A stochastic transport description for the single-particle density matrix is briefly discussed. It is shown that the stochastic description contains, in addition to incoherent binary collisions, a coherent damping mechanism due to coupling between mean-field fluctuations and single-particle motion, and an expression for the coherent collision term is derived. In the limit of small fluctuations around equilibrium, the collective and single-particle self-energies due to the coherent mechanism are deduced.A stochastic transport description for the single-particle density matrix is briefly discussed. It is shown that the stochastic description contains, in addition to incoherent binary collisions, a coherent damping mechanism due to coupling between mean-field fluctuations and single-particle motion, and an expression for the coherent collision term is derived. In the limit of small fluctuations around equilibrium, the collective and single-particle self-energies due to the coherent mechanism are deduced.

Physical Review CJul 3, 20017 citations

Transport Theories for Strongly-Interacting Systems

W. Cassing

Lecture notes in physicsJan 1, 202115 citations

Frequency-Dependent Transport through a Quantum Dot in the Kondo Regime

Michael Sindel, Walter Hofstetter, Jan von Delft +1 more

We study the ac conductance and equilibrium current fluctuations of a Coulomb-blockaded quantum dot in the Kondo regime. To this end we have developed an extension of the numerical renormalization group suitable for the nonperturbative calculation of finite-frequency transport properties. We demonstrate that ac transport gives access to the many-body resonance in the equilibrium spectral density. It provides a new route for measuring this key signature of Kondo physics, which so far has defied direct experimental observation.We study the ac conductance and equilibrium current fluctuations of a Coulomb-blockaded quantum dot in the Kondo regime. To this end we have developed an extension of the numerical renormalization group suitable for the nonperturbative calculation of finite-frequency transport properties. We demonstrate that ac transport gives access to the many-body resonance in the equilibrium spectral density. It provides a new route for measuring this key signature of Kondo physics, which so far has defied direct experimental observation.

arXiv:cond-mat/0406312Physical Review LettersMay 19, 200530 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

Finite-Frequency Transport Through A Quantum Dot In The Kondo Regime

Michael Sindel, Walter Hofstetter, Jan von Delft +1 more

We study the ac conductance and equilibrium current fluctuations of a Coulomb blockaded quantum dot in the Kondo regime. To this end we have developed an extension of the numerical renormalization group suitable for the nonperturbative calculation of finite‐frequency transport properties. We demonstrate that ac transport gives access to the many‐body resonance in the equilibrium spectral density. It provides a new route to measuring this key signature of Kondo physics, which so far has defied direct experimental observation.We study the ac conductance and equilibrium current fluctuations of a Coulomb blockaded quantum dot in the Kondo regime. To this end we have developed an extension of the numerical renormalization group suitable for the nonperturbative calculation of finite‐frequency transport properties. We demonstrate that ac transport gives access to the many‐body resonance in the equilibrium spectral density. It provides a new route to measuring this key signature of Kondo physics, which so far has defied direct experimental observation.

AIP conference proceedingsJan 1, 20060 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.