Time-dependent quantities are calculated in the linear response limit for a correlated one dimensional model atom driven by an external quadrupolar time-dependent field. Besides the analysis of the time-evolving energy change in the correlated two-particle system, and orthogonality of initial and final states, Mehler's formula is applied in order to derive a point-wise decomposition of the time-dependent one-matrix in terms of time-dependent occupation numbers and time-dependent orthonormal, natural orbitals. Based on such exact spectral decomposition on the time domain, Rényi's entropy is also investigated. Considering the structure of the exact time-dependent one-matrix, an independent-particle model is defined from it which contains exact information on the single-particle probability density and probability current. The resulting noninteracting auxiliary state is used to construct an effective potential and discuss its applicability.
Based on the correlated ground-state wave function of an exactly solvable interacting one-dimensional two-electron model Hamiltonian we address the switch-off of confining and interparticle interactions to calculate the exact time-evolving wave function from a prescribed correlated initial state. Using this evolving wave function, the time-dependent pair probability function $\mathcal{R}({x}_{1},{x}_{2},t)\ensuremath{\equiv}{n}_{2}({x}_{1},{x}_{2},t)/[n({x}_{1},t)\phantom{\rule{0.16em}{0ex}}n({x}_{2},t)]$ is determined via the pair density
n2(x1,x2,t) and single-particle density
n(x,t). It is found that $\mathcal{R}(0,0,t=\ensuremath{\infty})=\mathcal{R}(0,0,t=0)>1$, and
R(x1,x2,t∗)=1 at a finite
t∗ for $\ensuremath{\Lambda}\ensuremath{\ne}0$ interparticle interaction strength in the initial two-electron model. By expanding
n(x,t) in an infinite sum of closed-shell products of time-dependent normalized single-particle states and time-dependent occupation numbers ${P}_{k}(\ensuremath{\Lambda},t)$, the von Neumann entropy $S(\ensuremath{\Lambda},t)=\ensuremath{-}{\ensuremath{\sum}}_{k=0}^{\ensuremath{\infty}}{P}_{k}(t)\mathrm{ln}{P}_{k}(t)$ is calculated as well. The such-defined information entropy is zero at ${t}^{*}(\ensuremath{\Lambda})$ and its maximum in time is $S(\ensuremath{\Lambda},t=\ensuremath{\infty})=S(\ensuremath{\Lambda},t=0)$.
We study the long-time evolution of the bipartite entanglement in translationally invariant gapped harmonic lattice systems with finite-range interactions. A lower bound for the von Neumann entropy is derived in terms of the purity of the reduced density matrix. It is shown that starting from an initially Gaussian state the entanglement entropy increases at least linearly in time. This implies that the dynamics of gapped (non-critical) harmonic lattice systems cannot be efficiently simulated by algorithms based on matrix-product decompositions of the quantum state.
The time evolution of the purity (the trace of the square of the reduced density matrix) and von Neumann entropy in a symmetric two-level system coupled to a dissipative harmonic bath is investigated through analytical arguments and accurate path integral calculations on simple models and the singly excited bacteriochlorophyll dimer. A simple theoretical analysis establishes bounds and limiting behaviors. The contributions to purity from a purely incoherent term obtained from the diagonal elements of the reduced density matrix, a term associated with the difference of the two eigenstate populations, and a third term related to the square of the time derivative of a site population, are discussed in various regimes. In the case of tunneling dynamics from a localized initial condition, the complex interplay among these contributions leads to the recovery of purity under low-temperature, weakly dissipative conditions. Memory effects from the bath are found to play a critical role to the dynamics of purity. It is shown that the strictly quantum mechanical decoherence process associated with spontaneous phonon emission is responsible for the long-time recovery of purity. These analytical and numerical results show clearly that the loss of quantum coherence during the evolution toward equilibrium does not necessarily imply the decay of purity, and that the time scales relevant to these two processes may be entirely different.
We present a systematic study of entanglement control in one-dimensional systems of two distinguishable interacting particles in harmonic confinement. Using density matrix renormalization group calculations, we examine how the von Neumann entropy evolves under variations of mass ratio, trap-frequency asymmetry, interaction range, and localized external fields. Our results reveal a consistent picture connecting the real-space density overlap, the redistribution of quantum fluctuations, and the resulting entanglement. Within the parameter regimes investigated, mass imbalance produces more pronounced changes in entanglement than trap-frequency asymmetry. Furthermore, the competition between interaction range and field-induced polarization determines whether short- or long-range correlations dominate. By connecting the von Neumann entropy with measurable quantities such as the density difference Δ n ( x ) and the phase-space products 〈 x i 2 〉 〈 p x i 2 〉 , we establish experimentally accessible fingerprints of quantum correlation. Our analysis demonstrates how external and geometrical parameters can tune entanglement in confined two-particle models, providing a basis for exploring related control protocols in suitable experimental settings.
Analytical results on the correlation functions of strongly correlated many-body systems are rare in the literature and their importance cannot be overstated. We present determinant representations for the space-, time-, and temperature-dependent correlation functions of the strongly interacting one-dimensional Hubbard model in the presence of an external trapping potential. These representations are exact and valid in both equilibrium and nonequilibrium scenarios like the ones initiated by a sudden change of the confinement potential. In addition, they can be implemented numerically very easily, significantly outperforming other numerical approaches. As applications of our results we investigate the single-particle spectral functions of systems with harmonic trapping and show that dynamical quasicondensation occurs for both fermionic and bosonic spin-
1/2 systems released from a Mott insulator state.