Related papers: Quantum Flux and Quantum Ergodicity for Cross Sect…

We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators.…

Following a recent method introduced by C. Hainzl, J.P. Solovej and the second author of this article, we prove the existence of the thermodynamic limit for a system made of quantum electrons, and classical nuclei whose positions and…

We outline the content and theoretical support for the proposal of "hydrodynamics on (mini)superspace" (or a non-linear extension of quantum cosmology) as an effective framework for quantum gravity in a cosmological context. The basis for…

A family of maps or flows depending on a parameter $\nu$ which varies in an interval, spans a certain property if along the interval this property depends continuously on the parameter and achieves some asymptotic values along it. We…

In this short note we show that the lower bounds of Mangoubi on the inner radius of nodal domains can be improved for quantum ergodic sequences of eigenfunctions, according to a certain power of the radius of shrinking balls on which the…

In this short note, we establish a quantitative description of the genericity of transversality of $C^1$-submanifolds in $\mathbb{R}^n$: Let $\Sigma \subset \mathbb{R}^n$ be a $d$-dimensional $C^1$-embedded submanifold where $n \geq d+1$.…

Lower bounds are placed on the fermionic determinants of Euclidean quantum electrodynamics in two and four dimensions in the presence of a smooth, finite-flux, static, unidirectional magnetic field $B(r) =(0,0,B(r))$, where $B(r) \geq 0$ or…

We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within…

Recently, it has been argued by Kuklov et al., that unusual features associated with the superflow-through-solid effect observed in solid He4 can be explained by unique properties of dilute distribution of superfluid edge dislocations. We…

A 2D Schrodinger equation with interacting Mobius square potential model is solved using Nikiforov-Uvarov Functional Analysis (NUFA) formalism. The energy spectra and the corresponding wave function for the linearly and exponentially…

We investigate the QMCS in structure of the eigenfunctions, corresponding to mixed type classical dynamics in smooth potential of the surface quadrupole oscillations of a charged liquid drop. Regions of different regimes of classical motion…

A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…

We present a brief introduction to QCD, the QCD phase diagram, and non-equilibrium phenomena in QCD. We emphasize aspects of the theory that can be addressed using computational methods, in particular euclidean path integral Monte Carlo,…

Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when…

We study high codimension mean curvature flow of a submanifold $\mathcal{M}^n$ of dimension $n$ in Euclidean space $\mathbb{R}^{n+k}$ subject to the quadratic curvature condition $ |A|^{2}\leq c_n |H|^{2}, c _n = \min\{ \frac{4}{3n} ,…

A problem of defining the quantum analogues for semi-classical twists in $U(\mathfrak{g})[[t]]$ is considered. First, we study specialization at $q=1$ of singular coboundary twists defined in $U_{q}(\mathfrak{g})[[t]]$ for $\mathfrak{g}$…

In this study, we utilized the quantum flow (QFlow) method to perform quantum simulations of correlated systems. The QFlow approach allows for sampling large sub-spaces of the Hilbert space by solving coupled variational problems in reduced…

We analyze an experiment in which a thin wire is scanned across the overlap of two in phase photon beams. We find that unless the wire induces the formation of an interference pattern, the complementarity inequality is violated. Quantum…

We prove that flow of a generic geodesic on a flat surface with finite holonomy group is ergodic. We use this result to prove that flows of generic billiards on certain flat surfaces with boundary are also ergodic.

We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a…