Relaxation in finite fermion systems

We investigate the non-equilibrium relaxation dynamics of a one dimensional system of interacting spinless fermions near the XXZ integrable point. We observe two qualitatively different regimes: close to integrability and for low energies the relaxation proceeds in two steps (prethermalization scenario), while for large energies and/or away from integrability the dynamics develops in a single step. When the integrability breaking parameter is below a certain finite threshold and the energy of the system is sufficiently low the lifetime of the metastable states increases abruptly by several orders of magnitude, resembling the physics of glassy systems. This is reflected in a sudden jump in the relaxation timescales. We present results for finite but large systems and for large times compared to standard numerical methods. Our approach is based on the construction of equations of motion for one- and two-particle correlation functions using projection operator techniques.We investigate the non-equilibrium relaxation dynamics of a one dimensional system of interacting spinless fermions near the XXZ integrable point. We observe two qualitatively different regimes: close to integrability and for low energies the relaxation proceeds in two steps (prethermalization scenario), while for large energies and/or away from integrability the dynamics develops in a single step. When the integrability breaking parameter is below a certain finite threshold and the energy of the system is sufficiently low the lifetime of the metastable states increases abruptly by several orders of magnitude, resembling the physics of glassy systems. This is reflected in a sudden jump in the relaxation timescales. We present results for finite but large systems and for large times compared to standard numerical methods. Our approach is based on the construction of equations of motion for one- and two-particle correlation functions using projection operator techniques.

arXiv:1503.02507Mar 9, 201516 citations

Relaxation in a Fermi liquid

Annals of PhysicsOct 1, 19850 citations

Relaxation in a fermi liquid

J. Vogel, E. Vogel, C. Toepffer

Annals of PhysicsOct 1, 198512 citations

Reversal of relaxation due to a dephasing environment

Marcin Mierzejewski, J. Bonča, Jerzy Dajka

We show that any finite quantum system $S$ can be coupled to a dephasing environment in such a way that the internal mechanism responsible for relaxation of observables acting on $S$ can be effectively canceled. By adjusting this coupling, the difference between the initial and the long--time expectation values of any observable on $S$ can be tuned to an arbitrarily small, but nonzero, value. This statement is exemplified and visualized by numerical studies of relaxation in a generic one-dimensional system of interacting fermions.We show that any finite quantum system $S$ can be coupled to a dephasing environment in such a way that the internal mechanism responsible for relaxation of observables acting on $S$ can be effectively canceled. By adjusting this coupling, the difference between the initial and the long--time expectation values of any observable on $S$ can be tuned to an arbitrarily small, but nonzero, value. This statement is exemplified and visualized by numerical studies of relaxation in a generic one-dimensional system of interacting fermions.

arXiv:1503.03618Physical Review AMay 20, 20153 citations

Quantum quenches and thermalization in one-dimensional fermionic systems

Marcos Rigol

We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function $[n(k)]$ and the density-density structure factor $[N(k)]$ , respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of $N(k)$ for fermions is very similar to the one of hardcore bosons, the behavior of $n(k)$ is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of $n(k)$ in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function $[n(k)]$ and the density-density structure factor $[N(k)]$, respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of $N(k)$ for fermions is very similar to the one of hardcore bosons, the behavior of $n(k)$ is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of $n(k)$ in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.

arXiv:0908.3188Physical Review ANov 9, 2009243 citations

We show that any finite quantum system

S

can be coupled to a dephasing environment in such a way that the internal mechanism responsible for relaxation of observables acting on

S

can be effectively canceled. By adjusting this coupling, the difference between the initial and the long--time expectation values of any observable on

S

can be tuned to an arbitrarily small, but nonzero, value. This statement is exemplified and visualized by numerical studies of relaxation in a generic one-dimensional system of interacting fermions.

[n(k)]

and the density-density structure factor

[N(k)]

, respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of

N(k)

for fermions is very similar to the one of hardcore bosons, the behavior of

n(k)

is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of

n(k)

in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.