Related papers: Exceptional points in Gaussian channels: diffusion…
We consider a specific continuous-spin Gibbs distribution $\mu_{t=0}$ for a double-well potential that allows for ferromagnetic ordering. We study the time-evolution of this initial measure under independent diffusions. For `high…
We consider the dynamics of systems with arbitrary friction and diffusion. These include, as a special case, systems for which friction and diffusion are connected by Einstein fluctuation-dissipation relation, e.g. Brownian motion. We study…
Recent progress in experimental techniques such as single particle tracking allows to analyze both nonequilibrium properties and approach to equilibrium. There are examples showing that processes occurring at finite timescales are…
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small…
In charged fluids obeying particle-hole symmetry, such as the Dirac fluid in graphene, charge transport is diffusive despite the presence of ballistically propagating sound waves: sound waves "hydrodynamically decouple" from the slower…
Realistic multi-qubit noise processes often result in error mechanisms that are not captured by the probabilistic, Markovian error models commonly employed in circuit-level analyses of quantum fault-tolerance. By working within an…
At high temperature, generic strongly interacting spin systems are expected to display hydrodynamics: local transport of conserved quantities, governed by classical partial differential equations like the diffusion equation. I argue that…
Usually, when investigating exceptional points (EPs) of an open Markovian bosonic system, one deals with spectral degeneracies of a non-Hermitian Hamiltonian (NHH), which can correctly describe the system dynamics only in the semiclassical…
We address propagation and entanglement of Gaussian states in optical media characterised by non-trivial spectral densities. In particular, we consider environments with a finite bandwidth and show that in the low temperature regime: i)…
This work develops a duality theory for partially observed linear Gaussian models in discrete time. The state process evolves according to a causal but non-Markovian (or higher-order Gauss-Markov) structure, captured by a lower-triangular…
We present the starblade algorithm, a method to separate superimposed point sources from auto-correlated, diffuse flux using a Bayesian model. Point sources are assumed to be independent from each other and to follow a power-law brightness…
Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously…
We consider the problem of parameter estimation in the case of observation of the trajectory of diffusion process. We suppose that the drift coefficient has a singularity of cusp-type and the unknown parameter corresponds to the position of…
Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate towards the steady state, but it does not necessarily give a correct estimate of the…
Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into…
In view of controlling finite dimensional open quantum systems, we provide a unified Lie-semigroup framework describing the structure of completely positive trace-preserving maps. It allows (i) to identify the Kossakowski-Lindblad…
We propose that quantum physics is the continuous approximation of a more fundamental, discrete graph theory (theory X). Accordingly, the Euclidean transition amplitude Z provides a partition function for geometries over the graph, which is…
We establish the large deviation principle for the slow variables in slow-fast dynamical system driven by both Brownian noises and L\'evy noises. The fast variables evolve at much faster time scale than the slow variables, but they are…
Being concerned with ergodicity of McKean--Vlasov SDEs, we establish a general result on exponential ergodicity in the $L^1$-Wasserstein distance. The result is successfully applied to non-degenerate and multiplicative Brownian motion…
Spectral degeneracies in Liouvillian generators of dissipative dynamics generically occur as exceptional points, where the corresponding non-Hermitian operator becomes non-diagonalizable. Steady states, i.e. zero-modes of Liouvillians, are…