Related papers: The Structure of Operators in Effective Particle-C…
We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect it's arrival at a particular chosen set of sites. The projective measurements are made at regular time…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
Modern effective-theory techniques are applied to the nuclear many-body problem. A novel approach is proposed for the renormalization of operators in a manner consistent with the construction of the effective potential. To test this…
Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We introduce a systematic framework for counting and finding independent operators in effective field theories, taking into account the redundancies associated with use of the classical equations of motion and integration by parts. By…
Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger topological order. Such schemes are particularly promising for generating non-trivial energy bands and gauge structures in quantum-matter…
In the last years, we have been witnessing a tremendous push to demonstrate that quantum computers can solve classically intractable problems. This effort, initially focused on the hardware, progressively included the simplification of the…
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…
Synthetic dimensions have generated great interest for studying many types of topological, quantum, and many-body physics, and they offer a flexible platform for simulation of interesting physical systems, especially in high dimensions. In…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…
We review results about entanglement (or modular) Hamiltonians of quantum many-body systems in field theory and statistical mechanics models, as well as recent applications in the context of quantum information and quantum simulation.
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…
We develop an effective theory for heavy baryons and their excited states. The approach is based on the contracted O(8) symmetry recently shown to emerge from QCD for these states in the combined large N_c and heavy quark limits. The…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…