Related papers: Quantum Dynamics via Score Matching on Bohmian Tra…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
We present exact solutions of the Schr\"odinger equation for a quantum system with complex mass subjected to a complex Morse potential in the extended complex phase space. The normalized eigenfunctions and corresponding eigenspectra are…
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…
We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…
According to Bohmian dynamics, the particles of a quantum system move along trajectories, following a velocity field determined by the wave-function Psi(x,t). We show that for simple one-dimensional systems any initial probability…
The measurement problem of quantum mechanics concerns the question under which circumstances coherent wave evolution becomes disrupted to produce eigenstates of observables, instead of evolving superpositions of eigenstates. The problem…
A classical computer simulating Schrodinger dynamics of a quantum system requires resources which scale exponentially with the size of the system, and is regarded as inefficient for such purposes. However, a quantum computer made up of a…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in experiment a quantum simulation of the two-dimensional non-Hermitian quantum…
One approach to the development of quantum search algorithms is the quantum walk. A spatial search can be effected by the continuous-time evolution of a single quantum particle on a graph containing a marked site. In many physical…
We regard the non-relativistic Schrodinger equation as an ensemble mean representation of the stochastic motion of a single particle in a vacuum, subject to an undefined stochastic quantum force. The local mean of the quantum force is found…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
In this paper, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a classical quantum molecule involving a possibly large number of nuclei and electrons, described by a Schr\"odinger equation. In the spirit of Born and…
Recent years have seen great progress in quantum computing, providing opportunities to overcome computational bottlenecks in many scientific applications. In particular, the intersection of computational fluid dynamics (CFD) and quantum…
Solving the quantum many-body Schr\"odinger equation is a fundamental and challenging problem in the fields of quantum physics, quantum chemistry, and material sciences. One of the common computational approaches to this problem is Quantum…
We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the…
Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…
The direct solution of the many-particle Schr\"odinger equation is computationally inaccessible for more than very few electrons. In order to surpass this limitation, one of the authors [X. Oriols, Phys. Rev. Lett. 2007, 98 (066803)] has…
The paper consists of two parts. In the first part Schroedinger's equation for a charged quantum particle in a Galilei-Newton curved space-time is derived in a fully geometrical way. Gravitational and electromagnetic fields are coded into…