Related papers: The Feedback Hamiltonian is the Score Function: A …
Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction…
We show how methods from Hamiltonian Floer theory can be used to establish lower bounds for the number of different time-periodic measures of time-periodic Hamiltonian systems with diffusion. After proving the existence of closed random…
Suppose a quantum system starts to evolve under a Hamiltonian from some initial state. When for the first time, will an observable attain a preassigned value? To answer this question, one method often adopted is to make instantaneous…
We consider a {\em Hamiltonian setup} $\sextuple$, where $(\mathcal M,\omega)$ is a symplectic manifold, $\mathfrak L$ is a distribution of Lagrangian subspaces in $\mathcal M$, $\mathcal P$ a Lagrangian submanifold of $ \mathcal M$, $H$ is…
Given a planar domain $D$, the harmonic measure distribution function $h_D(r)$, with base point $z$, is the harmonic measure with pole at $z$ of the parts of the boundary which are within a distance $r$ of $z$. Equivalently it is the…
Diffusion is an ubiquitous phenomenon. It is a widespread belief that as long as the area under a current autocorrelation function converges in time, the corresponding spatiotemporal density dynamics should be diffusive. This may be viewed…
We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how…
We introduce a framework that unifies quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows. We do so by providing explicit expressions for stochastic Hamiltonians that produce state dynamics identical to…
Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data,…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
In many practical reinforcement learning tasks, feedback is only provided at the end of a long horizon, leading to sparse and delayed rewards. Existing reward redistribution methods typically assume that per-step rewards are independent,…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
Oftentimes, environments for sequential decision-making problems can be quite sparse in the provision of evaluative feedback to guide reinforcement-learning agents. In the extreme case, long trajectories of behavior are merely punctuated…
In this work, we study the generalizability of diffusion models by looking into the hidden properties of the learned score functions, which are essentially a series of deep denoisers trained on various noise levels. We observe that as…
The microscopic origin of dissipation of a driven quantum many body system is addressed in the framework of a parametric banded random matrix approach. We find noticeable violations of the fluctuation-dissipation theorem and we observe also…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
Time-continuous quantum measurement allows for the tracking of a quantum system in real time via sequences of short, and individually weak, measurement intervals. Such measurements are necessarily invasive, imparting backaction to the…
Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of…