Related papers: Quantum extended crystal PDE's
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
The construction of a universal static quantum computer actually provides another proof of the NP-hardness of spin-glass problems.
Complex scalar fields charged under a global U(1) symmetry can admit non-topological soliton configurations called Q-balls which are stable against decay into individual particles or smaller Q-balls. These Q-balls are interesting objects…
the stability criterion is constructed for open quantum systems which govern by quantum stochastic differential equations (QSDE) both for quantum observable flow and the stochastic density operator. We derive stability criteria (local,…
We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…
We present a classification and an explicit form of all constant solutions of the Yang-Mills equations with ${\rm SU}(2)$ gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space ${\mathbb R}^{p,q}$ of…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing…
In recent years, experimental data were published which point to the possibility of the existence of superfluidity in solid helium. To investigate this phenomenon theoretically we employ a hierarchy of equations for reduced density matrices…
Scalars carrying a conserved global charge $Q$ can form stable localized field configurations composed of a large number of particles. These non-topological solitons are spherically symmetric and are called Q-balls. While usually analyzed…
We establish the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in $n \geq 4$ spacetime dimension. This generalizes Friedrich's Einstein-Yang-Mills…
In this work we deal with non-topological solutions of the Q-ball type in two space-time dimensions, in models described by a single complex scalar field that engenders global symmetry. The main novelty is the presence of stable Q-balls…
We categorize the global structure of spherically symmetric static solutions of Einstein SU(2) Yang Mills equations with positive cosmological constant that are smooth at the center of spherical symmetry.
I was asked to make my, by now quite old PhD thesis, available on the arxiv, for parts of it was never submitted for publication. The thesis offers a systematic study of stochastic differential equations (SDEs) on non-compact spaces. In…
Static, spherically symmetric solutions of the Yang-Mills-Dilaton theory are studied. It is shown that these solutions fall into three different classes. The generic solutions are singular. Besides there is a discrete set of globally…
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
The stability of Yang-Mills bundles over the usual $S^4$ space-time manifold is investigated according to the topological methods. The necessary gauge- and topological invaraint criterion for the exsitence of the related critical points is…
We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological…
For the first time, a complete classification of all constant solutions of the Yang-Mills-Dirac equations with SU(2) gauge symmetry in Minkowski space ${\mathbb R}^{1,3}$ is given. The explicit form of all solutions is presented. We use the…