We investigate a $(d+1)$ -dimensional ``correlated'' random-field system with d spatial dimensions and one Trotter dimension along which randomness is ``correlated'' or striped. In the sense of universality this model is equivalent to a d-dimensional quantum random-field system. We investigate the dissipative Langevin dynamics of this ``striped'' $(d+1)$ -dimensional systems within a replica symmetric framework, employing the perturbative $\ensuremath{\epsilon}$ expansion around the upper critical dimension to explore the effect of an additional dimension (along which the randomness is correlated) on the dynamical scaling. We argue that the $\ensuremath{\epsilon}$ expansion fails to capture the activated nature of dynamics. We also extend the phenomenological renormalization-group calculations to investigate the critical behavior of a $(d+1)$ -dimensional correlated random-field Ising systems.We investigate a $(d+1)$-dimensional ``correlated'' random-field system with d spatial dimensions and one Trotter dimension along which randomness is ``correlated'' or striped. In the sense of universality this model is equivalent to a d-dimensional quantum random-field system. We investigate the dissipative Langevin dynamics of this ``striped'' $(d+1)$-dimensional systems within a replica symmetric framework, employing the perturbative $\ensuremath{\epsilon}$ expansion around the upper critical dimension to explore the effect of an additional dimension (along which the randomness is correlated) on the dynamical scaling. We argue that the $\ensuremath{\epsilon}$ expansion fails to capture the activated nature of dynamics. We also extend the phenomenological renormalization-group calculations to investigate the critical behavior of a $(d+1)$-dimensional correlated random-field Ising systems.

Physical review. B, Condensed matterJan 1, 20003 citations

Random quantum dynamics

Winton Brown

Jan 1, 20101 citation

Activated dynamics in the quantum random field Ising model

Ivan Balog, Lovro Šaravanja, Andrei A. Fedorenko

We study the critical dynamics of the quantum random-field Ising model using the nonperturbative functional renormalization group (NP-FRG). The static critical behavior is found to be controlled by the zero-temperature fixed point of the classical random-field Ising model, where both thermal and quantum fluctuations are dangerously irrelevant. Considering a family of quantum dynamical universality classes defined by a bare dynamical kernel $F_Λ(ω)\sim |ω|^σ$ , we show how this fluctuationless fixed point nevertheless controls the quantum dynamics by computing the full Matsubara-frequency dependence of the running dynamical kernel $F_k(ω)$ . This is essential at zero temperature: a naive treatment of the dynamical kernel flow leads to a divergence at a finite length scale, resulting in apparent localization. In contrast, keeping the full frequency dependence of the dynamical kernel and choosing a regulator adapted to its running scale yields a controlled flow. The resulting dynamics is of activated form, with a relaxation time given by $\ln τ\sim ξ^Ψ$ . The exponent $Ψ$ is determined by the static RFIM fixed-point exponents and by $σ$ . At finite temperature, the flow crosses over to the classical thermally activated scaling of the random-field Ising model. These results provide a quantitative field-theoretic realization of the heuristic activation scenario proposed earlier for the quantum random-field model and establish a framework for analyzing the dynamics of other disordered quantum systems that may exhibit similar tentative localization-like singularities.We study the critical dynamics of the quantum random-field Ising model using the nonperturbative functional renormalization group (NP-FRG). The static critical behavior is found to be controlled by the zero-temperature fixed point of the classical random-field Ising model, where both thermal and quantum fluctuations are dangerously irrelevant. Considering a family of quantum dynamical universality classes defined by a bare dynamical kernel $F_Λ(ω)\sim |ω|^σ$, we show how this fluctuationless fixed point nevertheless controls the quantum dynamics by computing the full Matsubara-frequency dependence of the running dynamical kernel $F_k(ω)$. This is essential at zero temperature: a naive treatment of the dynamical kernel flow leads to a divergence at a finite length scale, resulting in apparent localization. In contrast, keeping the full frequency dependence of the dynamical kernel and choosing a regulator adapted to its running scale yields a controlled flow. The resulting dynamics is of activated form, with a relaxation time given by $\ln τ\sim ξ^Ψ$. The exponent $Ψ$ is determined by the static RFIM fixed-point exponents and by $σ$. At finite temperature, the flow crosses over to the classical thermally activated scaling of the random-field Ising model. These results provide a quantitative field-theoretic realization of the heuristic activation scenario proposed earlier for the quantum random-field model and establish a framework for analyzing the dynamics of other disordered quantum systems that may exhibit similar tentative localization-like singularities.

arXiv:2606.31663Jun 30, 20260 citations

Computer simulations of quantum random dynamics

Zbigniew Haba

Springer eBooksJan 1, 19990 citations

Quantum Random Systems

Josef Honerkamp

Graduate texts in physicsJan 1, 20120 citations

Stochastic quantization of a system with quenched random fields

FERDINANDO DE PASQUALE, Patrizia Ruggiero, Marco Zannetti

A quantum system with quenched random fields linearly coupled to the order parameter is considered in the framework of stochastic quantization. By this method we give, in the large- $n$ limit, the unified treatment of static and dynamic properties at any temperature. We find that the random fields, contrary to what happens in the static case, do not affect the quantum-classical dynamical crossover.A quantum system with quenched random fields linearly coupled to the order parameter is considered in the framework of stochastic quantization. By this method we give, in the large-$n$ limit, the unified treatment of static and dynamic properties at any temperature. We find that the random fields, contrary to what happens in the static case, do not affect the quantum-classical dynamical crossover.

Physical review. B, Condensed matterSep 1, 19841 citation

We investigate a

(d+1)

-dimensional ``correlated'' random-field system with d spatial dimensions and one Trotter dimension along which randomness is ``correlated'' or striped. In the sense of universality this model is equivalent to a d-dimensional quantum random-field system. We investigate the dissipative Langevin dynamics of this ``striped''

(d+1)

-dimensional systems within a replica symmetric framework, employing the perturbative $\ensuremath{\epsilon}$ expansion around the upper critical dimension to explore the effect of an additional dimension (along which the randomness is correlated) on the dynamical scaling. We argue that the $\ensuremath{\epsilon}$ expansion fails to capture the activated nature of dynamics. We also extend the phenomenological renormalization-group calculations to investigate the critical behavior of a

(d+1)

-dimensional correlated random-field Ising systems.

F_Λ(ω)\sim |ω|^σ

, we show how this fluctuationless fixed point nevertheless controls the quantum dynamics by computing the full Matsubara-frequency dependence of the running dynamical kernel

F_k(ω)

. This is essential at zero temperature: a naive treatment of the dynamical kernel flow leads to a divergence at a finite length scale, resulting in apparent localization. In contrast, keeping the full frequency dependence of the dynamical kernel and choosing a regulator adapted to its running scale yields a controlled flow. The resulting dynamics is of activated form, with a relaxation time given by

\ln τ\sim ξ^Ψ

. The exponent

Ψ

is determined by the static RFIM fixed-point exponents and by

σ

. At finite temperature, the flow crosses over to the classical thermally activated scaling of the random-field Ising model. These results provide a quantitative field-theoretic realization of the heuristic activation scenario proposed earlier for the quantum random-field model and establish a framework for analyzing the dynamics of other disordered quantum systems that may exhibit similar tentative localization-like singularities.

A quantum system with quenched random fields linearly coupled to the order parameter is considered in the framework of stochastic quantization. By this method we give, in the large-

n

limit, the unified treatment of static and dynamic properties at any temperature. We find that the random fields, contrary to what happens in the static case, do not affect the quantum-classical dynamical crossover.