Related papers: Fermi-Bose transformation for the time-dependent L…
We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact…
Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N…
Spontaneous symmetry breaking is examined by regarding it as a phenomenon in the eternal intermediate state due to sequential perturbations. The concept of the relativistic many-body state is applied to this intermediate state occurring in…
We demonstrate that the thermodynamics of one-dimensional Lieb-Liniger bosons can be accurately calculated in analytic fashion using the polylog function in the framework of the thermodynamic Bethe ansatz. The approach does away with the…
We obtain a time-dependent Schrodinger equation for the Friedmann - Robertson - Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necesary to include an additional action invariant…
We continue our study of the emergence of Non-Equilibrium Steady States in quantum integrable models focusing on the expansion of a Lieb-Liniger gas for arbitrary repulsive interaction. As a first step towards the derivation of the…
The zero-temperature dynamical structure factor of the one-dimensional Bose gas with delta-function interaction (Lieb-Liniger model) is computed using a hybrid theoretical/numerical method based on the exact Bethe Ansatz solution, which…
Within a Lagrangian formalism we derive the time-dependent Gutzwiller approximation for general multi-band Hubbard models. Our approach explicitly incorporates the coupling between time-dependent variational parameters and a time-dependent…
Many-fermion Hilbert space has the algebraic structure of a free module generated by a finite number of antisymmetric functions called shapes. Physically, each shape is a many-body vacuum, whose excitations are described by symmetric…
In this paper we use a similarity transformation connecting some families of Nonlinear Schrodinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrodinger equation. This transformation allows one to apply…
Solutions of the time-dependent Schr\"odinger equation are mapped to other solutions for a (possibly) different potential by so-called form-preserving transformations. These time-dependent transformations of the space and time coordinates…
Exactly solved models provide rigorous understanding of many-body phenomena in strongly correlated systems. In this article, we report a breakthrough in uncovering universal many-body correlated properties of quantum integrable Lieb-Liniger…
We study the collective association dynamics of a cold Fermi gas of $2N$ atoms in $M$ atomic modes into a single molecular bosonic mode. The many-body fermionic problem for $2^M$ amplitudes is effectively reduced to a dynamical system of…
In non-relativistic quantum mechanics of $N$ particles in three spatial dimensions, the wave function $\psi(q_1,\ldots,q_N,t)$ is a function of $3N$ position coordinates and one time coordinate. It is an obvious idea that in a relativistic…
We solve the Schr\"odinger equation from first principles to investigate the many-body effects in the expansion dynamics of one-dimensional repulsively interacting bosons released from a harmonic trap. We utilize the multiconfigurational…
The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the…
Many-body eigenfunctions of the total spin operator can be constructed from the spin and spatial wavefunctions with non-trivial permutation symmetries. Spin-dependent interactions can lead to relaxation of the spin eigenstates to the…
The time-dependent Schr\"odinger equation (TDSE) in real space is fundamental to understanding the dynamics of many-electron quantum systems, with applications ranging from quantum chemistry to condensed matter physics and materials…
We study systems of few two-component fermions interacting in a Harmonic Oscillator trap. The fermion-fermion interaction is generated in a finite basis with a unitary transformation of the exact two-body spectrum given by the Busch…
The dynamics of an atom waveguide X-junction beam splitter becomes truly 1D in a regime of low temperatures and densities and large positive scattering lengths where the transverse mode becomes frozen and the many-body Schrodinger dynamics…