arXiv subjects

Elizaveta Safonova

Publications and source records attributed to Elizaveta Safonova.

4 recordsLinked to original sources

arXiv2026

Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach

By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $ρ(E)$ for the Lévy and the Lévy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-law tails. This makes the standard Hubbard-Stratonovich transformation inapplicable to such problems. We used, instead, the functional Hubbard-Stratonovich transformation which allowed to solve the problem analytically for large sizes of matrices. We show that $ρ(E)$ depends crucially on the control parameter that drives the system through the transition between the ergodic and the fractal phases and it can be used as an order parameter.

cond-mat.dis-nn↗

arXiv2026

Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach

We studied global density-of-states correlation function $R(ω)$ for Lévy-Rosenzweig-Porter random matrix ensemble in the non-ergodic extended phase. Using an extension of Efetov's supersymmetry approach we calculated $R(ω)$ exactly in all relevant ranges of $ω$. At relatively low $ω\leq Γ$\, (with $Γ\gg Δ$ being the effective miniband width) we found GUE-type oscillations with period of level spacing $Δ$, decaying exponentially at the Thouless energy scale $E_{Th} = \sqrt{ΔΓ/2π}$. At high energies $ω\gg E_{Th}$ our results coincide with those obtainen via cavity equation approach. Inverse of the effective miniband width, $1/Γ$, is shown to be given by the average of the local decay times over Lévy distribution.

cond-mat.dis-nn↗

arXiv2026

Analytical Theory for Anomalous Diffusion in the Anderson Model with Heavy Tails

We develop an analytical theory of anomalous transport in a noninteracting Anderson model with heavy-tailed hopping amplitudes. The broad distribution of hopping amplitudes gives rise to an extended intermediate-time regime with a subdiffusive effective exponent, despite the absence of interactions or genuine many-body effects. By solving the transport equations analytically, we derive the time dependence of the mean-square displacement and identify a continuous crossover from an intermediate anomalous regime to asymptotically diffusive transport. As the localization transition is approached, the spatial extent of the subdiffusive window diverges parametrically, while the crossover to conventional diffusion remains finite in units of $Γ_0^{-1}$. This produces an increasingly broad anomalous transport regime in space that can closely resemble Griffiths-type transport observed near the many-body localization transition. Our results demonstrate that rare hopping processes alone provide a microscopic single-particle mechanism for robust transport anomalies, establishing an analytical benchmark for distinguishing interaction-induced effects from disorder-driven dynamics.

cond-mat.dis-nn↗

arXiv2023

Intensity statistics inside an open wave-chaotic cavity with broken time-reversal invariance

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number $M$ of open channels the probability density ${\cal P}(I)$ for the single-point intensity $I$ decays as a power law for large intensities: ${\cal P}(I)\sim I^{-(M+2)}$, provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law ${\cal P}(I)\sim \exp(-I/\overline{I})$ which turns out to be valid only in the limit $M\to \infty$. We also find the joint probability density of intensities $I_1, \ldots, I_L$ in $L>1$ observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For $L\to \infty$ the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

cond-mat.dis-nn↗