Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userError analysis of free probability approximations to the density of states of disordered systems
92
0
0.0
(
0
)
Authors
Jiahao Chen
Ask ChatGPT about the research
No Arabic abstract
Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with the perturbation theory and isotropic entanglement theory.
rate research
Read More
We study the dynamics of one and two dimensional disordered lattice bosons/fermions initialized to a Fock state with a pattern of $1$ and $0$ particles on $A$ and ${bar A}$ sites. For non-interacting systems we establish a universal relation between the long time density imbalance between $A$ and ${bar A}$ site, $I(infty)$, the localization length $xi_l$, and the geometry of the initial pattern. For alternating initial pattern of $1$ and $0$ particles in 1 dimension, $I(infty)=tanh[a/xi_l]$, where $a$ is the lattice spacing. For systems with mobility edge, we find analytic relations between $I(infty)$, the effective localization length $tilde{xi}_l$ and the fraction of localized states $f_l$. The imbalance as a function of disorder shows non-analytic behaviour when the mobility edge passes through a band edge. For interacting bosonic systems, we show that dissipative processes lead to a decay of the memory of initial conditions. However, the excitations created in the process act as a bath, whose noise correlators retain information of the initial pattern. This sustains a finite imbalance at long times in strongly disordered interacting systems.
We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a fluctuating-elasticity landscape, capable of trapping the vibrational excitations.
We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suitably chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.
We present experimental evidence for the different mechanisms driving the fluctuations of the local density of states (LDOS) in disordered photonic systems. We establish a clear link between the microscopic structure of the material and the frequency correlation function of LDOS accessed by a near-field hyperspectral imaging technique. We show, in particular, that short- and long-range frequency correlations of LDOS are controlled by different physical processes (multiple or single scattering processes, respectively) that can be---to some extent---manipulated independently. We also demonstrate that the single scattering contribution to LDOS fluctuations is sensitive to subwavelength features of the material and, in particular, to the correlation length of its dielectric function. Our work paves a way towards a complete control of statistical properties of disordered photonic systems, allowing for designing materials with predefined correlations of LDOS.
It is commonly believed that Anderson localized states and extended states do not coexist at the same energy. Here we propose a simple mechanism to achieve the coexistence of localized and extended states in a band in a class of disordered quasi-1D and quasi-2D systems. The systems are partially disordered in a way that a band of extended states always exists, not affected by the randomness, whereas the states in all other bands become localized. The extended states can overlap with the localized states both in energy and in space, achieving the aforementioned coexistence. We demonstrate such coexistence in disordered multi-chain and multi-layer systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
