Generalized nonlinear Langevin equation from quantum nonlinear projection operator
arXiv:2403.15825 · doi:10.1103/PhysRevD.110.056042
Abstract
We systematically derive the quantum generalized nonlinear Langevin equation using Morozov's projection operator method. This approach extends the linear Mori-Zwanzig projection operator technique, allowing for the inclusion of nonlinear interactions among macroscopic modes. Additionally, we obtain the quantum generalized Fokker-Planck equation within the Heisenberg picture, which is consistent with Morozov's original formulation. These equations are fundamentally significant in non-equilibrium statistical physics, particularly in scenarios characterized by enhanced fluctuations, such as anomalous transport phenomena near critical points. The quantum nature of the derived generalized Langevin and Fokker-Planck equations is anticipated to provide a more detailed description than their classical equivalents. Specifically, the noise kernel in the quantum generalized Langevin equation is multiplicative, which broadens the applicability beyond Gaussian approximations. Given specific interactions, these equations are expected to be instrumental in investigating critical transport phenomena.
arXiv commentThe version published in PRD. Title and structure of the article changed to emphasize the key points. Any questions, comments, and criticism are welcome
References in corpus (24)
- Signatures of the Tricritical Point in QCD
- Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
- Critical point of QCD at finite T and μ, lattice results for physical quark masses
- Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential
- Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC
- Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview
- Universal properties of bulk viscosity near the QCD phase transition
- Properties of hot and dense matter from relativistic heavy ion collisions
- QCD at finite chemical potential with six time slices
- Non-monotonic energy dependence of net-proton number fluctuations
- New Critical Point Induced by the Axial Anomaly in Dense QCD
- Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at energies available at the BNL Relativistic Heavy Ion Collider
- Collision Energy Dependence of Moments of Net-Kaon Multiplicity Distributions at RHIC
- Coarse-Grained Modelling Out of Equilibrium
- Measurement of higher cumulants of net-charge multiplicity distributions in AuAu collisions at GeV
- Energy Dependence of Multiplicity Fluctuations in Heavy Ion Collisions at the CERN SPS
- Multiplicity and transverse momentum fluctuations in inelastic proton-proton interactions at the CERN Super Proton Synchrotron
- Enhancement of Critical Slowing Down in Chiral Phase Transition -- Langevin Dynamics Approach --
- Beam energy dependence of net- fluctuations measured by the STAR experiment at RHIC
- Relativistic hydrodynamics from projection operator method
- Higher moment fluctuations of identified particle distributions from ALICE
- Multiplicity fluctuations of identified hadrons in p+p interactions at SPS energies
- Dynamics near QCD critical point by dynamic renormalization group
- Pseudorapidity dependence of multiplicity and transverse momentum fluctuations in pp collisions at SPS energies