We construct a quantum kinetic theory of a weakly interacting critical boson gas using the expectation values of products of Heisenberg field operators in the grand canonical ensemble. Using a functional representation for the Wick theorem for time-ordered products, we construct a perturbation theory for the generating functional of these time-dependent Green’s functions at a finite temperature. We note some problems of the functional-integral representation and discuss unusual apparent divergences of the perturbation expansion. We propose a regularization of these divergences using attenuating propagators. Using a linear transformation to variables with well-defined scaling dimensions, we construct an infrared effective field theory. We show that the structure of the regularized model is restored by renormalization. We propose a multiplicatively renormalizable infrared effective model of the quantum dynamics of a boson gas.We construct a quantum kinetic theory of a weakly interacting critical boson gas using the expectation values of products of Heisenberg field operators in the grand canonical ensemble. Using a functional representation for the Wick theorem for time-ordered products, we construct a perturbation theory for the generating functional of these time-dependent Green’s functions at a finite temperature. We note some problems of the functional-integral representation and discuss unusual apparent divergences of the perturbation expansion. We propose a regularization of these divergences using attenuating propagators. Using a linear transformation to variables with well-defined scaling dimensions, we construct an infrared effective field theory. We show that the structure of the regularized model is restored by renormalization. We propose a multiplicatively renormalizable infrared effective model of the quantum dynamics of a boson gas.

Theoretical and Mathematical PhysicsSep 1, 20196 citations

Some consequences of kinetic theory for bosons

German A. Skorobogatov, B.E. Dzevitskii

Soviet physics. DokladyApr 1, 19740 citations

Adiabatic dynamics of a quantum critical system coupled to an environment: Scaling and kinetic equation approaches

Dario Patanè, Luigi Amico A, Alessandro Silva +2 more

We study the dynamics of open quantum many-body systems driven across a critical point by quenching a parameter of the Hamiltonian at a certain velocity. General scaling laws are derived for the density of excitations and of energy produced during the quench as a function of the quench velocity and the bath temperature. The scaling laws and their regimes of validity are verified for the $XY$ spin chain locally coupled to bosonic baths. A detailed derivation and analysis of the kinetic equations for the problem is presented.We study the dynamics of open quantum many-body systems driven across a critical point by quenching a parameter of the Hamiltonian at a certain velocity. General scaling laws are derived for the density of excitations and of energy produced during the quench as a function of the quench velocity and the bath temperature. The scaling laws and their regimes of validity are verified for the $XY$ spin chain locally coupled to bosonic baths. A detailed derivation and analysis of the kinetic equations for the problem is presented.

arXiv:0812.3685Physical Review BJul 2, 200960 citations

On the kinetics of subsystems interacting with Bosons

Victor F. Los, A.G. Martynenko

Physica A Statistical Mechanics and its ApplicationsOct 1, 19863 citations

On the microscopic theory of interacting bosons

Peter A. Ring, Y. K. Gambhir, S. Iwasaki +1 more

Progress in Particle and Nuclear PhysicsJan 1, 19831 citation

Thermal conductivity in one-dimensional electronic fluids

Dmitri B. Gutman, Ivan V. Protopopov, Rickmoy Samanta +1 more

We study thermal conductivity in one-dimensional electronic fluids combining kinetic [R. Samanta, I. V. Protopopov, A. D. Mirlin, and D. B. Gutman, Thermal transport in one-dimensional electronic fluid, Phys. Rev. Lett. 122, 206801 (2019)] and hydrodynamic [I. V. Protopopov, R. Samanta, A. D. Mirlin, and D. B. Gutman, Anomalous hydrodynamics in one-dimensional electronic fluid, Phys. Rev. Lett. 126, 256801 (2021)] theories. The kinetic approach is developed by partitioning the Hilbert space into bosonic and fermionic sectors. We focus on the regime where the long-living thermal excitations are fermions and compute thermal conductivity. From the kinetic theory standpoint, the fermionic part of thermal conductivity is normal, while the bosonic one is anomalous, that scales as ω–1/3 and thus dominates in the infrared limit. The multi-mode hydrodynamic theory is obtained by projecting the fermionic kinetic equation on the zero modes of its collision integral. On a bare level, both theories agree and the thermal conductivity computed in hydrodynamic theory matches the result of the kinetic equation. The interaction between hydrodynamic modes leads to renormalization and consequently to anomalous scaling of the transport coefficients. In a four-mode regime, all modes are ballistic and the anomaly manifests itself in Kardar-Parisi-Zhang-like broadening with asymmetric power-law tails. “Heads” and “tails” of the pulses contribute equally to thermal conductivity, leading to ω–1/3 scaling of heat conductivity. In the three-mode regime, the system is in the universality class of a classical viscous fluid [Herbert Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014); O. Narayan and S. Ramaswamy, Anomalous heat conduction in one-dimensional momentum-conserving systems, Phys. Rev. Lett. 89, 200601 (2002)].We study thermal conductivity in one-dimensional electronic fluids combining kinetic [R. Samanta, I. V. Protopopov, A. D. Mirlin, and D. B. Gutman, Thermal transport in one-dimensional electronic fluid, Phys. Rev. Lett. 122, 206801 (2019)] and hydrodynamic [I. V. Protopopov, R. Samanta, A. D. Mirlin, and D. B. Gutman, Anomalous hydrodynamics in one-dimensional electronic fluid, Phys. Rev. Lett. 126, 256801 (2021)] theories. The kinetic approach is developed by partitioning the Hilbert space into bosonic and fermionic sectors. We focus on the regime where the long-living thermal excitations are fermions and compute thermal conductivity. From the kinetic theory standpoint, the fermionic part of thermal conductivity is normal, while the bosonic one is anomalous, that scales as ω–1/3 and thus dominates in the infrared limit. The multi-mode hydrodynamic theory is obtained by projecting the fermionic kinetic equation on the zero modes of its collision integral. On a bare level, both theories agree and the thermal conductivity computed in hydrodynamic theory matches the result of the kinetic equation. The interaction between hydrodynamic modes leads to renormalization and consequently to anomalous scaling of the transport coefficients. In a four-mode regime, all modes are ballistic and the anomaly manifests itself in Kardar-Parisi-Zhang-like broadening with asymmetric power-law tails. “Heads” and “tails” of the pulses contribute equally to thermal conductivity, leading to ω–1/3 scaling of heat conductivity. In the three-mode regime, the system is in the universality class of a classical viscous fluid [Herbert Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014); O. Narayan and S. Ramaswamy, Anomalous heat conduction in one-dimensional momentum-conserving systems, Phys. Rev. Lett. 89, 200601 (2002)].

Low Temperature PhysicsDec 1, 20231 citation

XY

spin chain locally coupled to bosonic baths. A detailed derivation and analysis of the kinetic equations for the problem is presented.