Relativistic Systems in One Dimension

Eric A. Galapon, Joseph Raphael R. Bunao

We construct a TOA operator canonically conjugate to the system Hamiltonian describing a free relativistic spin−0 charged particle in one spatial dimension. The true one-particle operator T is then obtained by taking the even operator part. It is also seen that T reduces to the free non-relativistic TOA operator in the c →∞ limit.

Tom Solomon, Stavros Fallieros

Mario Collura, Gabriele Martelloni

We consider a non-interacting Fermi gas in $d$ dimensions, both in the non-relativistic and relativistic case. The system of size $L^{d}$ is initially prepared into two halves $\mathcal{L}$ and $\mathcal{R}$, each of them thermalized at two different temperatures, $T_{\mathcal{L}}$ and $T_{\mathcal{R}}$ respectively. At time $t=0$ the two halves are put in contact and the entire system is left to evolve unitarily. We show that, in the thermodynamic limit, the time evolution of the particle and energy densities is perfectly described by a semiclassical approach which permits to analytically evaluate the correspondent stationary currents. In particular, in the case of non-relativistic fermions, we find a low-temperature behavior for the particle and energy currents which is independent from the dimensionality $d$ of the system, being proportional to the difference $T_{\mathcal{L}}^{2}-T_{\mathcal{R}}^{2}$. Only in one spatial dimension ($d=1$), the results for the non-relativistic case agree with the massless relativistic ones.

Lloyd Armstrong

Mario Collura, Gabriele Martelloni

Abstract. We consider a non-interacting Fermi gas in d dimensions, both in the non-relativistic and relativistic case. The system of size Ld is initially prepared into two halves L and R, each of them thermalized at two different temperatures, TL and TR respectively. At time t = 0 the two halves are put in contact and the entire system is left to evolve unitarily. We show that, in the thermodynamic limit, the time evolution of the particle and energy densities is perfectly described by a semiclassical approach which permits to analytically evaluate the correspondent stationary currents. In particular, in the case of non-relativistic fermions, we find a low-temperature behavior for the particle and energy currents which is independent from the dimensionality d of the system, being proportional to the difference T 2L − T 2R. Only in one spatial dimension (d = 1), the results for the non-relativistic case agree with the massless relativistic ones. 1.