Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model
نویسندگان
چکیده
منابع مشابه
Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model
We consider Hermitian and symmetric random band matrices H in d > 1 dimensions. The matrix elements Hxy, indexed by x, y ∈ Λ ⊂ Z, are independent, uniformly distributed random variables if |x − y| is less than the band width W , and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales t W . We also show that the localiza...
متن کاملQuantum Diffusion and Delocalization for Band Matrices with General Distribution
We consider Hermitian and symmetric random band matrices H in d > 1 dimensions. The matrix elements Hxy, indexed by x, y ∈ Λ ⊂ Z, are independent and their variances satisfy σ xy := E|Hxy| = W−df((x− y)/W ) for some probability density f . We assume that the law of each matrix element Hxy is symmetric and exhibits subexponential decay. We prove that the time evolution of a quantum particle subj...
متن کاملQuantum Diffusion and Tunneling with Parametric Banded Random Matrix Hamiltonians
The microscopic origin of dissipation of a driven quantum many body system is addressed in the framework of a parametric banded random matrix approach. We find noticeable violations of the fluctuation–dissipation theorem and we observe also that the energy diffusion has a markedly non–Gaussian character. Within the Feynman–Vernon path integral formalism and in the Markovian limit, we further co...
متن کاملEigenfunction entropy and spectral compressibility for critical random matrix ensembles.
Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D(1) and the spectral compressibility χ are related by the simple equation χ+D(1)/d=1, where d is system dimensionality.
متن کاملRandom matrix model of adiabatic quantum computing
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT san NPcomplete problemd in terms of random matrix theory sRMTd. We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2011
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-011-1204-2