Related papers: Equilibration in low-dimensional quantum matrix mo…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by…
We discuss in details a simple, purely bosonic, quantum field theory belonging to larger class of models with the following properties: a) They are asymptotically free, with a dynamically generated mass scale. b) They have a space of…
The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their…
We primarily study a special a weighted low-rank approximation of matrices and then apply it to solve the background modeling problem. We propose two algorithms for this purpose: one operates in the batch mode on the entire data and the…
We investigate the problem of mapping, through the Morita equivalence, odd dimensional noncommutative lattice gauge theories onto suitable matrix models. We specialize our analysis to noncommutative three dimensional QED (NCQED) and scalar…
Rotating systems in thermal equilibrium are ubiquitous in our world. In the context of high energy physics, rotations would affect the phase structure of QCD. However, the standard Monte-Carlo methods in rotating systems are problematic…
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Mean field approach, although a generally reliable tool that captures major short range correlations, often fails in symmetric low dimensional strongly correlated electronic systems like those described by the Hubbard model. In these…
Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly…
Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…