16,392 research outputs found
Exponential decay of correlation for the Stochastic Process associated to the Entropy Penalized Method
In this paper we present an upper bound for the decay of correlation for the
stationary stochastic process associated with the Entropy Penalized Method. Let
L(x, v):\Tt^n\times\Rr^n\to \Rr be a Lagrangian of the form
L(x,v) = {1/2}|v|^2 - U(x) + .
For each value of and , consider the operator
\Gg[\phi](x):= -\epsilon h {ln}[\int_{\re^N} e
^{-\frac{hL(x,v)+\phi(x+hv)}{\epsilon h}}dv], as well as the reversed operator
\bar \Gg[\phi](x):= -\epsilon h {ln}[\int_{\re^N}
e^{-\frac{hL(x+hv,-v)+\phi(x+hv)}{\epsilon h}}dv], both acting on continuous
functions \phi:\Tt^n\to \Rr. Denote by the solution of
\Gg[\phi_{\epsilon,h}]=\phi_{\epsilon,h}+\lambda_{\epsilon,h}, and by the solution of \bar \Gg[\phi_{\epsilon,h}]=\bar
\phi_{\epsilon,h}+\lambda_{\epsilon,h}. In order to analyze the decay of
correlation for this process we show that the operator has a maximal
eigenvalue isolated from the rest of the spectrum
Majorana Fermions Signatures in Macroscopic Quantum Tunneling
Thermodynamic measurements of magnetic fluxes and I-V characteristics in
SQUIDs offer promising paths to the characterization of topological
superconducting phases. We consider the problem of macroscopic quantum
tunneling in an rf-SQUID in a topological superconducting phase. We show that
the topological order shifts the tunneling rates and quantum levels, both in
the parity conserving and fluctuating cases. The latter case is argued to
actually enhance the signatures in the slowly fluctuating limit, which is
expected to take place in the quantum regime of the circuit. In view of recent
advances, we also discuss how our results affect a -junction loop.Comment: 10 pages, 11 figure
A dynamical point of view of Quantum Information: entropy and pressure
Quantum Information is a new area of research which has been growing rapidly
since last decade. This topic is very close to potential applications to the so
called Quantum Computer. In our point of view it makes sense to develop a more
"dynamical point of view" of this theory. We want to consider the concepts of
entropy and pressure for "stationary systems" acting on density matrices which
generalize the usual ones in Ergodic Theory (in the sense of the Thermodynamic
Formalism of R. Bowen, Y. Sinai and D. Ruelle). We consider the operator
acting on density matrices over a finite
-dimensional complex Hilbert space where and , are
operators in this Hilbert space. is not a linear operator. In
some sense this operator is a version of an Iterated Function System (IFS).
Namely, the , , play the role of the
inverse branches (acting on the configuration space of density matrices )
and the play the role of the weights one can consider on the IFS. We
suppose that for all we have that . A
family determines a Quantum Iterated Function System
(QIFS) , $\mathcal{F}_W=\{\mathcal{M}_N,F_i,W_i\}_{i=1,...,
k}.
A dynamical point of view of Quantum Information: Wigner measures
We analyze a known version of the discrete Wigner function and some
connections with Quantum Iterated Funcion Systems. This paper is a follow up of
"A dynamical point of view of Quantum Information: entropy and pressure" by the
same authors
Spectral Properties of the Ruelle Operator for Product Type Potentials on Shift Spaces
We study a class of potentials on one sided full shift spaces over finite
or countable alphabets, called potentials of product type. We obtain explicit
formulae for the leading eigenvalue, the eigenfunction (which may be
discontinuous) and the eigenmeasure of the Ruelle operator. The uniqueness
property of these quantities is also discussed and it is shown that there
always exists a Bernoulli equilibrium state even if does not satisfy
Bowen's condition. We apply these results to potentials of the form with . For , we obtain the existence of
two different eigenfunctions. Both functions are (locally) unbounded and exist
a.s. (but not everywhere) with respect to the eigenmeasure and the measure of
maximal entropy, respectively.Comment: To appear in the Journal of London Mathematical Societ
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