Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement

Abstract

Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with l_{2}/l_1 \sim l_1^γ , where $l_1$ and $l_2$ are the single and two particle localization lengths and the exponent $\gamma$ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all ($l_2\approx l_1$).

23 pages, REVTEX, 3 eps figures, improved version accepted for publication in Phys. Rev. B

References in corpus (1)

• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach

Cited by in corpus (32)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Multifractality and critical fluctuations at the Anderson transition
• From the Fermi glass towards the Mott insulator in one dimension: Delocalization and strongly enhanced persistent currents
• Statistics of wave interactions in nonlinear disordered systems
• Decay of Quasi-Particle in a Quantum Dot: the role of Energy Resolution
• Anomalously large critical regions in power-law random matrix ensembles
• Chaos Thresholds in finite Fermi systems
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Two Interacting Electrons in a Quasiperiodic Chain
• Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
• Disorder and Two-Particle Interaction in Low-Dimensional Quantum Systems
• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Taming two interacting particles with disorder
• Dynamical thermalization in Bose-Hubbard systems
• Interaction effects on dynamical localization in driven helium
• Two-level correlation function of critical random-matrix ensembles
• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Critical properties in long-range hopping Hamiltonians
• Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains
• Towards rigorous analysis of the Levitov-Mirlin-Evers recursion
• Multiscaling Anderson localization of cosmic electromagnetic fields
• Logarithmic expansion of many-body wave packets in random potentials
• Scaling the localisation lengths for two interacting particles in one-dimensional random potentials
• Magnetic Field Effect for Two Electrons in a Two Dimensional Random Potential
• Non-Rayleigh signal of interacting quantum particles
• Statistical properties of the critical eigenstates in power-law random banded matrices across the band
• Two particles on a chain with disordered interaction: Localization and dissociation of bound states and mapping to chaotic billiards
• Single-particle Entanglement of the Entanglement Hamiltonian Eigen-modes
• Sparse random matrix configurations for two or three interacting electrons in a random potential
• Universal fluctuations of localized two interacting particles in one dimension
• 2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes
• Statistical properties of two-particle transmission at Anderson transition