We study how a system of one-dimensional spin- $\frac{1}{2}$ fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find the exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.We study how a system of one-dimensional spin-$\frac{1}{2}$ fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find the exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.

arXiv:2006.10883Physical review. B./Physical review. BJul 1, 20204 citations

Dynamics of Photoexcited States in Strongly Correlated Electron Systems

Akira Takahashi, Hiroki Gomi, Masaki Aihara

We theoretically investigate the dynamics of the photoexcited state in the strongly correlated low-dimensional electron systems. In the two-dimensional case, the ultrafast relaxation originating from the transfer of photogenerated charges in the antiferromagnetic background is followed by the slower one originating from the spin structure rearrangement with the new charge distributions. This clearly shows the difference in the relaxation between charge and spin degrees of freedom. In the one-dimensional case, spin-charge separation holds and the mechanical coherence is preserved.We theoretically investigate the dynamics of the photoexcited state in the strongly correlated low-dimensional electron systems. In the two-dimensional case, the ultrafast relaxation originating from the transfer of photogenerated charges in the antiferromagnetic background is followed by the slower one originating from the spin structure rearrangement with the new charge distributions. This clearly shows the difference in the relaxation between charge and spin degrees of freedom. In the one-dimensional case, spin-charge separation holds and the mechanical coherence is preserved.

Physical Review LettersOct 29, 200233 citations

On the theory of spin-spin relaxation

R. H. Terwiel, Paweł O. Mazur

PhysicaOct 1, 196636 citations

NMR Relaxation Rate for One-Dimensional Multicomponent Spin-Orbital Systems

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

The NMR relaxation rate $1/T_{1}$ is studied for one-dimensional multicomponent spin-orbital systems. By combining the bosonization techniques and the exact solution of the SU( $n$ ) model, we evaluate the power-law exponent and the enhancement factor for $1/T_1$ at low temperatures. We discuss how the band splitting affects the relaxation rate, and find that $1/T_{1}$ may be enhanced around the critical value of the band splitting. The crossover behavior in $1/T_1$ around the critical point is discussed in terms of the low-frequency dynamical spin susceptibility. The effect of the hole-doping is also addressed.The NMR relaxation rate $1/T_{1}$ is studied for one-dimensional multicomponent spin-orbital systems. By combining the bosonization techniques and the exact solution of the SU($n$) model, we evaluate the power-law exponent and the enhancement factor for $1/T_1$ at low temperatures. We discuss how the band splitting affects the relaxation rate, and find that $1/T_{1}$ may be enhanced around the critical value of the band splitting. The crossover behavior in $1/T_1$ around the critical point is discussed in terms of the low-frequency dynamical spin susceptibility. The effect of the hole-doping is also addressed.

arXiv:cond-mat/0101422Journal of the Physical Society of JapanSep 1, 20005 citations

On a one-dimensional spin system

Stanislav Alekseevich Molchanov, Nguyen The Long

Theoretical and Mathematical PhysicsOct 1, 19750 citations

We study how a system of one-dimensional spin-

\frac{1}{2}

fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find the exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.

The NMR relaxation rate

1/T_{1}

is studied for one-dimensional multicomponent spin-orbital systems. By combining the bosonization techniques and the exact solution of the SU(

n

) model, we evaluate the power-law exponent and the enhancement factor for

1/T_1

at low temperatures. We discuss how the band splitting affects the relaxation rate, and find that

1/T_{1}

may be enhanced around the critical value of the band splitting. The crossover behavior in

1/T_1

around the critical point is discussed in terms of the low-frequency dynamical spin susceptibility. The effect of the hole-doping is also addressed.