Related papers: Adiabatic Limit, Theta Function, and Geometric Qua…

For an ergodic hyperbolic measure $\omega$ of a $C^{1+{\alpha}}$ diffeomorphism, there is an $\omega$ full-measured set $\tilde\Lambda$ such that every nonempty, compact and connected subset $V$ of $\mathbb{M}_{inv}(\tilde\Lambda)$…

We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by $N \gg 1$ particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature $\beta^{-1}$. Given a fixed ${1\leq m \ll N}$, we…

The adiabatic limit procedure associates with every solution of Abelian Higgs model in (2+1) dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg--Witten equations on 4-dimensional…

We present a graphical analysis of the adiabatic connections underlying double-hybrid density-functional methods that employ second-order perturbation theory. Approximate adiabatic connection formulae relevant to the construction of these…

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 consider an XXZ spin-1/2 chain coupled to optical phonons with non-zero frequency $\omega_0$. In the adiabatic limit (small $\omega_0$), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become…

Let the complex reflection group $G(m,p,n)$ act on the unit polydisc $\mathbb D^n$ in $\mathbb C^n.$ A $\boldsymbol\Theta_n$-contraction is a commuting tuple of operators on a Hilbert space having…

In this article, we study the relation between wavefunction overlap and adiabatic continuity in gapped quantum systems. We show that for two band insulators, a scalar function can be defined in the momentum space, which characterizes the…

We show meromorphic extension and analyze the divisors of a Selberg zeta function of odd type $Z_{\Gamma,\Sigma}^{\rm o}(\lambda)$ associated to the spinor bundle $\Sigma$ on odd dimensional convex co-compact hyperbolic manifolds…

We develop and test a method that integrates many-electron weak-field asymptotic theory (ME-WFAT) [Phys. Rev. A 89, 013421 (2014)] in the integral representation (IR) into the density functional theory (DFT) framework. In particular, we…

This is an extended version of the first part of a forthcoming paper where we will study the local Zeta functions of the minimal spherical series for the symmetric spaces arising as open orbits of the parabolic prehomogeneous spaces of…

Let $\mathfrak{J}$ be a JB$^*$-algebra with no quotients isomorphic to $S_2(\mathbb{C})$. Let $\mu$ be a local quasi-linear Jordan functional on $\mathfrak{J}_{sa}$. We show that $\mu$ is a linear functional on $\mathfrak{J}_{sa}$ if and…

Several misprints and small mistakes were in the initial version. They have been corrected. Following the recent experimental realization of synthetic gauge magnetic forces, Jean Dalibard adressed the question whether the adiabatic ansatz…

A precise definition of an adiabaticity parameter $\nu$ of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator…

Let $F$ be a non--Archimedean locally compact field (${\rm car}(F)\geq 0$), ${\bf G}$ be a connected reductive group defined over $F$, $\theta$ be an $F$--automorphism of ${\bf G}$, and $\omega$ be a character of ${\bf G}(F)$. We fix a Haar…

The nonadiabatic geometric quantum computation may be achieved using coupled low-capacitance Josephson juctions. We show that the nonadiabtic effects as well as the adiabatic condition are very important for these systems. Moreover, we find…

Given two Morse functions $f, \mu$ on a compact manifold $M$, we study the Morse homology for the Lagrange multiplier function on $M \times {\mathbb R}$ which sends $(x, \eta)$ to $f(x) + \eta \mu(x)$. Take a product metric on $M \times…

The quantum adiabatic theorem is a fundamental result in quantum mechanics, with a multitude of applications, both theoretical and practical. Here, we investigate the dynamics of adiabatic processes for quantum many-body systems %in detail…

A quantum thermodynamic cycle with a chiral multiferroic working substance such as $\textrm{LiCu}_{2}\textrm{O}_{2}$ is presented. Shortcuts to adiabaticity are employed to achieve an efficient, finite time quantum thermodynamic cycle which…

We concentrate on the geometric potential in the invariant perturbation theory of quantum adiabatic process which is presented in our recent papers. It is found out to be related to the geodesic curvature of the spherical curve in…