Related papers: Why Calculate in Infinite Dimensions?
In this work, we use tools from non-standard analysis to introduce infinite-dimensional quantum systems and quantum fields within the framework of Categorical Quantum Mechanics. We define a dagger compact category *Hilb suitable for the…
The recent interest in aspects common to quantum information and condensed matter has prompted a prosperous activity at the border of these disciplines that were far distant until few years ago. Numerous interesting questions have been…
Many-body forces are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. Their precise structure is generally difficult to uncover. So, phenomenological effective forces are often used in…
Knowledge of all correlation functions of a system is equivalent to solving the corresponding many-body problem. Already a finite set of correlation functions can be sufficient to describe a quantum many-body system if correlations…
A recent surge of research in many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function.…
Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCM), which lie at the foundation of quantum computing and have tight…
We calculate the zero-temperature gap and quasiparticle weight of the half-filled Hubbard model with a random dispersion relation. After extrapolation to the thermodynamic limit, we obtain reliable bounds on these quantities for the Hubbard…
Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a…
I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system…
We investigate the thermoelectric properties of a system near a pressure driven Mott-Hubbard transition. The dependence of the thermopower and the figure of merit on pressure and temperature within a degenerate Hubbard model for integer…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures, reflecting the distinction between chaotic, mixed or integrable classical dynamics, and the corresponding…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
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…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…
The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the…
In a model with more than one scalar doublet, the parameter space encloses both physical and unphysical information. Invariant theory provides a detailed description of the counting and characterization of the physical parameter space. The…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…