Related papers: Quantum-Classical Liouville Dynamics in the Mappin…
The study of phase transitions in dissipative quantum systems based on the Liouvillian is often hindered by the difficulty of constructing a time-local master equation when the system-environment coupling is strong. To address this issue,…
In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to…
Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources.…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…
The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The…
We present a new way of deriving classical mechanics from quantum mechanics. A key feature of the method is its compatibility with the standard approach used to derive transition rates between quantum states due to interactions. We apply…
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough…
We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of…
We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-1/2 coherent state, we…
We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical…
The Brownian dynamics of the density operator for a quantum system interacting with a classical heat bath is described using a stochastic, non-linear Liouville equation obtained from a variational principle. The environment's degrees of…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the…
The conditions of quantum-classical correspondence for a system of two interacting spins are investigated. Differences between quantum expectation values and classical Liouville averages are examined for both regular and chaotic dynamics…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
The classical Landau-Lifshitz equation has been derived from quantum mechanics. Starting point is the assumption of a non-Hermitian Hamilton operator to take the energy dissipation into account. The corresponding quantum mechanical time…
Starting from the Wigner-Moyal equation coupled to Poisson's equation, a simplified set of equations describing nonlinear Landau damping of Langmuir waves is derived. This system is studied numerically, with a particular focus on the…