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A Short Survey on the Integral Identity Conjectureand Theories of Motivic Integration
(2016-12-16)
In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ...
The challenge of brain complexity: A brief discussion about a fractal intermittency-based approach
(2016-10-30)
In the last years, the complexity paradigm is gaining momentum in many research fields where large multidimensional datasets are made available by the advancements in instrumental technology. A complex system is a ...
Geometric inequalities from phase space translations
(2016-07-22)
We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results ...
Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory
(2016-01-01)
We generalize to multi–commutators the usual Lieb–Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expan- sions) ...
Fractional kinetics emerging from ergodicity breaking in random media
(2016)
We present a modelling approach for diffusion in a complex medium characterized by a random lengthscale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle ...
Diagonalizing quadratic bosonic operators by non-autonomous flow equations volker bach
(2016-01-01)
We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics ...
Equisingularity in One-Parameter Families of Generically Reduced Curves
(2016-01-01)
We explore some equisingularity criteria in one-parameter families of generically reduced curves. We prove the equivalence between Whitney regularity and Zariski’s discriminant criterion. We prove that topological triviality ...
Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction
(2016-01-01)
We study the time evolution of a system of $N$ spinless fermions in $\mathbb{R}^3$ which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation ...
Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles
(2016-01-01)
We apply Lieb–Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) ...
Universal Bounds for Large Determinants from Non–Commutative Ho ̈lder Inequalities in Fermionic Constructive Quantum Field Theory
(2016-01-01)
Efficiently bounding large determinants is an essential step in non–relati- vistic fermionic constructive quantum field theory, because, together with the summability of the interaction and the covariance, it implies the ...