  Time-dependent density functional theory is widely used to describe
excitations of many-fermion systems. In its many applications, 3D
coordinate-space representation is used, and infinite-domain calculations are
limited to a finite volume represented by a box. For finite quantum systems
(atoms, molecules, nuclei), the commonly used periodic or reflecting boundary
conditions introduce spurious quantization of the continuum states and
artificial reflections from boundary; hence, an incorrect treatment of
evaporated particles. These artifacts can be practically cured by introducing
absorbing boundary conditions (ABC) through an absorbing potential in a certain
boundary region sufficiently far from the described system. But also the
calculations of infinite matter (crystal electrons, quantum fluids, neutron
star crust) suffer artifacts from a finite computational box. In this regime,
twist- averaged boundary conditions (TABC) have been used successfully to
diminish the finite-volume effects. In this work, we extend TABC to
time-dependent framework and apply it to resolve the box artifacts for finite
quantum systems using as test case small- and large-amplitude nuclear
vibrations. We demonstrate that by using such a method, one can reduce finite
volume effects drastically without adding any additional parameters. While they
are almost equivalent in the linear regime, TABC and ABC differ in the
nonlinear regime in their treatment of evaporated particles.
