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Extrasolar planetary systems commonly exhibit planets on eccentric orbits, with many systems located near or within mean-motion resonances, showcasing a wide diversity of orbital architectures. Such complex systems challenge traditional…
Quantum dynamics of the Bose-Hubbard Model is investigated through a semiclassical hamiltonian picture provided by the Time-Dependent Variational Principle method. The system is studied within a factorized slow/fast dynamics. The…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2,R) group manifold. Applied to the cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to split the…
The objective of this article is to complete preliminary results concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by Lindblad equations. The extremal system is described by a…
Extending many-body numerical techniques which are powerful in the context of simple model calculations to the realm of realistic material simulations can be a challenging task. Realistic systems often involve multiple active orbitals,…
Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we…
The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and…
Even simplified models of quantum many-body systems can be difficult to analyse. However, taking inspiration from the foundations of physics, one may wonder whether there are practical advantages to constructing alternative beyond-quantum…
In quantum many-body problems, one of the main difficulties comes from the description of non-negligible interactions which require, at least in principle, an exponential amount of information. Recently, in the context of spin glasses and…
In this paper we describe optimal reduction for the system of two bodies in $\mathbb{R}^3$ whose Hamiltonian is invariant under rotations and translations. In doing this, we introduce parametrizations and charts which help giving explicit…
We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in…
We present a numerical method to simulate the dynamics of continuous-variable quantum many-body systems. Our approach is based on custom neural-network many-body quantum states. We focus on dynamics of two-dimensional quantum rotors and…
We consider a system of two spins that are coupled via an isotropic Heisenberg Hamiltonian. For the first time, a two-step method for the preparation of an arbitrary quantum state of two qubits in the form of the Schmidt decomposition is…
In this work we semiclassically analyzed the high lying eigenstates of a mixed type Hamiltonian system. For the regular states we employ the Einstein-Brillouin-Keller quantization, while for the chaotic states, following the principle of…
This paper summarizes several recent developments in the area of estimation and robust control of quantum systems and outlines several directions for future research. Quantum state tomography via linear regression estimation and adaptive…
We study the dynamics of particles coupled to gravity in (2 + 1) dimensions. Using the ADM formalism, we derive the general Hamiltonian for an N-body system and analyze the dynamics of a two-particle system. Non-linear terms are found up to…
This work uncovers a fundamental connection between doped stabilizer states, a concept from quantum information theory, and the structure of eigenstates in perturbed many-body quantum systems. We prove that for Hamiltonians consisting of a…