English
Related papers

Related papers: Beyond adiabatic elimination: A hierarchy of appro…

200 papers

In the study of evolution equations, the method of adiabatic approximation is an essential tool to reduce an infinite-dimensional dynamical system to a simpler, possibly finite-dimensional one. In this paper, we formulate a generic scheme…

Analysis of PDEs · Mathematics 2022-03-09 Jingxuan Zhang

An approach to non-adiabatic dynamics of atoms in molecular and condensed matter systems under general non-equilibrium conditions is proposed. In this method interaction between nuclei and electrons is considered explicitly up to the second…

Materials Science · Physics 2018-08-01 L. Kantorovich

We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the maximum absolute deviation of errors. Such problems find application in the solution of…

Optimization and Control · Mathematics 2020-12-22 Nikolai Krivulin

It is believed that the presence of anticrossings with exponentially small gaps between the lowest two energy levels of the system Hamiltonian, can render adiabatic quantum optimization inefficient. Here, we present a simple adiabatic…

Quantum Physics · Physics 2013-05-30 Neil G. Dickson , Mohammad H. Amin

Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and…

Quantum Physics · Physics 2008-11-26 Kazuo Fujikawa

The coupled cluster iteration scheme is analysed as a multivariate discrete-time map using nonlinear dynamics and synergetics. The nonlinearly coupled set of equations to determine the cluster amplitudes are driven by a fraction of the…

Computational Physics · Physics 2021-10-13 Valay Agarawal , Chayan Patra , Rahul Maitra

In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For iterative algorithms, implicit differentiation alleviates…

Optimization and Control · Mathematics 2023-05-24 Jérôme Bolte , Edouard Pauwels , Samuel Vaiter

We prove that, for a quantum system that undergoes a strong perturbation, the solution of the leading order equation of the strong field approximation (M.Frasca, Phys. Rev. A, {\bf 45}, 43 (1992)) can be derived by the adiabatic…

Quantum Physics · Physics 2007-05-23 Marco Frasca

We consider an ensemble of cavity-coupled two-level emitters interacting via full (coherent and dissipative) dipole-dipole interactions. Using an adiabatic elimination procedure we derive effective equations of motion for a subsystem…

Quantum Physics · Physics 2020-07-22 David Hagenmüller , Stefan Schütz , Guido Pupillo , Johannes Schachenmayer

We present a graphical analysis of the adiabatic connections underlying double-hybrid density-functional methods that employ second-order perturbation theory. Approximate adiabatic connection formulae relevant to the construction of these…

Chemical Physics · Physics 2013-06-26 Yann Cornaton , Odile Franck , Andrew M. Teale , Emmanuel Fromager

We explain the concept of superadiabatic approximations and show how in the context of the Born- Oppenheimer approximation they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula,…

Chemical Physics · Physics 2016-06-29 Volker Betz , Benjamin D. Goddard , Uwe Manthe

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…

We introduce high-order dynamical decoupling strategies for open system adiabatic quantum computation. Our numerical results demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding…

Quantum Physics · Physics 2013-04-23 Gregory Quiroz , Daniel A. Lidar

We investigate the adiabatic elimination of fast variables in relativistic stochastic mechanics, which is analyzed by using the equation of motion and the distribution function, with relativistic corrections explicitly derived. A new…

Statistical Mechanics · Physics 2026-02-24 Tao Wang , Yu Shi

We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a…

Quantum Physics · Physics 2011-12-22 J. Salmilehto , P. Solinas , J. Ankerhold , M. Möttönen

Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of…

In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…

We show how the dynamics of a specific subset of states can be separated from the dynamic of the total quantum state via a time-dependent projector-based formalism of adiabatic elimination. Within our formalism, we assume explicit time…

Quantum Physics · Physics 2026-03-03 Samuel Böhringer , Alexander Bott , Eric P. Glasbrenner

Shortcuts to adiabaticity are alternative fast processes which reproduce the same final state as the adiabatic process in a finite or even shorter time, which have been extended from Hermitian systems to non-Hermitian systems in recent…

Quantum Physics · Physics 2024-04-15 T. Z. Luan , H. Z. Shen , X. X. Yi

The principle of indirect elimination states that an algorithm for solving discretized differential equations can be used to identify its own bad-converging modes. When the number of bad-converging modes of the algorithm is not too large,…

High Energy Physics - Lattice · Physics 2015-06-25 Martin Bäker