1,721,159 research outputs found
A Doob h-Transform of the Gross-Pitaevskii Hamiltonian
No full textWe perform a Doob h-transformation of the N-body
Hamiltonian for N trapped interacting Bose particles starting from
the unique real strictly positive ground state. This identifies the
unitarily equivalent Markov generator describing the N interacting
diffusion processes. By applying the convergence results coming
from the Gross-Pitaevskii (GP) scaling limit to the energy form
associated with this Markov generator we obtain the asymptotic
generator uniquely corresponding to the GP Hamiltonian, which
has been rigorously derived from the N-body Hamiltonian by performing
the same scaling limit. Our asymptotic generator is a
non linear diffusion generator with a killing rate governed by the
GP order parameter. The associated stochastic process properly
describes the single particle motion in the Bose-Einstein condensate
including the self-interaction which acts here as a probability
density-dependent killing rate. Finally, in a one-dimensional setting,
we discuss under which conditions the process conditioned to
survival converges to a quasi-stationary distribution having density
with respect to the speed measure given by the principal eigenfunction
of the diffusion generator with killing
Complex Dirichlet Forms: Non symmetric Diffusion Processes and Schoedinger Operators
No full textThe concept of complex Dirichlet forms epsilon_c resp.operators L_c in complex weighted L^2-spaces is introduced. Perturbations of classical Dirichlet forms by forms associated with complex first-order differential operators provide examples of complex Dirichlet forms. Complex Dirichlet operators L_c are unitarily equivalent with (a family of) Schroedinger operators with electromagnetic potentials. To epsilon_c there is associated a pair of real-valued non symmetric Dirichlet forms on the corresponding real weighted L^2-spaces, which in turn are associated with (non-symmetric) diffusion processes. Results by Stannat on non symmetric Dirichlet forms and their perturbations can be used for discussing the essential self-adjointness of L_c. New closability criteria for (perturbation of) non symmetric Dirichlet forms are obtained
Some results for the exponential interaction in two or more dimensions
No full textWe show that for the regularized exponential interaction \lambda
:e^{\alpha \varphi_x in space-time dimensions the Schwinger functions
converge, upon cut-off removal, to the Schwinger functions for the free
field if for all or if for all such that
$|\alpha|>\alpha_0>0
On the Fourier transform and the spectral properties of the -adic momentum and Schrödinger operators.
No full textThe exponential interaction in
No full textWe prove that removing the ultraviolet cut-off the exponential interaction field theory becomes trivial in space-time dimension >2 at all non zero couplings
and in dimension 2 at large enough couplings
Non-symmetric diffusions and related Hamiltonians
No full textWe exhibit a unitary correspondence between (equivalence classes) of Hamiltonians H (Φ, A), involving electromagnetic potentials (A, Φ), and generators of 'bi-directional' Markov semigroups associated with non-symmetric diffusion processes
An extended Kohonen phonetic map
No full textThis letter contains an approach to improve the Kohonen phonetic typewriter [1] by enlarging the phonetic objects which are used to label the phonetic map: the transitions between phonemes are introduced as new labels of neurons
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