Contributor info: Dr Aleksey Lunkin

Elizaveta Safonova, Aleksey Lunkin, Mikhail Feigel'man

SciPost Phys. 20, 003 (2026) · published 12 January 2026 | Toggle abstract · pdf

We studied global density-of-states correlation function $R(\omega)$ for Lévy-Rosenzweig-Porter random matrix ensemble in the non-ergodic extended phase. Using an extension of Efetov's supersymmetry approach we calculated $R(\omega)$ exactly in all relevant ranges of $\omega$. At relatively low $\omega ≤ \Gamma$ (with $\Gamma \gg \Delta$ being the effective miniband width) we found GUE-type oscillations with period of level spacing $\Delta$, decaying exponentially at the Thouless energy scale $E_{Th} = \sqrt{\Delta \Gamma/2\pi}$. At high energies $\omega \gg E_{Th}$ our results coincide with those obtained in [A. V. Lunkin and K. Tikhonov, SciPost Phys. 19, 015 (2025)] via cavity equation approach. Inverse of the effective miniband width, $1/\Gamma$, is shown to be given by the average of the local decay times over Lévy distribution.

Mustafa E. Ismagambetov, Aleksey V. Lunkin, Pavel M. Ostrovsky

SciPost Phys. 19, 021 (2025) · published 17 July 2025 | Toggle abstract · pdf

We study localization effects in Josephson junctions with two superconductors connected by a strongly disordered metallic wire of length $L$. The conventional description of the Josephson effect in such systems, based on the quasiclassical Usadel equation, neglects electron interference and is only applicable when $L$ is shorter than the localization length $\xi$ in the wire. We develop a more general theory for the Josephson effect using the non-linear sigma model that fully accounts for electron interference, and hence localization. We show that for $L \gg \xi$, three qualitatively different regimes of the Josephson current arise depending on the ratio of the superconducting order parameter $\Delta$ and the mean level spacing in the localization volume $\Delta_\xi$. We derive the average supercurrent as a function of the phase difference for all three regimes. Quite unexpectedly, we observe that the Ambegaokar-Baratoff relation between the average critical current and the normal-state conductance still holds in the strongly localized state when $\Delta_\xi \gg \Delta$ and $\xi \ll L \ll (\xi/\pi^2) \ln^2(\Delta_\xi/\Delta)$.

Aleksey Lunkin, Konstantin Tikhonov

SciPost Phys. 19, 015 (2025) · published 16 July 2025 | Toggle abstract · pdf

We present an analytical calculation of the local density of states correlation function $ \beta(\omega) $ in the Lévy-Rosenzweig-Porter random matrix ensemble at energy scales larger than the level spacing but smaller than the bandwidth. The only relevant energy scale in this limit is the typical level width $\Gamma_0$. We show that $\beta(\omega \ll \Gamma_0) \sim W/\Gamma_0$ (here $W$ is width of the band) whereas $\beta(\omega \gg \Gamma_0) \sim (W/\Gamma_0) (\omega/\Gamma_0)^{-\mu} $ where $\mu$ is an index characterising the distribution of the matrix elements. We also provide an expression for the average return probability at long times: $\ln [R(t\gg\Gamma_0^{-1})] \sim -(\Gamma_0 t)^{\mu/2}$. Numerical results based on the pool method and exact diagonalization are also provided and are in agreement with the analytical theory.

Aleksey. V. Lunkin, Mikhail . V. Feigel'man

SciPost Phys. 13, 073 (2022) · published 29 September 2022 | Toggle abstract · pdf

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range $T \gg T_{FL}$. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric $\sigma(\omega,p)$ and thermal $\kappa(\omega,p)$ conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter $\mathcal{E}$. At low-frequencies $\omega \ll T$ we find the Lorenz ratio $L = \kappa(0,0)/T\sigma(0,0)$ to be non-universal and temperature-dependent. At $\omega \gg T$ the conductivity $\sigma(\omega,p)$ contains a pole with nearly linear dispersion $\omega \approx sp\sqrt{\ln\frac{\omega}{T}}$ reminiscent of the "zero-sound", known for Fermi-liquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large Kadowaki-Woods ratio.

Aleksey V. Lunkin, Mikhail V. Feigel’man

SciPost Phys. 12, 031 (2022) · published 20 January 2022 | Toggle abstract · pdf

We consider a non-equilibrium generalization of the mixed SYK$_4$+SYK$_2$ model and calculate the energy dissipation rate $W(\omega)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the polaron energy splitting $\omega_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $\omega_R$ and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.