Related papers: Lectures on the fourth order Q curvature equation
We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with…
In a previous article we have introduced an operator representing the three-dimensional scalar curvature in loop quantum gravity. In this article we examine the new curvature operator in the setting of quantum-reduced loop gravity. We…
The quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In $n>4$ dimensions, pure quadratic curvature lagrangian having second order trace constructed…
These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is…
We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly…
1. Quantized conductance 2. When 1 mode = 1 atom 3. Photons and Cooper pairs 4. Thermal analogues 5. Shot noise 6. Solid-state electron optics 7. Ultimate confinement 8. Landauer formulas
In this note, we study Q-curvature flow on $S^4$ with indefinite nonlinearity. Our result is that the prescribed Q-curvature problem on $S^4$ has a solution provided the prescribed Q-curvature $f$ has its positive part, which possesses…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
We discuss solutions of the spherically symmetric wave equation and Klein Gordon equation in an arbitrary number of spatial and temporal dimensions. Starting from a given solution, we present various procedures to generate futher solutions…
The status of QCD phenomena and open problems are reviewed
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
We give examples of smooth plane quartics over $\mathbb{Q}$ with complex multiplication over $\overline{\mathbb{Q}}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of…
We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…
In the studies of the squeezing it is customary to focus more attention on the particular squeezed states and their evolution than on the dynamical operations that could squeeze simultaneously some wider families of quantum states,…
This paper is the second part of our series of works to establish $L^2$ estimates and existence theorems for the $\overline{\partial}$ operators in infinite dimensions. In this part, we consider the most difficult case, i.e., the underlying…
We examine $q-$series related to higher forms. These forms are cubics, quartics, etc. In some points, in the article we add parts from previous works, in such a way, the article be more complete and readable.
In this paper, we consider a family of $n$-dimensional, higher-curvature theories of gravity whose action is given by a series of dimensionally extended conformal invariants. The latter correspond to higher-order generalizations of the…
Today's QCD problems, prospects and achievements are reviewed.
The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various…
This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second…