Hamiltonian equations of hydrodynamics of quantum liquid in the presence of solitons

2008 ◽  
pp. 36-46
Author(s):  
I. M. Khalatnikov ◽  
V. V. Lebedev
Keyword(s):  
Quantum Liquid ◽  
Hamiltonian Equations

FEW-PARTICLE ANYON EXCITON: EXACT SOLUTIONS

2003 ◽  
Vol 02 (06) ◽  
pp. 461-468
Author(s):  
D. G. W. PARFITT ◽  
M. E. PORTNOI
Keyword(s):  
Exact Solutions ◽  
Finite Size ◽  
Spherical Geometry ◽  
Planar Geometry ◽  
Quantum Liquid ◽  
Dimensional Electron ◽  
Adequate Description ◽  
Exciton Model ◽  
Finite Size Effects ◽  
Dimensional Electron Gas

The anyon exciton model, which describes an exciton against the background of an incompressible quantum liquid, is generalized to the case of an arbitrary number of anyons. Some mathematical aspects of this quantum-mechanical few-particle problem are considered and several exact solutions are obtained. The four-particle case is also considered in the classical limit in both planar and spherical geometries. Such a classical approach gives an adequate description of an anyon exciton at large separation between the valence hole and the two-dimensional electron gas. It is shown that in this limit in a planar geometry the anyon exciton is always energetically more favorable than a charged anyon ion. This indicates that the appearance of fractionally-charged anyon ions reported in recent numerical calculations is an artefact apparently caused by finite-size effects in a spherical geometry.

scholarly journals Possible quantum liquid crystal phases of helium monolayers

2016 ◽  
Vol 94 (18) ◽  
Author(s):  
S. Nakamura ◽  
K. Matsui ◽  
T. Matsui ◽  
Hiroshi Fukuyama
Keyword(s):  
Liquid Crystal ◽  
Quantum Liquid ◽  
Crystal Phases ◽  
Liquid Crystal Phases

QUANTUM REFLECTION, EVAPORATION, AND TRANSPORT CURRENTS AT 4He SURFACES

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5047-5056
Author(s):  
V. APAJA ◽  
E. KROTSCHECK ◽  
A. RIMNAC ◽  
R. E. ZILLICH
Keyword(s):  
Excited States ◽  
Theoretical Study ◽  
Transport Phenomena ◽  
Microscopic Theory ◽  
Second Order ◽  
Quantum Liquid ◽  
Quantum Reflection ◽  
Quantum Liquids ◽  
Inhomogeneous Quantum

In this work, we study transport currents in excited states. This requires the calculation of particle currents [Formula: see text] to second order in the excitation amplitudes. For that purpose, we take a well-tested microscopic theory of inhomogeneous quantum liquids and extend it to find the mass currents created when atoms scatter off a surface or when excitations evaporate atoms. This is the first theoretical study of transport phenomena in a quantum liquid based on a quantitative microscopic theory.

A HIERARCHY OF HAMILTONIAN EQUATIONS ASSOCIATED WITH THE MODIFIED JAULENT–MIODEK HIERARCHY

2010 ◽  
Vol 24 (02) ◽  
pp. 183-193
Author(s):  
HAI-YONG DING ◽  
HONG-XIANG YANG ◽  
YE-PENG SUN ◽  
LI-LI ZHU
Keyword(s):  
Eigenvalue Problem ◽  
Evolution Equations ◽  
Trace Identity ◽  
Liouville Integrability ◽  
Matrix Eigenvalue Problem ◽  
Hamiltonian Structures ◽  
Hamiltonian Equations ◽  
Matrix Eigenvalue ◽  
Integrable Evolution

By considering a new four-by-four matrix eigenvalue problem, a hierarchy of Lax integrable evolution equations with four potentials is derived. The Hamiltonian structures of the resulting hierarchy are established by means of the generalized trace identity. The Liouville integrability for the hierarchy of the resulting Hamiltonian equations is presented.

scholarly journals Role of Hydrogen in the Spin-Orbital-Entangled Quantum Liquid Candidate H3LiIr2O6

2018 ◽  
Vol 121 (24) ◽  
Author(s):  
Ying Li ◽  
Stephen M. Winter ◽  
Roser Valentí
Keyword(s):  
Quantum Liquid ◽  
Spin Orbital

Quantum Liquid Films: A Generic Many-Body Problem

1990 ◽  
pp. 77-87
Author(s):  
E. Krotscheck ◽  
J. L. Epstein ◽  
M. Saarela
Keyword(s):  
Body Problem ◽  
Liquid Films ◽  
Quantum Liquid ◽  
Many Body

A Plethora of Integrable Bi-Hamiltonian Equations

1997 ◽  
pp. 93-101 ◽  
Author(s):  
A. S. Fokas ◽  
P. J. Olver ◽  
P. Rosenau
Keyword(s):  
Hamiltonian Equations

Ergodic properties and Weyl M-functions for random linear Hamiltonian systems

2000 ◽  
Vol 130 (5) ◽  
pp. 1045-1079 ◽  
Author(s):  
R. Johnson ◽  
S. Novo ◽  
R. Obaya
Keyword(s):  
Hamiltonian Systems ◽  
Qualitative Description ◽  
Invariant Region ◽  
Absolutely Continuous ◽  
Hamiltonian Equations ◽  
Radial Limits ◽  
Ergodic Properties ◽  
Ergodic Measures ◽  
Linear Hamiltonian Systems ◽  
Dynamical Information

This paper provides a topological and ergodic analysis of random linear Hamiltonian systems. We consider a class of Hamiltonian equations presenting absolutely continuous dynamics and prove the existence of the radial limits of the Weyl M-functions in the L1-topology. The proof is based on previous ergodic relations obtained for the Floquet coefficient. The second part of the paper is devoted to the qualitative description of disconjugate linear Hamiltonian equations. We show that the principal solutions at ±∞ define singular ergodic measures, and determine an invariant region in the Lagrange bundle which concentrates the essential dynamical information. We apply this theory to the study of the n-dimensional Schrödinger equation at the first point of the spectrum.

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