In this work we examine the dynamics of one-dimensional systems. We present a continuum approach to the construction of the non-equilibrium Keldysh functional integral and derive a relation between the classical and quantum fields of the Keldysh formalism and the occupation of a state. Using the Keldysh formalism, we give a self-contained presentation of bosonization and refermionisation of fermionic and bosonic interacting particles. We derive the first two non-linear corrections to linear bosonization due to the fermionic spectrum curvature using the functional integral formalism. Using the previous results, we study the thermal dynamics of one-dimensional systems. We consider both the phonons, coming from bosonization, and fermionic quasiparticles, coming from refermionisation, in a single theory. Having them in a single theory is justified by a scale separation between them. Studying the dynamical structure factor we find three regimes. From higher to lower energies we have a ballistic and a collisional regimes of fermionic quasiparticles and a hydrodynamical regime of non-linear phonons. The phase field of the non-linear bosons satisfies the Kardar-Parisi-Zhang equation, thereby linking the dynamics of one-dimensional quantum systems to the universality class of surface growth. The time-scale separating the phononic and fermionic quasiparticle regimes is very long for up-to-date experiments, meaning that the ballistic regime of fermionic quasiparticles is the only one likely to be observed. Since this approach has a limited range of validity for weakly interacting bosons, we derive their dynamical structure factor using a semiclassical approach.
In this work we examine the dynamics of one-dimensional systems. We present a continuum approach to the construction of the non-equilibrium Keldysh functional integral and derive a relation between the classical and quantum fields of the Keldysh formalism and the occupation of a state. Using the Keldysh formalism, we give a self-contained presentation of bosonization and refermionisation of fermionic and bosonic interacting particles. We derive the first two non-linear corrections to linear bosonization due to the fermionic spectrum curvature using the functional integral formalism. Using the previous results, we study the thermal dynamics of one-dimensional systems. We consider both the phonons, coming from bosonization, and fermionic quasiparticles, coming from refermionisation, in a single theory. Having them in a single theory is justified by a scale separation between them. Studying the dynamical structure factor we find three regimes. From higher to lower energies we have a ballistic and a collisional regimes of fermionic quasiparticles and a hydrodynamical regime of non-linear phonons. The phase field of the non-linear bosons satisfies the Kardar-Parisi-Zhang equation, thereby linking the dynamics of one-dimensional quantum systems to the universality class of surface growth. The time-scale separating the phononic and fermionic quasiparticle regimes is very long for up-to-date experiments, meaning that the ballistic regime of fermionic quasiparticles is the only one likely to be observed. Since this approach has a limited range of validity for weakly interacting bosons, we derive their dynamical structure factor using a semiclassical approach.
We develop a self-contained approach to bosonization and refermionization using the Keldysh functional integral. Starting from fermionic particles, we bosonize the system and obtain a description in terms of the Tomonaga-Luttinger liquid, with, in addition, an infinite series of interaction terms arising from the curvature of the fermionic particle spectrum. We explicitly calculate the leading interaction term and check its consistency with a different approach based on the Matsubara framework, within which we calculate the second leading interaction term, as well. Moreover, we bosonize weakly and strongly interacting bosonic particles, and, finally, refermionize interacting phonons into non-interacting fermionic quasiparticles. The work culminates in a map between bosonic and fermionic particles and effective bosonic and fermionic excitations, representing phonons and fermionic quasiparticles.
We establish a nonequilibrium scaling regime in the short-time evolution of one-dimensional interacting open quantum systems subject to a generic heating mechanism. This dynamical regime is characterized by uncompensated phonon production and a superdiffusive, universal scaling of quasiparticle lifetimes with momentum $\ensuremath{\sim}{q}^{\ensuremath{-}5/3}$, distinct from the finite- and zero-temperature cases. It is separated from a high-momentum regime by a time-dependent scale fading out as ${q}_{0}(t)\ensuremath{\sim}{t}^{\ensuremath{-}4/5}$. In the latter region we observe thermalization to an effective time-dependent equilibrium with linearly increasing temperature. By mapping out the dynamical phase diagram and computing the dynamical structure factor within an open-system Keldysh functional integral approach, we show how these predictions can be explored in cold-atom experiments by means of Bragg spectroscopy.
While the mechanisms governing the equilibrium properties of quantum gases are today relatively well understood, their non-equilibrium counterparts remain largely unknown. In this thesis, we theoretically explore the non-equilibrium physics of low-dimensional, interacting Bose gases in two representative configurations. In the first one, we consider an isolated Bose superfluid in two dimensions following a quench of the coupling constant. Using a quantum hydrodynamic description combined with a Keldysh field formalism, we derive quantum kinetic equations for the low-energy phononic excitations of the system. This enables us to describe the system's evolution from its short-time (prethermal) coherent dynamics to its long-time thermalization. In particular, we derive and discuss the Landau-Beliaev damping rates both in the standard perturbative approach and within a self-consistent extension of the theory. The results are also discussed in the light of recent experiments. Our second study explores a one-dimensional, periodically-driven quantum system, a Bose gas subjected to periodically-kicked interactions. In the limit of infinitely short kicks, this system was previously shown to exhibit a fast exponential spreading of the wave function. By revisiting this problem for kicks of arbitrary duration, we demonstrate that, in this case, the spreading is not exponential but sub-diffusive at long time. Our findings indicate that the breakdown of exponential spreading occurs at very short times even for extremely short kicks, suggesting that sub-diffusion is more the rule than the exception in that system.
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 theoretically the nonequilibrium dynamics of a two-dimensional (2D) uniform Bose superfluid following a quantum quench, from its short-time (prethermal) coherent dynamics to its long-time thermalization. Using a quantum hydrodynamic description combined with a Keldysh field formalism, we derive quantum kinetic equations for the low-energy phononic excitations of the system and characterize both their normal and anomalous momentum distributions. We apply this formalism to the interaction quench of a 2D Bose gas and study the ensuing dynamics of its quantum structure factor and coherence function, both recently measured experimentally. Our results indicate that, in two dimensions, a description in terms of independent quasiparticles becomes quickly inaccurate and should be systematically questioned when dealing with nonequilibrium scenarios.
We propose a new method to study non-equilibrium dynamics of scalar fields starting from non-Gaussian initial conditions using Keldysh field theory. We use it to study dynamics of phonons coupled to bosonic and fermionic baths, starting from initial Fock states. We find that in one dimension long wavelength phonons coupled to fermionic baths do not thermalize both at low and high bath temperatures. At low temperature, constraints from energy-momentum conservation lead to a narrow bandwidth of particle-hole excitations and the phonons effectively do not feel the effects of this bath. On the other hand, the strong band edge divergence of particle-hole density of states leads to an undamped polariton-like mode of the dressed phonons above the band edge of the particle-hole excitations. These undamped modes contribute to the lack of thermalization of long wavelength phonons at high temperatures. In higher dimensions, these constraints and the divergence of density of states are weakened and leads to thermalization at all wavelengths.