Related papers: Some contributions to many-body quantum mathematic…
Computing dynamical distributions in quantum many-body systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in real-time and frequency space,…
The last two decades have seen the emergence of stunning interconnections among various previously remotely related disciplines such as condensed matter, nuclear physics, gravity and quantum information, fueled both by experimental advances…
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order…
In this article we describe recent progress in the computational many-body theory of metal surfaces, and focus on current techniques beyond the local-density approximation of density-functional theory. We overview various applications to…
We present a quantum theory of distances along a curve, based on a linear line element that is equal to the operator square root of the quadratic metric of Riemannian geometry. Since the linear line element is an operator, we treat it…
Simulating the dynamics of non-equilibrium matter under extreme conditions lies beyond the capabilities of classical computation alone. Remarkable advances in quantum information science and technology are profoundly changing how we…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
We discuss the possibility to modify many-body Hilbert quantum formalism that is necessary for the representation of quantum systems dynamics. The notion of effective classical algorithm and visualization of quantum dynamics play the key…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…
Future quantum computers are anticipated to be able to perform simulations of quantum many-body systems and quantum field theories that lie beyond the capabilities of classical computation. This will lead to new insights and predictions for…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…
Quantum kinetic theory is an important tool for studying non-equilibrium, non-perturbative and non-linear interactions within an open quantum system, and as such is able to provide an unprecedented view on particle production in the…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
Short review on entanglement, as seen from a quantum information perspective, and some simple applications to many-body quantum systems. Special emphasis in area laws, cold atoms, and efficient descriptions using tensor network states.