Quantum Joule expansion of one-dimensional systems

Abstract

We investigate the Joule expansion of nonintegrable quantum systems that contain bosons or spinless fermions in one-dimensional lattices. A barrier initially confines the particles to be in half of the system in a thermal state described by the canonical ensemble and is removed at time t = 0. We investigate the properties of the time-evolved density matrix, the diagonal ensemble density matrix and the corresponding canonical ensemble density matrix with an effective temperature determined by the total energy conservation using exact diagonalization. The weights for the diagonal ensemble and the canonical ensemble match well for high initial temperatures that correspond to negative effective final temperatures after the expansion. At long times after the barrier is removed, the time-evolved Rényi entropy of subsystems bigger than half can equilibrate to the thermal entropy with exponentially small fluctuations. The time-evolved reduced density matrix at long times can be approximated by a thermal density matrix for small subsystems. Few-body observables, like the momentum distribution function, can be approximated by a thermal expectation of the canonical ensemble with strongly suppressed fluctuations. The negative effective temperatures for finite systems go to nonnegative temperatures in the thermodynamic limit for bosons, but is a true thermodynamic effect for fermions, which is confirmed by finite temperature density matrix renormalization group calculations. We propose the Joule expansion as a way to dynamically create negative temperature states for fermion systems with repulsive interactions.

Entanglement dynamics of a hard-core quantum gas during a Joule expansion

“…Ref. [49,50]. This path would probably require to take into account higher order corrections to the Euler hydrodynamics not considered in this work, see [58,59].…”

“…In particular, we wish to understand whether the presence of boundaries for the expanding gas will eventually spoil the validity of the hydrodynamic approach and, if so, when this is expected to happen. An ideal testbed for these ideas is the so-called Joule expansion [45,46,[48][49][50], where the system undergoes a sudden expansion of the containing tank as detailed in the following section. For this problem, we characterize the entanglement dynamics across the reflections in the Euler scaling limit and we present a Floquet picture for its long time limit.…”

Entanglement dynamics of a hard-core quantum gas during a Joule expansion

“…On the other hand, it would be interesting to better explore the long time regime where hydrodynamics breaks down and the system eventually relaxes to a non-equilibrium steady state, see e.g. references [51,52]. This path would probably require to take into account higher order corrections to the Euler hydrodynamics not considered in this work, see [62,63].…”

“…In particular, we wish to understand whether the presence of boundaries for the expanding gas will eventually spoil the validity of the hydrodynamic approach and, if so, when this is expected to happen. An ideal testbed for these ideas is the so-called Joule expansion [47,48,[50][51][52][53][54], where the system undergoes a sudden expansion of the containing tank as detailed in the following section. For this problem, we characterize the entanglement dynamics across the reflections in the Euler scaling limit and we present a Floquet picture for its long time limit.…”

Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices

“…As a second application, we study the expansion of harmonically trapped SU(N ) fermions after suddenly turning off the trap. Those quenches provide a fertile playground to unveil remarkable properties of correlated many-body systems [23,52,54,59,71,88,[108][109][110][111][112][113][114][115][116][117]. They can be viewed as nontrivial time-of-flight expansions that occur in the presence of interactions.…”