相关论文: Spectral problems from quantum field theory

The aim of this article is to present a brief overview of spectral perturbation theory for matrices, bounded linear operators and holomorphic operator-valued functions. We focus on bounds for perturbed eigenvalues, eigenvectors and…

The paper is pertaining to the spectral theory of operators and boundary value problems for differential equations on manifolds. Eigenvalues of such problems are studied as functionals on the space of domains. Resolvent continuity of the…

We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…

A connection between integrable quantum field theory and the spectral theory of ordinary differential equations is reviewed, with particular emphasis being given to its relevance to certain problems in PT-symmetric quantum mechanics.

In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.

We study unbounded invariant and covariant derivations on the quantum disk. In particular we answer the question whether such derivations come from operators with compact parametrices and thus can be used to define spectral triples.

The general spectral boundary value problem framework is utilized to restate boundary value problems of Poincare, Hilbert, and Riemann for harmonic and analytic functions in abstract operator-theoretic terms.

We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of its essential range. Moreover, a notion of operator-valued variance is…

We establish stability inequalities for the problem of determining a Dirichlet-Laplace-Beltrami operator from its boundary spectral data. We study the case of complete spectral data as well as the case of partial spectral data.

Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…

Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…

In this work we study integral equations defined on the whole real line. Using a suitable Banach space, we look for solutions which satisfy some certain kind of asymptotic behavior. We will consider spectral theory in order to find fixed…

We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…

Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…

We consider hilbert spaces of holomorphic functions in Cartan domains (in particular in ball and polydisk) and operator of restriction of holomorphic function to a submanifold in Shilov boundary. We discuss conditions when this operator…

We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…

1.An expression for the smoothed counting function in terms of the fractional derivatives of the delta-function is presented. 2. The Neumann-Dirichlet (ND) boundary problem is introduced via some elementary examples based on a functorial…

We compute the far-from-equilibrium dynamics of relativistic scalar quantum fields in 3+1 space-time dimensions starting from over-occupied initial conditions. We determine universal scaling exponents and functions for two-point correlators…

The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are discussed. This analysis helps better understand…

We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…