Related papers: A time-dependent variational principle for dissipa…
Predicting the dynamical properties of topological matter is a challenging task, not only in theoretical and experimental settings, but also numerically. This work proposes a variational approach based on a time-dependent correlated Ansatz,…
We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous impulsive hybrid systems on Riemannian manifolds, i.e. systems where the manifold valued component of the hybrid state trajectory may have a…
A variational principle enabling one to compute individual Floquet states of a periodically time-dependent quantum system is formulated, and successfully tested against the benchmark system provided by the analytically solvable model of a…
We deliver a novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping by establishing a restricted Hamilton's principle. Fractional damping is a particular instance of non-local (in…
We introduce a variational hybrid classical-quantum algorithm to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our method is based on a direct representation…
The variational principle for conformational dynamics has enabled the systematic construction of Markov state models through the optimization of hyperparameters by approximating the transfer operator. In this note we discuss why lag time of…
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational…
The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular dynamics models to describe indistinguishable fermions. Early attempts to include effects of…
We demonstrate a surprising connection between pure steady state entanglement and relaxation timescales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems $A$ and $B$ interact locally with a common…
Extending our previous work on time optimal quantum state evolution, we formulate a variational principle for the time optimal unitary operation, which has direct relevance to quantum computation. We demonstrate our method with three…
We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…
We introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite…
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
We introduce and study the turnpike property for time-varying shapes, within the viewpoint of optimal control. We focus here on second-order linear parabolic equations where the shape acts as a source term and we seek the optimal…
The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the…
Simulations of chaotic systems can only produce high-fidelity trajectories if the initial and boundary conditions are well specified. When these conditions are unknown but measurements are available, variational state estimation can…
We study a time-inhomogeneous nonlinear SDE with drift and diffusion governed by state-dependent variable exponents. This framework generalizes models like the geometric Brownian motion (GBM) and the constant elasticity of variance (CEV),…