Related papers: On Integrability of Many-Body Problems with Point …
For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
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…
We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and,…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
We address the question of minimal requirements for the existence of quantum bound states. In particular, we demonstrate that a few-body system with zero-range momentum-independent two-body interactions is unstable against decay into…
Strongly interacting quantum many-body systems are fundamentally compelling and ubiquitous in science. However, their complexity generally prevents exact solutions of their dynamics. Precisely engineered ultracold atomic gases are emerging…
Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear…
We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The…
In this letter we consider the time dependent Kondo model where a magnetic impurity interacts with the electrons through a time dependent interaction strength $J(t)$. We develop a new framework based on Bethe ansatz and construct an exact…
We review recent results which clarify the role of the integrable many-body problems in the quantum field theory framework.They describe the dynamics of the topological degrees of freedom in the theories which are obtained by perturbing the…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
Recently a new formulation of quantum mechanics has been introduced, based on signed classical field-less particles interacting with an external field by means of only creation and annihilation events. In this paper, we extend this novel…
Quantum interference lies at the heart of several surprising equilibrium and non-equilibrium phenomena in many-body Physics. Here we discuss two recently explored non-equilibrium scenarios where external periodic drive applied to closed…
The hamiltonian with magnetic impurities coupled to the strongly correlated electron system is constructed from $t-J$ model. And it is diagonalized exactly by using the Bethe ansatz method. Our boundary matrices depend on the spins of the…
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions…
Integrability conditions for systems of bosons or fermions with seniority conserving hamiltonians are derived. The conditions are shown to be invariant under a large class of transformations of the interaction matrix elements. Previously…
We consider the problem of energy-mass transfer from scattering to bound states for a one body quantum system under the action of a time dependent point interaction. Under suitable assumptions on the initial state of the particle, we prove…
We present an exact solution of the nonstationary Schrodinger equation for the Kondo Hamiltonian with a time-dependent spin-exchange coupling $J(t)$ under periodic boundary conditions. Unlike previously studied time-dependent integrable…
As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine…