A many-body stochastic approach to rotational motions in liquids: a reassessment of the Hubbard-Einstein relation

1990 ◽  
Vol 174 (3-4) ◽  
pp. 338-346 ◽  
Author(s):  
Antonino Polimeno ◽  
Jack H. Freed
Science ◽  
2018 ◽  
Vol 363 (6425) ◽  
pp. 379-382 ◽  
Author(s):  
Peter T. Brown ◽  
Debayan Mitra ◽  
Elmer Guardado-Sanchez ◽  
Reza Nourafkan ◽  
Alexis Reymbaut ◽  
...  

Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold lithium-6 in a two-dimensional optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity by using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we developed in this study may be applied to measurements of other transport quantities, including the optical conductivity and thermopower.


2018 ◽  
Vol 15 ◽  
pp. 51-64
Author(s):  
Yu Lu Zhou ◽  
Xiao Ma Tao ◽  
Qing Hou ◽  
Yi Fang Ouyang

Molecular dynamics (MD) simulations, which treat atoms as point particles and trace their individual trajectories, are always employed to investigate the transport properties of a many-body system. The diffusion coefficients of atoms in solid can be obtained by the Einstein relation and the Green-Kubo relation. An overview of the MD simulations of atoms diffusion in the bulk, surface and grain boundary is provided. We also give an example of the diffusion of helium in tungsten to illustrate the procedure, as well as the importance of the choice of interatomic potentials. MD simulations can provide intuitive insights into the atomic mechanisms of diffusion.


2004 ◽  
Vol 13 (01) ◽  
pp. 203-211
Author(s):  
J. DUDEK ◽  
J. B. FAES

We develop a stochastic approach to obtain the energies and wave functions of the full spectrum of the nuclear pairing Hamiltonian (i.e. not only the ground-state but also the excited states of the nuclear many-body systems). We assume that nuclear Cooper pairs may spontaneously jump from one energy configuration to another, the mechanism resembling that of the random walk on a mesh of non-equidistant points. A probability distribution associated with such a random walk is modelled and the resulting solutions tested using an exact quantum algorithm. We use the Hamiltonian parameters characteristic for the nuclear scale: at present an agreement between the quantum and stochastic treatment is of the order of a few permille in terms of eigen-energies.


1999 ◽  
Vol 13 (05n06) ◽  
pp. 525-534
Author(s):  
G. ORTIZ ◽  
M. D. JONES

Solving the fundamental microscopic equations of interacting quantum particles is a goal of many-body physicists. Statistical methods reduce the complexity of the problem by sampling phase space selectively using random-walks and real states. Many interesting physical phenomena (e.g., electrons in external magnetic fields) involve systems whose state functions are inherently complex-valued. The Fixed-Phase method is a stochastic approach to deal with such problems. Its key ingredient is a trial phase that plays the role of gauge function in the transformation that maps the original fermion (or boson) problem to a boson problem for the modulus of the state function. The Released-Phase method relaxes that constraint and allows us to obtain, in principle, the "exact" properties, although it is subjected to the infamous "phase problem." In our tour of the (complex) Quantum World, we will show how these methods have been successfully applied to a wide variety of physical phenomena ranging from quantum Hall topological fluids and Wigner crystals to the study of the core structure of vortices in superfluid 4 He and atomic systems in superstrong magnetic fields found in astrophysical settings.


2016 ◽  
Vol 113 (39) ◽  
pp. 10807-10812 ◽  
Author(s):  
Kyle J. Welch ◽  
Alexander Liebman-Peláez ◽  
Eric I. Corwin

In conventional fluids, viscosity depends on temperature according to a strict relationship. To change this relationship, one must change the molecular nature of the fluid. Here, we create a metafluid whose properties are derived not from the properties of molecules but rather from chaotic waves excited on the surface of vertically agitated water. By making direct rheological measurements of the flow properties of our metafluid, we show that it has independently tunable viscosity and temperature, a quality that no conventional fluid possesses. We go on to show that the metafluid obeys the Einstein relation, which relates many-body response (viscosity) to single-particle dynamics (diffusion) and is a fundamental result in equilibrium thermal systems. Thus, our metafluid is wholly consistent with equilibrium thermal physics, despite being markedly nonequilibrium. Taken together, our results demonstrate a type of material that retains equilibrium physics while simultaneously allowing for direct programmatic control over material properties.


1998 ◽  
Vol 94 (3) ◽  
pp. 417-433 ◽  
Author(s):  
MARTIN VAN DER HOEF ◽  
PAUL MADDEN

1968 ◽  
Vol 111 (1) ◽  
pp. 392-416 ◽  
Author(s):  
K DIETRICH ◽  
K HARA

1970 ◽  
Vol 31 (C4) ◽  
pp. C4-99-C4-104
Author(s):  
T. P. DAS ◽  
C. M. DUTTA ◽  
N. C. DUTTA

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