Hydrodynamics of correlated systems. Emptiness Formation Probability and Random Matrices

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dc.creatorAbanov, Alexander G.
dc.date2005-04-12
dc.date.accessioned2026-07-07T03:04:42Z
dc.date.available2026-07-07T03:04:42Z
dc.descriptionA hydrodynamic approach is used to calculate an asymptotics of the Emptiness Formation Probability - the probability of a formation of an empty space in the ground state of a quantum one-dimensional many body system. Quantum hydrodynamics of a system is represented as a Euclidian path integral over configurations of hydrodynamic variables. In the limit of a large size of the empty space, the probability is dominated by an instanton configuration, and the problem is reduced to the finding of an instanton solution of classical hydrodynamic equations. After establishing a general formalism, we carry out this calculation for several simple systems -- free fermions with an arbitrary dispersion and Calogero-Sutherland model. For these systems we confirm the obtained results by comparison with exact results known in Random Matrix theory. We argue that the nonlinear hydrodynamic approach might be useful even in cases where the linearized hydrodynamics fails.
dc.description25 pages, 2 figures. This is an extended version of the seminar given at the School "Applications of Random Matrices in Physics", Les Houches, June 2004
dc.identifierhttps://arxiv.org/abs/cond-mat/0504307
dc.identifierhttp://arxiv.org/abs/cond-mat/0504307
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/26187
dc.subjectStrongly Correlated Electrons
dc.subjectStatistical Mechanics
dc.titleHydrodynamics of correlated systems. Emptiness Formation Probability and Random Matrices
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