Related papers: An efficient Wavelet-Based Hamiltonian Formulation…
In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
Some of the exciting phenomena uncovered in strongly correlated systems in recent years - for instance quantum topological order, deconfined quantum criticality, and emergent gauge symmetries -- appear in systems in which the Hilbert space…
We present an ``orbital'' free density functional theory for computing the quantum ground state of atomic clusters and liquids. Our approach combines the Bohm hydrodynamical description of quantum mechanics with an information theoretical…
We introduce a framework that unifies quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows. We do so by providing explicit expressions for stochastic Hamiltonians that produce state dynamics identical to…
Conventional formulation of QED since the 50s works very well for stationary states and for scattering problems, but with newly arisen challenges from the 80s on, where real time evolution of particles in a nonequilibrium setting are…
Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum…
This thesis explores Quantum Field Theory (QFT) on curved spacetimes using a geometric Hamiltonian approach to the Schr\"odinger-like representation. In particular it studies the theory of the scalar field described through its…
We focus our attention on the one dimensional scalar theories that result from dimensionally reducing the free scalar field theory in arbitrary d dimensions. As is well known, after integrating out the angular coordinates, the free scalar…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating…
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…
The method of flow equations is applied to QED on the light front. Requiring that the particle number conserving terms in the Hamiltonian are considered to be diagonal and the other terms off-diagonal an effective Hamiltonian is obtained…
One of the fundamental questions in Quantum Field Theory regards the determination of a measure of the degrees of freedom of theories that is consistent with the Renormalization Group flow. The answer seems to be encoded in the C-theorems,…
We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization…
We develop a systematic method for computing a renormalized light-front field theory Hamiltonian that can lead to bound states that rapidly converge in an expansion in free-particle Fock-space sectors. To accomplish this without dropping…
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…