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Journal of Experimental and Theoretical Physics

Experimental observation of "excitation trapping" in a system of strongly interacting particles

T. T. Vasiev, Yu. K. Voron’ko, В. В. Осико, Alexander M. Prokhorov, Ivan A Shcherbakov

Published Apr 1, 1976• 4 citations
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Energy-level statistics in strongly disordered systems with power-law hopping

Paraj Titum, Victor L. Quito, Sergey Syzranov

Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian $\ensuremath{\propto}1/{r}^{\ensuremath{\alpha}}$ in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focusing on the excitations in disordered electronic systems, we compute the energy-level correlation function ${R}_{2}(\ensuremath{\omega})$ in a finite system in the limit of sufficiently strong disorder. At small energy differences, the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by ${R}_{2}(\ensuremath{\omega},V)={A}_{3}\frac{\ensuremath{\omega}}{{\ensuremath{\omega}}_{V}}$ for small frequencies $\ensuremath{\omega}\ensuremath{\ll}{\ensuremath{\omega}}_{V}$ and ${R}_{2}(\ensuremath{\omega},V)=1\ensuremath{-}(\ensuremath{\alpha}\ensuremath{-}d){A}_{1}{\left(\frac{{\ensuremath{\omega}}_{V}}{\ensuremath{\omega}}\right)}^{\frac{d}{\ensuremath{\alpha}}}\ensuremath{-}{A}_{2}{\left(\frac{{\ensuremath{\omega}}_{V}}{\ensuremath{\omega}}\right)}^{2}$ for large frequencies $\ensuremath{\omega}\ensuremath{\gg}{\ensuremath{\omega}}_{V}$, where ${\ensuremath{\omega}}_{V}\ensuremath{\propto}{V}^{\ensuremath{-}\frac{\ensuremath{\alpha}}{d}}$ is the characteristic matrix element of excitation hopping in a system of volume $V$, and ${A}_{1},{A}_{2}$, and ${A}_{3}$ are coefficients of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.

arXiv:1803.11178•Physical review. B./Physical review. B•Jul 16, 2018•1 citation
It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f^{α} noise with 1≤α≤2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P(s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f^{α} noise is ubiquitous in nature.
We show that the analysis of the time evolution of the occupation of site and momentum modes of harmonically trapped lattice hard-core bosons, under driven dipole oscillations, allows one to determine the energy of the lowest one-particle excitations of the system in equilibrium. The analytic solution of a single particle in the absence of a lattice is used to identify which function of those time-dependent observables is best fit for the analysis, as well as to relate the dynamic response of the system to its single-particle spectrum. In the presence of the lattice and of multiple particles, a much richer and informative dynamical response is observed under the drive.
Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian $\ensuremath{\propto}1/{r}^{\ensuremath{\alpha}}$ in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focusing on the excitations in disordered electronic systems, we compute the energy-level correlation function ${R}_{2}(\ensuremath{\omega})$ in a finite system in the limit of sufficiently strong disorder. At small energy differences, the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by ${R}_{2}(\ensuremath{\omega},V)={A}_{3}\frac{\ensuremath{\omega}}{{\ensuremath{\omega}}_{V}}$ for small frequencies $\ensuremath{\omega}\ensuremath{\ll}{\ensuremath{\omega}}_{V}$ and ${R}_{2}(\ensuremath{\omega},V)=1\ensuremath{-}(\ensuremath{\alpha}\ensuremath{-}d){A}_{1}{\left(\frac{{\ensuremath{\omega}}_{V}}{\ensuremath{\omega}}\right)}^{\frac{d}{\ensuremath{\alpha}}}\ensuremath{-}{A}_{2}{\left(\frac{{\ensuremath{\omega}}_{V}}{\ensuremath{\omega}}\right)}^{2}$ for large frequencies $\ensuremath{\omega}\ensuremath{\gg}{\ensuremath{\omega}}_{V}$, where ${\ensuremath{\omega}}_{V}\ensuremath{\propto}{V}^{\ensuremath{-}\frac{\ensuremath{\alpha}}{d}}$ is the characteristic matrix element of excitation hopping in a system of volume VVV, and A1,A2{A}_{1},{A}_{2}A1​,A2​, and A3{A}_{3}A3​ are coefficients of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.