10,639 research outputs found
Spin Glass Field Theory with Replica Fourier Transforms
We develop a field theory for spin glasses using Replica Fourier Transforms
(RFT). We present the formalism for the case of replica symmetry and the case
of replica symmetry breaking on an ultrametric tree, with the number of
replicas and the number of replica symmetry breaking steps generic
integers. We show how the RFT applied to the two-replica fields allows to
construct a new basis which block-diagonalizes the four-replica mass-matrix,
into the replicon, anomalous and longitudinal modes. The eigenvalues are given
in terms of the mass RFT and the propagators in the RFT space are obtained by
inversion of the block-diagonal matrix. The formalism allows to express any
-replica vertex in the new RFT basis and hence enables to perform a standard
perturbation expansion. We apply the formalism to calculate the contribution of
the Gaussian fluctuations around the Parisi solution for the free-energy of an
Ising spin glass.Comment: 39 pages, 3 figure
A Laplace transform approach to the quantum harmonic oscillator
The one-dimensional quantum harmonic oscillator problem is examined via the
Laplace transform method. The stationary states are determined by requiring
definite parity and good behaviour of the eigenfunction at the origin and at
infinity
Variational Formulation for Quaternionic Quantum Mechanics
A quaternionic version of Quantum Mechanics is constructed using the
Schwinger's formulation based on measurements and a Variational Principle.
Commutation relations and evolution equations are provided, and the results are
compared with other formulations.Comment: Talk given at ICCA*, May 26-30 of 2008, Campinas, SP, Brazil. 18
pages, no figur
- …