1,160 research outputs found
Skeletons and Variation
Well known from the sixties, the pressure of e.g. massless phi-four theory
may be written as a series of 2PI-diagrams (skeletons) with the lines fully
dressed. Varying the self-energy Pi in this expression, it turns into a
functional U[Y] having a maximum in function space at Y=Pi. There is also the
Feynman-Jensen thermal variational principle V[S], a potentially
non-perturbative tool. Here actions S are varied.
It is shown, through a few formal but exact steps, that the functional U is
covered by V. The corresponding special subset of trial actions is made
explicit.Comment: 4 pages RevTeX; talk at the 5th Thermal Field Theory Workshop 1998 at
Regensburg, Germany, August 10-14; text around (9), (10) improve
Hamiltonian YM 2+1: note on point splitting regularization
The Hamiltonian of 2+1 dimensional Yang Mills theory was derived by Karabali,
Kim and Nair by using point splitting regularization. But in calculating e.g.
the vacuum wave functional this scheme was left in favour of arguments. Here we
follow up a conjecture of Leigh, Minic and Yelnikov of how this gap might be
filled by including all positive powers of the regularization parameter (\ep
\to +0). Admittedly, though we concentrate on the ground state in the large
limit, only two such powers could be included due to the increasing
complexity of the task.Comment: 25 page
Geometry of Weyl theory for Jacobi matrices with matrix entries
A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal
matrix with invertible blocks on the off-diagonals. The Weyl surface describing
the dependence of Green's matrix on the boundary conditions is interpreted as
the set of maximally isotropic subspace of a quadratic from given by the
Wronskian. Analysis of the possibly degenerate limit quadratic form leads to
the limit point/limit surface theory of maximal symmetric extensions for
semi-infinite Jacobi matrices with matrix entries with arbitrary deficiency
indices. The resolvent of the extensions is explicitly calculated
Perturbation theory for Lyapunov exponents of an Anderson model on a strip
It is proven that the inverse localization length of an Anderson model on a
strip of width is bounded above by for small values of the
coupling constant of the disordered potential. For this purpose, a
formalism is developed in order to calculate the bottom Lyapunov exponent
associated with random products of large symplectic matrices perturbatively in
the coupling constant of the randomness.Comment: to appear in GAF
The density of surface states as the total time delay
For a scattering problem of tight-binding Bloch electrons by a weak random
surface potential, a generalized Levinson theorem is put forward showing the
equality of the total density of surface states and the density of the total
time delay. The proof uses explicit formulas for the wave operators in the new
rescaled energy and interaction (REI) representation, as well as an index
theorem for adequate associated operator algebras.Comment: Suggestions of referees incorporated and errors corrected. To appear
in Lett. Math. Phy
Topological insulators from the perspective of non-commutative geometry and index theory
Topological insulators are solid state systems of independent electrons for
which the Fermi level lies in a mobility gap, but the Fermi projection is
nevertheless topologically non-trivial, namely it cannot be deformed into that
of a normal insulator. This non-trivial topology is encoded in adequately
defined invariants and implies the existence of surface states that are not
susceptible to Anderson localization. This non-technical review reports on
recent progress in the understanding of the underlying mathematical structures,
with a particular focus on index theory.Comment: to appear in Jahresberichte DM
Lifshitz tails for the 1D Bernoulli-Anderson model
By using the adequate modified Pr\"ufer variables, precise upper and lower
bounds on the density of states in the (internal) Lifshitz tails are proven for
a 1D Anderson model with bounded potential
Rotation numbers for Jacobi matrices with matrix entries
A selfadjoined block tridiagonal matrix with positive definite blocks on the
off-diagonals is by definition a Jacobi matrix with matrix entries. Transfer
matrix techniques are extended in order to develop a rotation number
calculation for its eigenvalues. This is a matricial generalization of the
oscillation theorem for the discrete analogues of Sturm-Liouville operators.
The three universality classes of time reversal invariance are dealt with by
implementing the corresponding symmetries. For Jacobi matrices with random
matrix entries, this leads to a formula for the integrated density of states
which can be calculated perturbatively in the coupling constant of the
randomness with an optimal control on the error terms
Persistence of spin edge currents in disordered quantum spin Hall systems
For a disordered two-dimensional model of a topological insulator (such as a
Kane-Mele model with disordered potential) with small coupling of spin
invariance breaking term (such as the Rashba coupling), it is proved that the
spin edge currents persist provided there is a spectral gap and the spin Chern
numbers are well-defined and non-trivial. These conditions on being in the
quantum spin Hall phase do not require time-reversal symmetry. The result
materializes the general philosophy that topological insulators are non-trivial
bulk systems with edge currents that are topologically protected against
Anderson localization.Comment: Final version to appear in Commun. Math. Phy
Resummation of phi^4 free energy up to an arbitrary order
The consistency condition, which guarantees a well organized small-coupling
asymptotic expansion for the thermodynamics of massless -theory, is
generalized to any desired order of the perturbative treatment. Based on a
strong conjecture about forbidden two-particle reducible diagrams, this
condition is derived in terms of functions of four-momentum in place of the
common toy mass in previous treatments. It has the form of a set of gap
equations and marks the position in the space of these functions at which the
free energy is extremal.Comment: 15 pages, latex, 3 figures using latex, more discussion below (4.14),
3 Ref's added, slight changes in notatio
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