Abstract We consider in this work the different possible stationary flows of a one-dimensional quantum fluid in the mean-field regime. We focus on the supersonic regime where a transition from a time-dependent flow to a stationary diffractive flow occurs at a given critical velocity. We give nonperturbative results for this critical velocity in the presence of a localised obstacle of arbitrary size and strength. In addition, we discuss the existence of superfluid-like solution in the supersonic regime due to resonant transport and provide a complete map of the different regimes of stationary transport of a quantum fluid.Abstract We consider in this work the different possible stationary flows of a one-dimensional quantum fluid in the mean-field regime. We focus on the supersonic regime where a transition from a time-dependent flow to a stationary diffractive flow occurs at a given critical velocity. We give nonperturbative results for this critical velocity in the presence of a localised obstacle of arbitrary size and strength. In addition, we discuss the existence of superfluid-like solution in the supersonic regime due to resonant transport and provide a complete map of the different regimes of stationary transport of a quantum fluid.

arXiv:2306.05048Europhysics Letters (EPL)Aug 1, 20231 citation

Dynamics and Transport Near Quantum-Critical Points

Subir Sachdev A

arXiv:cond-mat/9705266Springer eBooksJan 1, 19980 citations

Transverse transport in the vicinity of a quantum critical point

Karen Michaeli, Alexander M. Finkel’stein

APSMar 1, 20100 citations

Transient and universal regimes in quantum reaction-transport kinetics

Hossein Hosseinabadi, Roderich Moessner

Quantum reaction-transport systems consist of coherently propagating particles that irreversibly react upon encounter. Their relaxation is commonly classified as reaction-limited or transport-limited, depending on the relative timescales of reaction and particle transport. We show that this expectation fails in low dimensions by studying the quantum binary annihilation, $A+A \to \emptyset$ , where reaction processes acquire singular fluctuation corrections below the upper critical dimension $D_c=2$ . Consequently, fluctuations dominate the asymptotic kinetics for $D<2$ . In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime with $n\sim t^{-1/2}$ , governed by a quantum-Zeno scale even for arbitrarily weak loss. At $D=2$ , the kinetics acquires logarithmic corrections, whereas above two dimensions mean-field scaling is asymptotically restored. At and below the upper critical dimension, mean-field behavior can nevertheless persist over parametrically long crossover times before the asymptotic fluctuation-dominated regime emerges. We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions. In $D>1$ , these collisions redistribute momentum populations and are parametrically faster than losses in the transport-limited regime, allowing the system to approach a quasi-stationary thermal state.Quantum reaction-transport systems consist of coherently propagating particles that irreversibly react upon encounter. Their relaxation is commonly classified as reaction-limited or transport-limited, depending on the relative timescales of reaction and particle transport. We show that this expectation fails in low dimensions by studying the quantum binary annihilation, $A+A \to \emptyset$, where reaction processes acquire singular fluctuation corrections below the upper critical dimension $D_c=2$. Consequently, fluctuations dominate the asymptotic kinetics for $D<2$. In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime with $n\sim t^{-1/2}$, governed by a quantum-Zeno scale even for arbitrarily weak loss. At $D=2$, the kinetics acquires logarithmic corrections, whereas above two dimensions mean-field scaling is asymptotically restored. At and below the upper critical dimension, mean-field behavior can nevertheless persist over parametrically long crossover times before the asymptotic fluctuation-dominated regime emerges. We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions. In $D>1$, these collisions redistribute momentum populations and are parametrically faster than losses in the transport-limited regime, allowing the system to approach a quasi-stationary thermal state.

