The Adiabatic Method in the Theory of Many-Body Systems

Jia Wang, Written Jia Wang, Chris H. Greene +9 more

Hyperspherical coordinates provide a systematic way of describing three-body systems. Solving three-body Schrödinger equations in an adiabatic hyperspherical representation is the focus of this thesis. An essentially exact solution can be found numerically by including nonadiabatic couplings using either a slow variable discretization or a traditional adiabatic method. Two different types of three-body systems are investigated: (1) rovibrational states of the triatomic hydrogen ion H+3 and (2) ultracold collisions of three identical bosons.

Giampaolo Co’

拓矢 鳩村, Takuya Hatomura

Maziar Nekovee, W. M. C. Foulkes, A. J. Williamson +3 more

We present a new method for realizing the adiabatic connection approach in density functional theory, which is based on combining accurate variational quantum Monte Carlo calculations with a constrained optimization of the ground state many-body wavefunction for different values of the Coulomb coupling constant. We use the method to study an electron gas in the presence of a cosine-wave potential. For this system we present results for the exchange-correlation hole and exchange-correlation energy density, and compare our findings with those from the local density approximation and generalized gradient approximation. 1. Introduction 2. The Adiabatic connection 3. Quantum Monte Carlo realization 3.1 Variational Monte Carlo 3.2 Fixed-density variance minimization 4. Cosine-wave jellium 4.1 Many-body wavefunction 5. Results and discussion 1 Introduction Density functional theory (DFT) (1, 2) is the main computational tool for the treatment of many-body effects in solid state electroni...

Anna Minguzzi, Mario P. Tosi

Amy Skelt, Irene D’Amico

The quantum adiabatic theorem is fundamental to time-dependent quantum systems, but being able to characterize quantitatively an adiabatic evolution in many-body systems can be a challenge. This work demonstrates that the use of appropriate state and particle-density metrics is a viable method to quantitatively determine the degree of adiabaticity in the dynamic of a quantum many-body system. The method applies also to systems at finite temperature, which is important for quantum technologies and quantum thermodynamics related protocols. The importance of accounting for memory effects is discussed via comparison to results obtained by extending the quantum adiabatic criterion to finite temperatures: it is shown that this may produce false readings being quasi-Markovian by construction. As the proposed method makes it possible to characterize the degree of adiabatic evolution by tracking only the system local particle densities, it is potentially applicable to both theoretical calculations of very large many-body systems and to experiments.