On the classical hydrodynamic limit of quantum field theories

Hybrid Quantum-Classical Algorithm for Hydrodynamics

A new model of nonlinear charged quantum relativistic fluids is presented. This model can be discretized into Discrete Time Quantum Walks (DTQWs), and a new hybrid (quantum-classical) algorithm for implementing these walks on NISQ devices is proposed. High resolution (up to $N=2^{17}$ grid points) hybrid numerical simulations of relativistic and non-relativistic hydrodynamical shocks on current IBM NISQs are performed with this algorithm and shown to reproduce equivalent simulations on classical computers. This work demonstrates that nonlinear fluid dynamics can be simulated on NISQs, and open…

Bohmian mechanics versus Madelung quantum hydrodynamics

It is shown that the Bohmian mechanics and the Madelung quantum hydrodynamics are different theories and the latter is a better ontological interpretation of quantum mechanics. A new stochastic interpretation of quantum mechanics is proposed, which is the background of the Madelung quantum hydrodynamics. Its relation to the complex mechanics is also explored. A new complex hydrodynamics is proposed, which eliminates completely the Bohm quantum potential. It describes the quantum evolution of the probability density by a convective diffusion with imaginary transport coefficients.

A platform for investigating Bell correlations in pilot-wave hydrodynamics

Since its discovery in 2005, the hydrodynamic pilot-wave system has provided a concrete macroscopic realization of wave-particle duality and concomitant classical analogs of a growing list of quantum effects. The question naturally arises as to whether this system might support statistical states that violate Bell's inequality, and so yield a classical analog of quantum entanglement. We here introduce a new platform for addressing this question, a numerical model of coupled bipartite tunneling in the hydrodynamic pilot-wave system. We demonstrate that, under certain conditions, the Bell inequa…

Real surreal trajectories in pilot-wave hydrodynamics

In certain instances, the particle paths predicted by Bohmian mechanics are thought to be at odds with classical intuition. A striking illustration arises in the interference experiments envisaged by Englert, Scully, Süssmann and Walther, which lead the authors to claim that the Bohmian trajectories can not be real and so must be `surreal'. Through a combined experimental and numerical study, we here demonstrate that individual trajectories in the hydrodynamic pilot-wave system exhibit the key features of their surreal Bohmian counterparts. These real surreal classical trajectories are rationa…

遍历性与流体力学：从量子自旋系统到经典自旋系统

Ergodicity and hydrodynamics: from quantum to classical spin systems

本研究基于遍历性论证，证明经典自旋系统中可观测量自关联函数的晚期流体力学尾迹由动力学临界指数与平衡热力学性质决定，给出了一维和二维系统的数值结果，并将量子多体系统的弛豫-重叠不等式推广至经典框架。

From quantum hydrodynamics to Koopman wavefunctions I

Based on Koopman's theory of classical wavefunctions in phase space, we present the Koopman-van Hove (KvH) formulation of classical mechanics as well as some of its properties. In particular, we show how the associated classical Liouville density arises as a momentum map associated to the unitary action of strict contact transformations on classical wavefunctions. Upon applying the Madelung transform from quantum hydrodynamics in the new context, we show how the Koopman wavefunction picture is insufficient to reproduce arbitrary classical distributions. However, this problem is entirely overco…

From quantum hydrodynamics to Koopman wavefunctions II

Based on the Koopman-van Hove (KvH) formulation of classical mechanics introduced in Part I, we formulate a Hamiltonian model for hybrid quantum-classical systems. This is obtained by writing the KvH wave equation for two classical particles and applying canonical quantization to one of them. We illustrate several geometric properties of the model regarding the associated quantum, classical, and hybrid densities. After presenting the quantum-classical Madelung transform, the joint quantum-classical distribution is shown to arise as a momentum map for a unitary action naturally induced from the…

Quantum stochastic models with hydrodynamical behaviour

We construct a class of quantum stochastic models of reservoir driven many-particle systems that are the natural counterparts of certain extensively studied classical ones, which have been shown to exhibit good hydrodynamical behaviour. Our treatment of these models achieves two main aims. The first is to show that they enjoy the hydrodynamical properties of their classical counterparts. The second is to show that they satisfy the key assumptions of the general quantum macrostatistical scheme, presented in earlier works by the author, which served to expose certain generic large scale features…

量子-经典溶剂流体力学：一个哈密顿建模框架

Quantum-classical solvation hydrodynamics: a Hamiltonian modeling framework

本文提出了一种混合量子-经典的流体力学框架，用于建模量子溶质与经典极性溶剂非绝热演化的短时间惯性效应，通过哈密顿方法保持量子退相干并减少计算复杂度。

Finslerian geometrization of quantum mechanics in the hydrodynamical representation

We consider a Finslerian type geometrization of the non-relativistic quantum mechanics in its hydrodynamical (Madelung) formulation, by also taking into account the effects of the presence of the electromagnetic fields on the particle motion. In the Madelung representation the Schrödinger equation can be reformulated as the classical continuity and Euler equations of classical fluid mechanics in the presence of a quantum potential, representing the quantum hydrodynamical evolution equations. The equation of particle motion can then be obtained from a Lagrangian similar to its classical counter…

On a Multisymplectic Formulation of the Classical BRST Symmetry for First Order Field Theories Part II: Geometric Structures

A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic formulation of first-order field theories. The Lagrange-d'Alembert formalism is also developed in terms of the multisymplectic framework. The result is a covariant Hamiltonian BFV formalism.