Related papers: What is the Thouless Energy for Ballistic Systems?
It was shown using perturbation theory[1] that Thouless energy Ec for a quantum system scales linearly with the conductance of the system. We derive in an alternate way in 1-D that Ec scales with the conductance in a very different way. We…
Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for an instanton liquid partition function. We find that for energy differences $\delta E$ below an energy scale $E_c$, identified as the Thouless energy, the eigenvalue…
We consider the two-level correlation function in two-dimensional disordered systems. In the non-ergodic diffusive regime, at energy $\epsilon>E_{c}$ ($E_{c}$ is the Thouless energy), it is shown to be completely determined by the weak…
Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across the many-body localization transition (MBLT) in a…
In recent years the ergodicity of disordered spin chains has been investigated via extensive numerical studies of the level statistics or the transport properties. However, a clear relationship between these results has yet to be…
Electron energy distribution in a mesoscopic diffusive wire in the presence of an external ac voltage is obtained. At low temperatures the distribution has a form of a multi-step staircase, with the step width equal to the field energy…
Statistical properties of energy levels, wave functions and quantum-mechanical matrix elements in disordered conductors are usually calculated assuming diffusive electron dynamics. Mirlin has pointed out [Phys. Rep. 326, 259 (2000)] that…
Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences $\delta E$ below an energy scale $E_c$ the eigenvalue correlations are…
We study the ergodic side of the many-body localization transition in its standard model, the disordered Heisenberg quantum spin chain. We show that the Thouless energy, extracted from long-range spectral statistics and the power-spectrum…
Disorder-induced spectral correlations of mesoscopic quantum systems in the non-diffusive regime and their effect on the magnetic susceptibility are studied. We perform impurity averaging for non-translational invariant systems by combining…
The notion of Thouless energy plays a central role in the theory of Anderson localization. We investigate the scaling of Thouless energy across the many-body localization (MBL) transition in a Floquet model. We use a combination of methods…
The Thouless formula \(G = (e^2/h)(E_c/\Delta)\) for the two-probe dc conductance $G$ of a d-dimensional mesoscopic cube is re-analysed to relate its quantum capacitance $C_Q$ to the reciprocal of the level spacing $\Delta$. To this end,…
The free energies of static charges and center monopoles are given by their fluxes. While electric fluxes show the universal behaviour of the deconfinement transition, the monopole free energies vanish in the thermodynamic limit at all…
As a function of the disorder strength in a mesoscopic system, the electron dynamics crosses over from the ballistic through the diffusive towards the localized regime. The ballistic and the localized situation correspond to integrable or…
We calculated the effects of spin-orbit interaction (SOI) on the energy bands, ballistic conductance and the electron-diffusion thermoelectric power of a nanowire by varying the temperature, electron density and width of the wire. The…
We consider the mesoscopic normal persistent current (PC) in a very low-temperature superconductor with a bare transition temperature $T_c^0$ much smaller than the Thouless energy $E_c$. We show that in a rather broad range of pair-breaking…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
We define a characteristic energy density based on the measurement of the two first moments of the extrinsic injected power smoothed over time. Using the stationarity, we show that this definition characterizes an energy per degrees freedom…
In the ballistic regime, the metallic temperature dependence of the conductivity in a two-dimensional electron system in silicon is found to change non-monotonically with the degree of spin polarization. In particular, it fades away just…
We study disorder-induced spectral correlations and their effect on the magnetic susceptibility of mesoscopic quantum systems in the non-diffusive regime. By combining a diagrammatic perturbative approach with semiclassical techniques we…