Related papers: Transfer operators and topological field theory
Continuous spectrum operators (CSOs), characterized by spectra comprising continuous intervals rather than discrete eigenvalues, are pivotal in quantum mechanics, wave propagation, and systems governed by partial differential equations.…
For strongly continous semigroups on Hilbert spaces, we investigate admissibility properties of control and observation operators shifted along continuous scales of spaces built by means of either interpolation and extrapolation or…
Stochastic differential equations are ubiquitous modelling tools in physics and the sciences. In most modelling scenarios, random fluctuations driving dynamics or motion have some non-trivial temporal correlation structure, which renders…
In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as…
To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is…
Strontium titanate ($\mathrm{SrTiO_3, STO}$) dome-shaped superconducting transition temperature as a function of chemical potential, consistent with STO experiments, and shows that tunable s-wave and d-wave symmetries are modulated by…
We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as…
A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of…
We provide a new perspective on quantum dynamical phase transitions (DPTs) by explaining their origin in terms of caustics that form in the Fock space representation of the many-body state over time, using the fully connected transverse…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…
This paper introduces a randomized tamed Euler scheme tailored for L\'evy-driven stochastic differential equations (SDEs) with superlinear random coefficients and Carath\'eodory-type drift. Under assumptions that allow for time-irregular…
We consider a particular example of interplay between statistical models related to CFT on one hand, and to the spectral properties of ODE, known as ODE/IS correspondence, on the other hand. We focus at the representation of wave functions…
A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion…
We consider a family of potentials f, derived from the Hofbauer potentials, on the symbolic space Omega=\{0,1\}^\mathbb{N} and the shift mapping $\sigma$ acting on it. A Ruelle operator framework is employed to show there is a phase…
Transfer operators are conjectural "operators of functoriality," which transfer test measures and (relative) characters from one homogeneous space to another. In previous work, I computed transfer operators associated to spherical varieties…
Periodically driven quantum systems can host non-equilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover $temporal$ $entanglement$ $transitions$ (TET) in a Floquet spin chain, which…
Periodic orbit theory is an effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the…
We define the prequantization of a symplectic Anosov diffeomorphism f:M-> M, which is a U(1) extension of the diffeomorphism f preserving an associated specific connection, and study the spectral properties of the associated transfer…
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
A typical f-electron Kondo lattice system Ce exhibits the well-known isostructural transition, the so-called gamma-alpha transition, accompanied by an enormous volume collapse. Most interestingly, we have discovered that a topological-phase…