Related papers: An upper bound on transport
We prove an upper bound on the diffusivity of a general local and translation invariant quantum Markovian spin system: $D \leq D_0 + \left(\alpha \, v_\text{LR} \tau + \beta \, \xi \right) v_\text{C}$. Here $v_\text{LR}$ is the…
We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
Transport in strongly-disordered, metallic systems is governed by diffusive processes. Based on quantum mechanics, it has been conjectured that these diffusivities obey a lower bound $D/v^2\gtrsim \hbar/k_B T$, the saturation of which…
We study the presence of universal bounds on transport in homogeneous holographic models with broken translations. We verify numerically that, in holographic systems with momentum dissipation, the viscosity to entropy bound might be…
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…
In an incoherent metal, transport is controlled by the collective diffusion of energy and charge rather than by quasiparticle or momentum relaxation. We explore the possibility of a universal bound $D \gtrsim \hbar v_F^2/(k_B T)$ on the…
We study transport in a one-dimensional lattice system with two conserved quantities -- `volume' and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate…
The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone…
Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity…
The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed…
Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general arguments) universally for all theories.…
Transport of charge carriers in mechanically soft semiconductors is mainly limited by their interaction with slow intermolecular phonons. Carrier motion exhibits a crossover from superdiffusive to subdiffusive, producing a distinct…
We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken…
We characterize steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume $L^d$, where both mass and {\it center-of-mass} (CoM) remain conserved and detailed balance…
I explore a theory of transport and optical properties of strange metallic carriers in strongly correlated systems that follows from assuming that the diffusion constant has reached its quantum limit $D=\hbar/m$, and that such quantum…
We obtain a rigorous upper bound on the resistivity $\rho$ of an electron fluid whose electronic mean free path is short compared to the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a non-thermal…
Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is $1/\tau_\text{tr} = 2\pi \lambda T$, where $\lambda$ is a dimensionless strength of…
We consider the diffusive limit of an unsteady neutron transport equation in a two-dimensional plate with one-speed velocity. We show the solution can be approximated by the sum of interior solution, initial layer, and boundary layer with…
It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the…
We develop a general method to bound the spreading of an entire wavepacket under Schr\"odinger dynamics from above. This method derives upper bounds on time-averaged moments of the position operator from lower bounds on norms of transfer…