Related papers: The Accuracy of Perturbative Master Equations
In this paper, we consider stochastic master equations describing the evolutions of quantum systems interacting with electromagnetic fields undergoing continuous-time measurements. In particular, we study feedback control of quantum…
The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains the non-interacting sector and the diagonal elements of Fock space from the interacting terms. The…
We propose an improved scheme of perturbation theory based on our exact solution [An Min Wang, quant-ph/0611216] in general quantum systems independent of time. Our elementary start-point is to introduce the perturbing parameter as late as…
In this paper we present the details of our previous work on exact solutions in second-order conformal hydrodynamics together with a number of new solutions found by mapping Minkowski space onto various curved spacetimes such as anti-de…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
We present the growing mode solutions of cosmological perturbations to the second order in the matter dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in most general fluid…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
Approximations to the exact solutions for gravitational instability in the expanding Universe are extremely useful for understanding the evolution of large--scale structure. We report on a series of tests of Newtonian Lagrangian…
The existence of higher order entanglement in the stimulated and spontaneous Raman processes is established using the perturbative solutions of the Heisenberg equations of motion for various field modes that are obtained using the…
We investigate the time and the energy minimum optimal solutions for the robust control of two-level quantum systems against offset or control field uncertainties. Using the Pontryagin Maximum Principle, we derive the global optimal pulses…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
A direct numerical algorithm for solving the time-nonlocal non-Markovian master equation in the second Born approximation is introduced and the range of utility of this approximation, and of the Markov approximation, is analyzed for the…
Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of…
We propose a perturbative approach to determine the time-dependent Dyson map and the metric operator associated with time-dependent non-Hermitian Hamiltonians. We apply the method to a pair of explicitly time-dependent two dimensional…
In this paper, the out-of-time-order correlators (OTOC) in quantum harmonic oscillators are calculated analytically by second quantization method in perturbative approximation. We consider the coupled harmonic oscillators and anharmonic…
We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed balance…