English
Related papers

Related papers: A Trotter-Kato Theorem for Quantum Markov Limits

200 papers

We derive the Hamiltonian associated to a quantum stochastic flow by extending the Albeverio-Kurasov construction of self-adjoint extensions to finite rank perturbations of nonsemibounded operators to Fock space.

Mathematical Physics · Physics 2008-04-15 John Gough

A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…

Mathematical Physics · Physics 2009-11-11 V. P. Belavkin , P. Staszewski

Topological characteristics of quantum systems are typically determined by the closing of a gap, while the dynamical quantum phase transition (DQPT) during quantum real-time evolution has emerged as a nonequilibrium analog to the quantum…

Strongly Correlated Electrons · Physics 2024-11-26 Y. B. Shi , X. Z. Zhang , Z. Song

This paper is concerned with variational methods for nonlinear open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. The latter are driven by quantum Wiener processes of the…

Quantum Physics · Physics 2016-11-17 Igor G. Vladimirov

Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…

Quantum Physics · Physics 2024-07-09 Hongzheng Zhao , Marin Bukov , Markus Heyl , Roderich Moessner

We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…

Probability · Mathematics 2020-06-04 Matthias Erbar , Max Fathi , André Schlichting

We study a class of finite dimensional quantum dynamical semigroups exp(tL) whose generators L are sums of Lindbladians satisfying the detailed balance condition. Such semigroup arise in the weak coupling (van Hove) limit of Hamiltonian…

Mathematical Physics · Physics 2015-06-16 Vojkan Jaksic , Claude-Alain Pillet , Matthias Westrich

Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols…

Quantum Physics · Physics 2024-06-11 Hongzheng Zhao , Ao Chen , Shu-Wei Liu , Marin Bukov , Markus Heyl , Roderich Moessner

For the description of quantum evolution, the use of a manifestly time-dependent quantum Hamiltonian $\mathfrak{h}(t) =\mathfrak{h}^\dagger(t)$ is shown equivalent to the work with its simplified, time-independent alternative $G\neq…

Quantum Physics · Physics 2013-05-15 Miloslav Znojil

In this paper, we introduce formulations of the Trotter Kato theorem for approximation of bi continuous semigroups that provide a useful framework whenever convergence of numerical approximations to solutions of PDEs are studied with…

Numerical Analysis · Mathematics 2019-11-22 Abdulhameed Qahtan Abbood Altai

This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between…

Mathematical Physics · Physics 2026-03-25 Abdessatar Souissi

In a recent paper, Chatterjee et al. [Phys. Rev. Lett 135, 220202 (2025)] analyze and experimentally implement a specific unitary evolution of a simple quantum system. The authors refer to this type of dynamics as a "superposition of…

Quantum Physics · Physics 2026-01-27 Antoni Wójcik , Jan Wójcik

We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\"{o}dinger equation. In particular we will need the theory of…

Quantum Physics · Physics 2015-10-28 J. M. Pérez-Pardo , M. Barbero-Liñán , A. Ibort

The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime,…

Statistical Mechanics · Physics 2016-06-29 Kay Brandner , Udo Seifert

We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles"…

Quantum Physics · Physics 2009-11-11 V. P. Belavkin , O. Melsheimer

Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…

Probability · Mathematics 2025-03-25 Tristan Benoist , Arnaud Hautecoeur , Clément Pellegrini

Motivated by the work of T.E. Govindan in [5,8,9], this paper is concerned with a more general semilinear stochastic evolution equation. The difference between the equations considered in this paper and the previous one is that it makes…

Probability · Mathematics 2021-03-08 Xia Zhang , Lingfei Dai , Ming Liu

For the model Hamiltonian describing the electron-nuclear dynamics of a quantum dot, we obtained an exact expression for the limiting nuclear polarization as a function of the number of groups of equivalent nuclei. It is shown that the…

Mesoscale and Nanoscale Physics · Physics 2008-01-10 G. G. Kozlov

A natural counterpart to the Lie-Trotter product formula for norm-continuous one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic operator cocycles whose expectation semigroup is norm continuous. Compared…

Functional Analysis · Mathematics 2018-01-18 J. Martin Lindsay

We investigate the Kondo model with time-dependent couplings that are periodically switched on and off. On the Toulouse line we derive exact analytical results for the spin dynamics in the steady state that builds up after an infinite…

Strongly Correlated Electrons · Physics 2010-05-27 Markus Heyl , Stefan Kehrein