Stable and accurate simulation of phenomena in relativistic quantum mechanics

Weizhong Fu, Zhe Li, Yubing Qian +3 more

Real-time dynamics of interacting electrons lies at the interface between quantum mechanics and non-equilibrium physics, governing the microscopic origin of ultrafast phenomena of molecules and nano-materials. Though neural network variational Monte Carlo has achieved unprecedented accuracy for stationary state calculations, its extension to real-time evolution remains challenging. In this work, we introduce the neural basis time-dependent variational Monte Carlo framework, which achieves stable and highly accurate simulations of electron dynamics. By constraining the time evolution to a compact, customized manifold spanned by the neural basis, we effectively bypass instability issues and achieve long-term stable evolution. Moreover, we demonstrate that this framework yields benchmark-quality accuracy in simulating the laser-driven dipole responses of the hydrogen atom and a stretched hydrogen molecule, and accurately extracts the dynamic polarizabilities of helium and beryllium atoms. Our work reveals the vast potential of neural network wavefunctions for accurately describing real-time electron dynamics and establishes a promising new route for first-principles simulations of complex, time-dependent electronic phenomena.

Mark Goodall

Rodolfo Gambini, Rafael A. Porto

One of the most puzzling facts about quantum mechanics is that although quantum theory offers a very accurate framework encompassing phenomena going from chemistry to high energy physics, it does not provide us with clear indications favoring some world view in the relativistic domain. Consequently, many physicists have held an instrumentalist point of view. Even though in non-relativistic physics already exists a realistic interpretation of quantum mechanics due to Heisenberg, who considers quantum states as states of disposition (the real tendency interpretation), the efforts for extending this interpretation to the relativistic domain were found wanting. The basic problem is the dependence of the states on the frame within which collapse takes place. We show here that a suitable use of the causal structure of the devices involved in the measurement process allows us to introduce a covariant notion for the collapse of quantum states and to preserve the tendency interpretation in relativistic quantum mechanics. However, we shall see that this extended interpretation requires the introduction of a relational concept of reality.

Konstantin K. Likharev

Tommy Ohlsson B

Ralf Schützhold

The goal of this article is to review developments regarding the use of ultra-cold atoms as quantum simulators. Special emphasis is placed on relativistic quantum phenomena, which are presumably most interesting for the audience of this journal. After a brief introduction into the main idea of quantum simulators and the basic physics of ultra-cold atoms, relativistic quantum phenomena of linear fields are discussed, including Hawking radiation, the Unruh effect, cosmological particle creation, the Gibbons–Hawking and Ginzburg effects, super-radiance, Sauter–Schwinger and Breit–Wheeler pair creation, as well as the dynamical Casimir effect. After that, the focus is shifted to phenomena of non-linear fields, such as the sine–Gordon model, the Kibble–Zurek mechanism, false-vacuum decay, and quantum back-reaction. In order to place everything into proper context, the basic underlying mechanisms of these phenomena are briefly recapitulated before their simulators are discussed. Even though effort is made to provide a review as fair as possible, there can be no claim of completeness and the selection as well as the relative weights of the topics may well reflect the personal view and taste of the author.