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We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
We show that eigen-energies and energy eigenstates play different roles in the equilibration process of an isolated quantum system. Their roles are revealed numerically by exchanging the eigen-energies between an integrable model and a…
We consider the relativistic quantum mechanics of a two interacting fermions system. We first present a covariant formulation of the kinematics of the problem and give a short outline of the classical results. We then quantize the system…
Eigenstates in finite systems such as nuclei, atoms, atomic clusters and quantum dots with few excited particles are chaotic superpositions of shell model basis states. We study criterion for the equilibrium distribution of basis components…
Ground-state properties of a few attractively interacting ultra-cold atoms of different mass confined in a one-dimensional harmonic trap are studied in terms of the correlation noise. Depending on the mass ratio between the components'…
We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can…
All nuclei with even numbers of protons and of neutrons have ground states with zero angular momentum. This is ascribed to the pairing force between nucleons, but simulations with random interactions suggest a much broader many-body…
Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a non-zero projection of the electronic orbital angular momentum is presented. It is shown how the long-range…
In this paper, we discuss the regularities of energy of each angular momentum $I$ averaged over all the states for a fixed angular momentum (denoted as $\bar{E}_I$'s) in many-body systems interacting via a two-body random ensemble. It is…
A quantum model is considered for $N$ bosons populating two orthogonal single-particle modes with tunable energy separation in the presence of flavour-changing contact interaction. The quantum ground state is well approximated as a coherent…
We analyze the structure of eigenstates in many-body bosonic systems by modeling the Hamiltonian of these complex systems using Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) defined by a mean-field plus $k$-body random…
We study the properties of two quantum particles which are confined in a ring. The particles interact via a long-range gauge potential proportional to the distance between the particles. It is found that the two-body ground state…
Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system…
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin chains with an improvement on the conventional notation. The rest of this thesis is divided into two parts. The first part is devoted to…
With the eigenfunctional theory, we study a general interacting electron system, and give a rigorous expression of its ground state energy which is composed of two parts, one part is contributed by the non-interacting electrons, and another…
Information and correlations in a quantum system are closely related through the process of measurement. We explore such relation in a many-body quantum setting, effectively bridging between quantum metrology and condensed matter physics.…
Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on…
We propose a method to study the transition to chaos in isolated quantum systems of interacting particles. It is based on the concept of delocalization of eigenstates in the energy shell, controlled by the Gaussian form of the strength…
We consider the ground state of simple quantum systems coupled to an environment. In general the system is entangled with its environment. As a consequence, even at zero temperature, the energy of the system is not sharp: a projective…
We investigate the ground state properties of a family of $N$-body systems in 1-dimension, trapped in a polynomial potential and having long range 2-body interaction in addition to the inverse square potential studied in the…