Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of [43], seeing it as a quantisation of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial da ...
. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...
Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...
We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest a ...
Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of statistical physic ...
In spin systems, geometrical frustration describes the impossibility of minimizing simultaneously all the interactions in a Hamiltonian, often giving rise to macroscopic ground-state degeneracies and emergent low-temperature physics. In this thesis, combin ...
The Renyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field lambda that controls the partition function topology, all ...
Investigating the effect of isotope substitution on equilibrium and kinetic properties of molecules has become an important tool for estimating the importance of nuclear quantum effects. In this work, we discuss calculating both equilibrium and kinetic iso ...
It is known that not all summation methods are linear and stable. Zeta function regularization is in general nonlinear. However, in some cases formal manipulations with zeta function regularization (assuming linearity of sums) lead to correct results. We c ...
We consider the parabolic Anderson model on Zd driven by fractional noise. We prove that it has a mild solution given by Feynman-Kac representation which coincides with the partition function of a directed polymer in a fractional Brownian envir ...
We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit ...
A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibratio ...
Many different algorithms developed in statistical physics, coding theory, signal processing, and artificial intelligence can be expressed by graphical models and solved (either exactly or approximately) with iterative message-passing algorithms on the mod ...
We study the statistical properties of the potential energy landscape of a system of particles interacting via a very short-range square-well potential (of depth - u0) as a function of the range of attraction Δ to provide thermodynamic insights of the Noro ...
In this article, we describe the application of an enhanced genetic algorithm to the problem of hardware-software codesign. Starting from a source code written in a high-level language our algorithm determines, using a dynamically-weighted fitness function ...
