Charge and energy transport in the presence of disorder and interaction

Karen Michaeli

S. A. Parameswaran, Sarang Gopalakrishnan

In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the ``spin-incoherent Luttinger liquid'' (SILL) regime] where charge excitations are ``cold'' (i.e., have low entropy) whereas spin excitations are ``hot.'' We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against full localization, and act as a heat bath facilitating charge and energy transport on asymptotically long time scales. The charge, spin, and energy conductivities are widely separated from one another. The dominant carriers of energy in much of the SILL regime are neither charge nor spin excitations, but neutral ``phonon'' modes, which undergo an unconventional form of hopping transport that we discuss. We comment on the applicability of these ideas to experiments and numerical simulations.

Linda Sansoni

Lakshmija N K, Uma Divakaran

We study a quantum battery consisting of $N$ qubits interacting uniformly with each other. Starting from its ground state, the battery is charged by introducing periodic kicks in the transverse direction along with adding disorder in the interaction direction. Although the battery Hamiltonian along with the initial state preserves the permutation symmetry, the dynamics in presence of disorder during the charging phase takes the system out of the permutation symmetric subspace, resulting to a larger amount of stored energy as compared to that without disorder. In the limit of large disorder, this interplay brings in a possibility of a chaotic charging phase when stored energy can be exactly calculated using random matrix theory. More importantly, we also find that the energy fluctuations decrease and become negligible in the limit of large disorder, which is also when the energy stored is maximum, a condition highly desirable for the optimum functioning of the battery. We complete the battery cycle by considering the storage phase in the presence of dephasing noise. We find that for larger disorder strengths, the ergotropy remains close to the stored energy, indicating nearly complete energy extractability with an efficiency approaching unity.

Giancarlo Calvanese Strinati, Claudio Castellani, C. Di Castro

A description of quantum transport for electrons in the presence of a random impurity potential is provided in terms of a kinetic equation, which is obtained from the diagrammatic structure for the linear response functions. When the electron-electron interaction is neglected, the kinetic equation is of the Boltzmann type, with an effective scattering kernel that signals localization effects. With the further inclusion of the interaction, a suitable distribution function for the energy of the quasiparticles can be introduced even in the presence of strong disorder. In this case the kinetic equation has the diffusive form, with diffusion coefficient and Landau interaction parameters that get renormalized by the interplay of disorder and interaction. The quasiparticles kinetic equation is also shown to contain all known results for the hydrodynamic correlation functions.

Ferenc Iglói, Heiko Rieger