Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons

Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.

Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.

Hydrodynamic approach to the processing of core sample tests considering microstructural changes

In this paper, authors propose a method to create a complete hydrodynamic model of the polymer displacement process. It is based on the processing of the laboratory tests with core samples, considering the polymer substance properties and microstructural changes occurring in the porous matrix during the adsorption of polymer particles. Based on the adaptation of the mathematical model to the results of tests with polyacrylamide Flopaam and polysaccharide Gum Arabic, calculations of the effectiveness of polymer flooding application on samples of terrigenous deposits are carried out.

Submerging paddy cultivation area due to coastal flooding in Kuala Kedah, Malaysia

Kuala Kedah is a coastal area where the majority of the community are paddy farmers and fishermen. Almost the entire coastal area is used as a paddy cultivation area. However, this area faces the threat of seawater intrusion into land due to climate change driven sea-level rise. The rising seawater has affected the surrounding area, not only in terms of crop yields but also property and livelihood to the locals. Therefore, this study is designed to detect and analyze the progress of seawater on land at the Kuala Kedah coastal area using a hydrodynamic approach. Mike 21 software was used to simulate the hydrodynamic effects on 2 segments (NA and SA) in this study area by considering two conditions namely Condition 1 (K1) and Condition 2 (K2) which are respectively with and without coastal protection structure. However, this structure was only built along the 2.5 km shoreline in the NA segment and not in the SA segment. The findings show that the coastal protection structure in K2 is effective in reducing 50 % of the impact of sea level rise in year 2100 at NA segment, while only 10 % at SA segment. Therefore, the construction of these structures permanently should be given consideration by local authorities in planning future development to ensure lowland areas are protected from coastal floods.

Stability of Quantum Eigenstates and Collapse of Superposition of States in a Fluctuating Vacuum: The Madelung Hydrodynamic Approach

The paper investigates the quantum fluctuating dynamics by using the stochastic generalization of the Madelung quantum-hydrodynamic approach. By using the discrete approach, the path integral solution is derived in order to investigate how the final stationary configuration is obtained from the initial quantum superposition of states. The model shows that the quantum eigenstates remain stationary configurations with a very small perturbation of their mass density distribution and that any eigenstate, contributing to a quantum superposition of states, can be reached in the final stationary configuration. When the non-local quantum potential acquires a finite range of interaction, the work shows that the macroscopic coarse-grained description of the theory can lead to a really classical system. The minimum uncertainty attainable in the stochastic Madelung model is shown to be compatible with maximum speed of transmission of information and interactions. The theory shows that, in the quantum deterministic limit, the uncertainty relations of quantum mechanics are obtained. The connections with the decoherence theory and the Copenhagen interpretation of quantum mechanics are also discussed.

A Middle Way

This book focuses on a method for exploring, explaining, and understanding the behavior of large many-body systems. It describes an approach to non-equilibrium behavior that focuses on structures (represented by correlation functions) that characterize mesoscale properties of the systems. In other words, rather than a fully bottom-up approach, starting with the components at the atomic or molecular scale, the “hydrodynamic approach” aims to describe and account for continuum behaviors by largely ignoring details at the “fundamental” level. This methodological approach has its origins in Einstein’s work on Brownian motion. He gave what may be the first instance of “upscaling” to determine an effective (continuum) value for a material parameter—the viscosity. His method is of a kind with much work in the science of materials. This connection and the wide-ranging interdisciplinary nature of these methods are stressed. Einstein also provided the first expression of a fundamental theorem of statistical mechanics called the Fluctuation-Dissipation theorem. This theorem provides the primary justification for the hydrodynamic, mesoscale methodology. Philosophical consequences include an argument to the effect that mesoscale parameters can be the natural variables for characterizing many-body systems. Further, the book offers a new argument for why continuum theories (fluid mechanics and equations for the bending of beams) are still justified despite completely ignoring the fact that fluids and materials have lower scale structure. The book argues for a middle way between continuum theories and atomic theories. A proper understanding of those connections can be had when mesoscales are taken seriously.

Hydrodynamic Approach to Electronic Transport in Graphene: Energy Relaxation

In nearly compensated graphene, disorder-assisted electron-phonon scattering or “supercollisions” are responsible for both quasiparticle recombination and energy relaxation. Within the hydrodynamic approach, these processes contribute weak decay terms to the continuity equations at local equilibrium, i.e., at the level of “ideal” hydrodynamics. Here we report the derivation of the decay term due to weak violation of energy conservation. Such terms have to be considered on equal footing with the well-known recombination terms due to nonconservation of the number of particles in each band. At high enough temperatures in the “hydrodynamic regime” supercollisions dominate both types of the decay terms (as compared to the leading-order electron-phonon interaction). We also discuss the contribution of supercollisions to the heat transfer equation (generalizing the continuity equation for the energy density in viscous hydrodynamics).