Related papers: Algebraic topology and the quantization of fluctua…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
We present a new approach to study the thermodynamic properties of $d$-dimensional classical systems by reducing the problem to the computation of ground state properties of a $d$-dimensional quantum model. This classical-to-quantum mapping…
We study the quantization of real-valued bandlimited signals on graphs, focusing on low-bit representations. We propose iterative noise-shaping algorithms for quantization, including sampling approaches with and without vertex replacement.…
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
We propose a highly-scalable method to compute the statistics of charge transfer in driven conductors. The framework can be applied in situations of non-zero temperature, strong coupling to terminals and in the presence of non-periodic…
In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged…
In this work we investigate the stability of an algebraically localized phase subject to periodic driving. First, we focus on a non-interacting model exhibiting algebraically localized single-particle modes. For this model we find…
The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a…
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the…
The interplay between chaos and thermalization in weakly non-integrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical…
This paper applies the formalism of classical, Gibbs-Boltzmann statistical mechanics to the phenomenon of non-thermal damage. As an example, a non-thermal fiber-bundle model with the global uniform (meanfield) load sharing is considered.…
Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial…
In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality…
The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new…
Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
Controllability of complex networks arises in many technological problems involving social, financial, road, communication, and smart grid networks. In many practical situations, the underlying topology might change randomly with time, due…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…