Related papers: Secular master equation for adiabatically time dep…
Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…
Recently, an effective Lindblad master equation for quantum systems whose dynamics are coupled to dissipative bosonic modes has been introduced [Phys. Rev. Lett. 129, 063601 (2022)]. In this approach, the bosonic modes are adiabatically…
A new class of time-energy uncertainty relations is directly derived from the Schr\"odinger equations for time-dependent Hamiltonians. Only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full…
Treatment of a singular Lagrangian with constraints using the canonical Hamiltonian approach is studied. We investigate Landau-Ginzburg theory as a constrained system using the Euler-Lagrange equation for the field system and the canonical…
The Lindblad master equation is a foundational tool for modeling the dynamics of open quantum systems. As its use has extended far beyond its original domain, the boundaries of its validity have grown opaque. In particular, the rise of new…
We study well posedness of time--dependent Hamilton--Jacobi equations on a network, coupled with a continuous initial datum and a flux limiter. We show existence and uniqueness of solutions as well as stability properties. The novelty of…
We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a…
We study two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation. Adopting a minimal lattice model of a handful of interacting fermions with single-particle dissipation, we show…
In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone,…
For multi-level open quantum system, the interaction between different levels could pose challenge to understand the quantum system both analytically and numerically. In this work, we study the approximation of the dynamics of the…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the {\it time-dependent} Schr\"{o}dinger equations which govern the various Lie-algebraic quantum systems in atomic…
Thermal state preparation is a central challenge in the simulation of quantum many-body systems. Yet, provably efficient algorithms for this task were only introduced recently [Chen et al. Nature 646, 561 (2025)]. These algorithms are based…
Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on Berry's transitionless driving algorithm or on dynamical invariants. We work out the basic…
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…
We prove an adiabatic theorem for the Landau-Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fr\"ohlich Hamiltonian with large coupling…
Since the discovery of adiabatic quantum computing, a need has arisen for rigorously proven bounds for the error in the adiabatic approximation. We present in this paper, a rigorous and elementary derivation of upper and lower bounds on the…
In this work, we consider simple systems that are influenced by Hamiltonians with time periodicity. Our analysis is mainly focussed on the density matrix approach and aims to solve the Liouville equation of motion from which one can extract…
We study a class of weakly coupled systems of Hamilton{Jacobi equations at the critical level. We associate to it a family of scalar discounted equation. Using control{theoretic tech- niques we construct an algorithm which allows obtaining…
Sped-up protocols (shortcuts to adiabaticity) that drive a system quickly to the same populations than a slow adiabatic process may involve Hamiltonian terms difficult to realize in practice. We use the dynamical symmetry of the Hamiltonian…