cond-mat.stat-mechCross-listedarXiv:2609.09305Sep 10, 20260 citations

Quantum Critical Ballistic Transport in Two-Dimensional Fermi Liquids

Mani Chandra, Gitansh Kataria, Deshdeep Sahdev

Electronic transport in Fermi liquids is usually Ohmic, because of momentum-relaxing scattering due to defects and phonons. These processes can become sufficiently weak in two-dimensional materials, giving rise to either ballistic or hydrodynamic transport, depending on the strength of electron-electron scattering. We show that the ballistic regime is a quantum critical point (QCP) on the regime boundary separating Ohmic and hydrodynamic transport. The QCP corresponds to a \emph{free} conformal field theory (CFT) with a dynamical scaling exponent $z = 1$ . Its nontrivial aspects emerge in device geometries with shear, wherein the regime has an intrinsic universal dissipation, a nonlocal current-voltage relation, and exhibits the critical scaling of the underlying CFT. The Fermi surface has electron-hole pockets across all angular scales and the current flow has \emph{vortices} at all spatial scales. We image the fluctuations in high-definition and animate their emergence as experimental parameters are tuned to the QCP (movie links in comments). The vortices clearly demonstrate that Pauli exclusion alone can produce collective effects, with low-frequency AC transport mediated by vortex dynamics. The scale-invariant spatial structure is much richer than that of an interaction-dominated hydrodynamic regime, which only has a single vortex at the device scale. Our findings provide a theoretical framework for both interaction-free and interaction-dominated non-Ohmic transport in two-dimensional materials, as seen in several contemporary experiments.Electronic transport in Fermi liquids is usually Ohmic, because of momentum-relaxing scattering due to defects and phonons. These processes can become sufficiently weak in two-dimensional materials, giving rise to either ballistic or hydrodynamic transport, depending on the strength of electron-electron scattering. We show that the ballistic regime is a quantum critical point (QCP) on the regime boundary separating Ohmic and hydrodynamic transport. The QCP corresponds to a \emph{free} conformal field theory (CFT) with a dynamical scaling exponent $z = 1$. Its nontrivial aspects emerge in device geometries with shear, wherein the regime has an intrinsic universal dissipation, a nonlocal current-voltage relation, and exhibits the critical scaling of the underlying CFT. The Fermi surface has electron-hole pockets across all angular scales and the current flow has \emph{vortices} at all spatial scales. We image the fluctuations in high-definition and animate their emergence as experimental parameters are tuned to the QCP (movie links in comments). The vortices clearly demonstrate that Pauli exclusion alone can produce collective effects, with low-frequency AC transport mediated by vortex dynamics. The scale-invariant spatial structure is much richer than that of an interaction-dominated hydrodynamic regime, which only has a single vortex at the device scale. Our findings provide a theoretical framework for both interaction-free and interaction-dominated non-Ohmic transport in two-dimensional materials, as seen in several contemporary experiments.

arXiv:1910.13737Bulletin of the American Physical SocietyOct 30, 20190 citations

Out-of-Equilibrium Transport near a Quantum Phase Transition

Stefan Kirchner, Lijun Zhu, Qimiao Si A

Bulletin of the American Physical SocietyMar 23, 20050 citations

A+A \to \emptyset

, where reaction processes acquire singular fluctuation corrections below the upper critical dimension

D_c=2

. Consequently, fluctuations dominate the asymptotic kinetics for

D<2

. In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime with

n\sim t^{-1/2}

, governed by a quantum-Zeno scale even for arbitrarily weak loss. At

D=2

, the kinetics acquires logarithmic corrections, whereas above two dimensions mean-field scaling is asymptotically restored. At and below the upper critical dimension, mean-field behavior can nevertheless persist over parametrically long crossover times before the asymptotic fluctuation-dominated regime emerges. We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions. In

D>1

, these collisions redistribute momentum populations and are parametrically faster than losses in the transport-limited regime, allowing the system to approach a quasi-stationary thermal state.

z = 1

. Its nontrivial aspects emerge in device geometries with shear, wherein the regime has an intrinsic universal dissipation, a nonlocal current-voltage relation, and exhibits the critical scaling of the underlying CFT. The Fermi surface has electron-hole pockets across all angular scales and the current flow has \emph{vortices} at all spatial scales. We image the fluctuations in high-definition and animate their emergence as experimental parameters are tuned to the QCP (movie links in comments). The vortices clearly demonstrate that Pauli exclusion alone can produce collective effects, with low-frequency AC transport mediated by vortex dynamics. The scale-invariant spatial structure is much richer than that of an interaction-dominated hydrodynamic regime, which only has a single vortex at the device scale. Our findings provide a theoretical framework for both interaction-free and interaction-dominated non-Ohmic transport in two-dimensional materials, as seen in several contemporary experiments.