Hydrodynamics of correlated systems. Emptiness Formation Probability and Random Matrices

Abstract

A 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.

25 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

References in corpus (5)

• Collective fields, Calogero-Sutherland model and generalized matrix models
• Correlation Function of the Spin-1/2 XXX Antiferromagnet
• Large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain
• Emptiness Formation Probability for the Anisotropic XY Spin Chain in a Magnetic Field
• Probability of phase separation for the Bose gas with delta interactions

Cited by in corpus (8)

• Conformal field theory out of equilibrium: a review
• Dynamics of hard rods with initial domain wall state
• Void formation in diffusive lattice gases
• The density profile of the six vertex model with domain wall boundary conditions
• Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
• Emptiness and Depletion Formation Probability in spin models with inverse square interaction
• Metal or Insulator? Dirac operator spectrum in holographic QCD
• Emptiness Instanton in Quantum Polytropic Gas