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Related papers: Lindblad evolution as gradient flow

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Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum jumps'' techniques, which solve the master equation by unraveling its evolution into stochastic trajectories in…

Quantum Physics · Physics 2009-10-30 Todd A. Brun

Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the…

Quantum Physics · Physics 2013-05-29 Michael M. Wolf , David Perez-Garcia

The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which…

Statistical Mechanics · Physics 2025-02-20 Markus Kraft , Mariel Kempa , Jiaozi Wang , Robin Steinigeweg

The dynamics of Gaussian states for open quantum systems described by Lindblad equations can be solved analytically for systems with quadratic Hamiltonians and linear Lindbladians, showing the familiar phenomena of dissipation and…

Quantum Physics · Physics 2022-11-23 Robson Christie , Jessica Eastman , Roman Schubert , Eva-Maria Graefe

We study geometric properties of the gradient flow for learning deep linear convolutional networks. For linear fully connected networks, it has been shown recently that the corresponding gradient flow on parameter space can be written as a…

Machine Learning · Computer Science 2026-04-07 El Mehdi Achour , Kathlén Kohn , Holger Rauhut

We investigate the dissipative dynamics yielded by the Lindblad equation within the coexistence region around a first order phase transition. In particular, we consider an exactly-solvable fullyconnected quantum Ising model with n-spin…

Statistical Mechanics · Physics 2019-09-11 Andrea Nava , Michele Fabrizio

We investigate the physical consequences of having a spectrum that satisfies random matrix theory (RMT) for generic Lindbladians, and compare its implications for spatially local and completely random Lindblad dynamics in one spatial…

Quantum Physics · Physics 2025-11-21 Sanket Chirame , Fiona J. Burnell

The quantum jump approach allows to characterize the stochastic dynamics associated to an open quantum system submitted to a continuous measurement action. In this paper we show that this formalism can consistently be extended to…

Quantum Physics · Physics 2013-09-03 Adrian A. Budini

In recent years, growing attention has been devoted to the possibility that theories with deformed symmetries, associated with certain models of non-commutative spacetime, may encode a fundamental form of decoherence. This effect should be…

Quantum Physics · Physics 2026-02-10 Michele Arzano , Antonio Del Prete , Domenico Frattulillo

This work is concerned with the gradient flow of absolutely $p$-homogeneous convex functionals on a Hilbert space, which we show to exhibit finite ($p<2$) or infinite extinction time ($p \geq 2$). We give upper bounds for the finite…

Analysis of PDEs · Mathematics 2020-12-25 Leon Bungert , Martin Burger

We propose a way to understand the evolution of an open quantum system using a description that dispenses a continuous evolution in time, by discrete operators entangled states, in its most direct and fundamental way. We show that the…

Quantum Physics · Physics 2016-02-17 Bernabé Mejía , Hernán A. Castillo

This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space $(X,\mathsf{d})$ that can be characterized by Evolution Variational Inequalities. We present new results concerning the…

Functional Analysis · Mathematics 2018-10-10 Matteo Muratori , Giuseppe Savaré

We show that the continuous-time gradient descent in Rn can be viewed as an optimal controlled evolution for a suitable action functional; a similar result holds for stochastic gradient descent. We then provide an analogous characterization…

Optimization and Control · Mathematics 2025-11-03 Yongxin Chen , Tryphon Georgiou , Michele Pavon

We introduce a dynamical evolution operator for dealing with unstable physical process, such as scattering resonances, photon emission, decoherence and particle decay. With that aim, we use the formalism of rigged Hilbert space and…

Quantum Physics · Physics 2018-07-16 Marcelo Losada , Sebastian Fortin , Manuel Gadella , Federico Holik

We introduce an encoder-only approach to learn the evolution operators of large-scale non-linear dynamical systems, such as those describing complex natural phenomena. Evolution operators are particularly well-suited for analyzing systems…

Machine Learning · Computer Science 2025-05-27 Giacomo Turri , Luigi Bonati , Kai Zhu , Massimiliano Pontil , Pietro Novelli

We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal…

Mathematical Physics · Physics 2016-08-25 Volker Bach , Jean-Bernard Bru

Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…

Optimization and Control · Mathematics 2017-10-31 Abhishek Halder , Tryphon T. Georgiou

We present an alternative form of master equation, applicable on the analysis of non-equilibrium dynamics of fermionic open quantum systems. The formalism considers a general scenario, composed by a multipartite quantum system in contact…

Quantum Physics · Physics 2017-11-15 Fabrício M. Souza , L. Sanz

We consider an open quantum Fermi-system which consists of a single degenerate level with pairing interactions embedded into a superconducting bath. The time evolution of the reduced density matrix for the system is given by Linblad master…

Superconductivity · Physics 2015-05-28 Daniel S. Kosov , Tomaz Prosen , Bojan Zunkovic

In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum…

Quantum Physics · Physics 2023-11-14 Dhrumil Patel , Mark M. Wilde