Investigating the behavior of noninteracting fermions subjected to local dephasing, we reveal that quasi-particle dephasing can induce superdiffusive transport. This superdiffusion arises from nodal points within the momentum distribution of local dephasing quasi-particles, leading to asymptotic long-lived modes. By studying the dynamics of the Wigner function, we rigorously elucidate how the dynamics of these enduring modes give rise to Lévy walk processes, a renowned mechanism underlying superdiffusion phenomena. Our research demonstrates the controllability of dynamical scaling exponents by selecting quasi-particles and extends its applicability to higher dimensions, underlining the pervasive nature of superdiffusion in dephasing models.
We introduce a class of interacting fermionic quantum models in d dimensions with nodal interactions that exhibit superdiffusive transport. We establish nonperturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we find that the charge mode acquires an anomalous dispersion relation at long wavelength ω(q)∼q^{z} with dynamical exponent z=min[(2n+d)/2n,2], where n is the order of the nodal point in momentum space. We verify our predictions in one-dimensional systems using tensor-network techniques.
Quantum transport in nonequilibrium settings plays a fundamental role in understanding the properties of systems ranging from quantum devices to biological systems. Dephasing---a key aspect of out-of-equilibrium systems---arises from interactions with a noisy environment and can profoundly modify transport properties. Here we investigate the impact of dephasing on the nonequilibrium steady-state transport properties of noninteracting fermions on a one-dimensional lattice with long-range hopping (proportional to $1/{r}^{\ensuremath{\alpha}}$), where $\ensuremath{\alpha}>1$. We demonstrate the emergence of distinct transport regimes as the long-range hopping parameter, $\ensuremath{\alpha}$, is tuned. In the short-range limit ($\ensuremath{\alpha}\ensuremath{\gg}1$), transport is diffusive. Conversely, in the long-range limit $[\ensuremath{\alpha}\ensuremath{\sim}\mathcal{O}(1)]$, we observe a superdiffusive transport regime. Using numerical simulations of the Lindblad master equation and corroborating these with an analysis of the current-operator norm, we identify a critical long-range hopping parameter, ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.5$, below which superdiffusive transport becomes pronounced and rapidly becomes independent of the dephasing strength. Our results elucidate the intricate balance between dephasing and unitary dynamics, revealing steady-state transport features.
Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far been proposed on fine-tuned, artificial Hamiltonians, posing a significant challenge for experimental observation. In this work, we propose a broad class of models for generating superdiffusion potentially realizable in condensed matter systems across different spatial dimensions. A robust nodal structure emerges from the hybridization between the itinerant electrons and the local impurity orbitals, protected by the intrinsic symmetry and topology of the electronic band. We derive a universal scaling law for the conductance,
G∼L−γ, revealing how the exponent is dictated by the dimensionality of the nodal structure (
Dnode) and its order
n, and the dimensionality of the system
(D) at high temperatures or that of the Fermi surface (
DF) at low temperatures. Through numerical simulations, we validate these scaling relations at zero temperature for various models, including those based on graphene and multi-Weyl semimetals, finding excellent agreement between our theory and the computed exponents. Beyond the scaling of conductance, our framework predicts a suite of experimentally verifiable signatures, notably a new mechanism for linear-in-temperature resistivity (
ρ∼T) and a divergent low-frequency optical conductivity (
σ(ω)∼ωγ−1), establishing a practical route to discovering and engineering anomalous transport in quantum materials.
We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $\ensuremath{\alpha}$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a nonequilibrium steady-state charge transport, and (ii) time dynamics of an initially localized single-particle excitation in the absence of boundary reservoirs. In both variants, anomalous superdiffusive behavior is observed for $1<\ensuremath{\alpha}<1.5$, and for $\ensuremath{\alpha}>1.5$ the setup is effectively short ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behavior in open quantum systems.
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so-called ballistic behavior, which is generally expected for the spreading in a quantum process. We have experimentally investigated the superdiffusive behavior of a quantum walk, whose dynamics can be related to energy transport phenomena, with a resolution which is high enough to clearly distinguish between different disorder regimes. By our experimental setup, the region between ballistic and diffusive spreading can be effectively scanned by suitably setting few degrees of freedom and without applying any decoherence to the quantum walk evolution.
We study how discrete-time quantum walks behave under short-range correlated noise. By considering noise as a source of inhomogeneity of quantum gates, we introduce a primitive relaxation in the assumption of uncorrelated stochastic noise: binary pair correlations manifesting in the random distribution. Using different quantum gates, we examined the transport properties for both spatial and temporal noise regimes. For spatial inhomogeneities, we unveil noise correlations driving quantum walks from the well-known exponentially localized regime to superdiffusive spreading. This scenario displays an intriguing performance in which the superdiffusive exponent is almost invariant to the degree of inhomogeneity. The time-asymptotic regime and the finite-size scaling also unveil an emergent superdiffusive behavior for quantum walks undergoing temporal noise correlation, replacing the diffusive regime exhibited when noise is random and uncorrelated. However, some quantum gates are insensitive to correlations, contrasting with the spatial noise scenario. Numerical and analytical results provide valuable insights into the underlying mechanism of superdiffusive quantum walks, including those arising from deterministic aperiodic inhomogeneities.