arXiv subjects

Razvan Teodorescu

Publications and source records attributed to Razvan Teodorescu.

23 records · Page 2Linked to original sources

arXiv2008

Belief Propagation and Loop Series on Planar Graphs

We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of [1, 2] is used to evaluate the resulting series expansion for the partition function. We show that, for planar graphs, truncating the series at single-connected loops reduces, via a map reminiscent of the Fisher transformation [3], to evaluating the partition function of the dimer matching model on an auxiliary planar graph. Thus, the truncated series can be easily re-summed, using the Pfaffian formula of Kasteleyn [4]. This allows to identify a big class of computationally tractable planar models reducible to a dimer model via the Belief Propagation (gauge) transformation. The Pfaffian representation can also be extended to the full Loop Series, in which case the expansion becomes a sum of Pfaffian contributions, each associated with dimer matchings on an extension to a subgraph of the original graph. Algorithmic consequences of the Pfaffian representation, as well as relations to quantum and non-planar models, are discussed.

cond-mat.stat-mech↗

arXiv2007

Non-equilibrium thermodynamics for functionals of current and density

We study a stochastic many-body system maintained in an non-equilibrium steady state. Probability distribution functional of the time-integrated current and density is shown to attain a large-deviation form in the long-time asymptotics. The corresponding Current-Density Cramer Functional (CDCF) is explicitly derived for irreversible Langevin dynamics and discrete-space Markov chains. We also show that the Cramer functionals of other linear functionals of density and current, like work generated by a force, are related to CDCF in a way reminiscent of variational relations between different thermodynamic potentials. The general formalism is illustrated with a model example.

cond-mat.stat-mech↗

arXiv2007

Coherent oscillations in superconducting cold Fermi atoms and their applications

Recent achievements in experiments with cold fermionic atoms indicate the potential for developing novel superconducting devices which may be operated in a wide range of regimes, at a level of precision previously not available. Unlike traditional, solid-state superconducting devices, the cold-atom systems allow the fast switching on of the BCS phase, and the observation of non-equilibrium, coherent oscillations of the order parameter. The integrable and non-linear nature of the equations of motions makes this operating regime particularly rich in potential applications, such as quantum modulation and encoding, or nonlinear mixing of quantum coherent oscillations, to name only two. From a mathematical point of view, such systems can be described using the Knizhnik-Zamolodchikov-Bernard equation, or more generally, by the matrix Kadomtsev-Petviashvilii integrable hierarchy. This identification is particularly useful, since it allows a direct application of the known non-linear phenomena described by particular solutions of these equations. Other important features of this formulation, such as the relation to the spin Calogero-Sutherland model, also have relevant physical interpretations. In this work, a complete description of these relationships is presented, along with their potential practical consequences.

cond-mat.str-el↗

arXiv2005

Relaxation of nonlinear oscillations in BCS superconductivity

The diagonal case of the $sl(2)$ Richardson-Gaudin quantum pairing model \cite{Richardson1,Richardson2,Richardson3,Richardson4,Richardson5,Richardson6,G audin76} is known to be solvable as an Abel-Jacobi inversion problem \cite{SOV,Kuznetzov,Kuz1,Kuz2,Kuz3,Kuz4,Kuz5,YAKE04}. This is an isospectral (stationary) solution to a more general integrable hierarchy, in which the full time evolution can be written as isomonodromic deformations. Physically, the more general solution is appropriate when the single-particle electronic spectrum is subject to external perturbations. The asymptotic behavior of the nonlinear oscillations in the case of elliptic solutions is derived.

nlin.SI↗

arXiv2005

Generic critical points of normal matrix ensembles

The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian Growth. It is shown that the scaling behavior at a critical point of singular geometry $x^3 \sim y^2$ is described by the first Painlevé transcendent. The regularization of the curve resulting from discretization is discussed.

math-ph↗