential. I show that a duality identity for determinants and Jensen's
identity for subharmonic functions, give a formula for the spectrum in terms of
eigenvalues of the Hamiltonian with non-Hermitian boundary conditions. The
formula is exact; it involves an average over a Bloch phase, rather than
disorder. A preliminary investigation of non-Hermitian spectra of Anderson's
model in D=1,2 and on the smallest exponent is presented.Comment: 8 pages, 10 figure
Cosmological perfect-fluids in f(R) gravity
We show that an n-dimensional generalized Robertson-Walker (GRW) space-time
with divergence-free conformal curvature tensor exhibits a perfect fluid
stress-energy tensor for any f(R) gravity model. Furthermore we prove that a
conformally flat GRW space-time is still a perfect fluid in both f(R) and
quadratic gravity where other curvature invariants are considered.Comment: 13 pages, final versio
Devil's staircase phase diagram of the fractional quantum Hall effect in the thin-torus limit
After more than three decades the fractional quantum Hall effect still poses
challenges to contemporary physics. Recent experiments point toward a fractal
scenario for the Hall resistivity as a function of the magnetic field. Here, we
consider the so-called thin-torus limit of the Hamiltonian describing
interacting electrons in a strong magnetic field, restricted to the lowest
Landau level, and we show that it can be mapped onto a one-dimensional lattice
gas with repulsive interactions, with the magnetic field playing the role of a
chemical potential. The statistical mechanics of such models leads to interpret
the sequence of Hall plateaux as a fractal phase diagram, whose landscape shows
a qualitative agreement with experiments.Comment: 5 pages main text, 11 pages supplementary, 2 figure
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