Related papers: Feshbach projection formalism for open quantum sys…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
We derive a new expansion of the Heisenberg equation of motion based on the projection operator method proposed by Shibata, Hashitsume and Shing\=u. In their projection operator method, a certain restriction is imposed on the initial state.…
The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
These notes are a short introduction to the mathematical theory of open quantum systems. They are meant to serve as an entry point into a broad research area which has applications across the quantum sciences dealing with systems subjected…
We propose a geometric model predictive control framework for quantum systems subject to smoothness and state constraints. By formulating quantum state evolution intrinsically on the projective Hilbert space, we penalize covariant…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
We give an exposition of a technique, based on the Zwanzig projection formalism, to construct the evolution equation for the reduced density matrix corresponding to the n-particle sector of a field theory. We consider the case of a scalar…
We introduce a new method for representing the low energy subspace of a bosonic field theory on the qubit space of digital quantum computers. This discretization leads to an exponentially precise description of the subspace of the…
Faithfully simulating the dynamics of open quantum systems requires efficiently addressing the challenge of an infinite Hilbert space. Inspired by the shifted boson operator technique used in ground-state studies of the spin-boson model…
In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…
The dynamics of open quantum systems is formulated in a minimally extended state space comprising the degrees of freedom of a system of interest and a finite set of non-unitary, pure-state reservoir modes. This formal structure, derived…
A new variant of the Feshbach map, called smooth Feshbach map, has been introduced recently by Bach et al., in connection with the renormalization analysis of non-relativistic quantum electrodynamics. We analyze and clarify its algebraic…
We develop an optimization framework for high-efficiency quantum cycles implemented with a trapped Bose-Einstein condensate, whose control parameters are the trap stiffness and the interaction strength tuned via a Feshbach resonance.…
The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the…
We define an ensemble of projection operators, each of which has an exact associated Nakajima-Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields, for an…