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It is well-established that the spectral measure for one-frequency Schr\"odinger operators with Diophantine frequencies exhibits optimal $1/2$-H\"older continuity within the absolutely continuous spectrum. This study extends these findings…

A continuous unitary transformation is introduced which realizes Landau's mapping of the elementary excitations (quasi-particles) of an interacting Fermi liquid system to those of the system without interaction. The conservation of the…

The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…

For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.

We study the spectral properties of discrete one-dimensional Schr\"odinger operators with Sturmian potentials. It is shown that the point spectrum is always empty. Moreover, for rotation numbers with bounded density, we establish purely…

We introduce computational strategies for measuring the ``size'' of the spectrum of bounded self-adjoint operators using various metrics such as the Lebesgue measure, fractal dimensions, the number of connected components (or gaps), and…

We study the large N operator spectrum of the (1,0) superconformal chiral six-dimensional theory with E_8 global symmetry. This spectrum is dual to the Kaluza-Klein spectrum of supergravity on AdS_7 X S^4/Z_2 with a ten-dimensional E_8…

We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal…

We introduce three metrics on the set of quantum probability measures over a compact Hausdorff space and characterize them in terms of the completely bounded norm of the corresponding unital completely positive maps. We extend the existing…

Using an abstract notion of semiclassical quantization for self-adjoint operators, we prove that the joint spectrum of a collection of commuting semiclassical self-adjoint operators converges to the classical spectrum given by the joint…

The theme of this work is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl operators which we call "Landau--Weyl pseudodifferential…

We discuss a combination of unitary and anti-unitary symmetry of quantum Liouvillian dynamics, in the context of open quantum systems, which implies a D2 symmetry of the complex Liovillean spectrum. For sufficiently weak system-bath…

Consider the $n!$ different unitary matrices that permute $n$ $d$-dimensional quantum systems. If $d\geq n$ then they are linearly independent. This paper discusses a sense in which they are approximately orthogonal (with respect to the…

We study disorder operator, defined as a symmetry transformation applied to a finite region, across a continuous quantum phase transition in $(2+1)d$. We show analytically that at a conformally-invariant critical point with U(1) symmetry,…

Consider a quasi-periodic Schr\"odinger operator $H_{\alpha,\theta}$ with analytic potential and irrational frequency $\alpha$. Given any rational approximating $\alpha$, let $S_+$ and $S_-$ denote the union, respectively, the intersection…

In this paper, we prove that any analytic quasi-periodic cocycle close to constant is the Poincar\'{e} map of an analytic quasi-periodic linear system close to constant. With this local embedding theorem, we get fruitful new results. We…

In this paper, we prove the quasi-compactness of the Frobenius-Perron operator for a piecewise convex map $\tau$ with a countably infinite number of branches on the interval $I=[0,1]$. We establish that for high enough $n$ iterates of…

It is a well-established fact in quantum information theory, that uniform averaging over the collective action of a unitary group on a multipartite quantum state projects the state to a form equivalent to a permutation operator of the…

Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we…

In this article we compute and analyze the spectrum of operators defined by the metaplectic representation $\mu$ on the unitary group $\mathbb{U}(d)$ or operators defined by the corresponding induced representation $d\mu$ of the Lie algebra…