Related papers: Adiabatic Limits, Vanishing Theorems and the Nonco…
In this paper, we first establish an $L^2$-type Dolbeault isomorphism for logarithmic differential forms by H\"{o}rmander's $L^2$-estimates. By using this isomorphism and the construction of smooth Hermitian metrics, we obtain a number of…
We provide an elementary proof of the quantum adiabatic theorem.
Let $f:X\rightarrow Y$ be a smooth fibration between two complex manifolds $X$ and $Y$, and let $L$ be a pseudo-effective line bundle on $X$. We obtain a sufficient condition for $R^{q}f_{\ast}(K_{X/Y}\otimes L)$ to be reflexive and hence…
The scalar curvature for the noncommutative four torus $\mathbb{T}_\Theta^4$, where its flat geometry is conformally perturbed by a Weyl factor, is computed by making the use of a noncommutative residue that involves integration over the…
Given an $n$-dimensional compact complex Hermitian manifold $X$, a $C^\infty$ complex line bundle $L$ equipped with a connection $D$ whose $(0,\,1)$-component $D''$ squares to zero and a real-valued function $\eta$ on $X$, we prove that the…
We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding GNS-Hamiltonian…
We consider general, non-linear curvature perturbations on scales greater than the Hubble horizon scale by invoking an expansion in spatial gradients, the so-called gradient expansion. After reviewing the basic properties of the gradient…
We consider area-preserving deformations of the plane, acting on electronic wavefunctions through "quantomorphisms" that change both the underlying metric and the confining potential. We show that adiabatic sequences of such transformations…
We study the semiclassical limit and the adiabatic limit with a second-quantized two-mode model, which describes a many-boson interacting system. When its mean-field interaction is small, these two limits are commutable. However, when the…
We study the scalar curvature of incomplete wedge metrics in certain stratified spaces with a single singular stratum (wedge spaces). Building upon several well established technical tools for this category of spaces (the corresponding…
In this paper, we consider the scalar curvature in the distributional sense of \cite{MR3366052} and the scalar curvature lower bound in the $\beta-$weak $(\beta\in(0, \frac{1}{2}))$ sense of \cite{MR4685089} on an asymptotically flat…
The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the…
Adiabatic subtraction is a popular method of renormalization of observables in quantum field theories on a curved spacetime. When applied to the computation of the power spectra of light ($m\ll H$) fields on de Sitter space with flat…
We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class…
We study the late time evolution of negatively curved Friedmann--Le\-ma\^{\i}tre--Robert\-son--Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. Since, under mild assumptions on the…
We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum…
We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalised super-adiabatic theorem for the automorphism group…
The generation of non-gaussianity is studied in a three fluid curvaton model. By utilizing second order perturbation theory we derive general formulae for the large scale temperature fluctuation and non-gaussianity parameter, $f_{NL}$, that…
A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. One way to describe…
In this article we study the triangulated category of singularities associated with a non-commutative resolution of singularities. In particular, we give a complete description of this category in the case of a curve with nodal…