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We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding…

We study the behavior of the density of states and the $B_{1g}$ nematic susceptibility extracted from Raman response data across the doping-driven Lifshitz transition comparing the weak and strong interaction cases. Our results were…

We define a finite-field version of Appell-Lauricella hypergeometric functions built from period functions in several variables, paralleling the development by Fuselier, et. al in the single variable case. We develop geometric connections…

Glauber-Sudarshan diagonal coherent state P-representation has been used to determine geometric phase for non-classical states of light. For a given density operator $\hat{\rho_1}$ of two mode optical beam, we evolve it in complex…

We reconsider the quantum inverse scattering approach to the one-dimensional Hubbard model and work out some of its basic features so far omitted in the literature. It is our aim to show that $R$-matrix and monodromy matrix of the Hubbard…

The spectral analysis of discretized one-dimensional Schr\"{o}dinger operators is a very difficult problem which has been studied by numerous mathematicians. A natural problem at the interface of numerical analysis and operator theory is…

We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes the Wang-Landau algorithm to quantum systems with continuous degrees of freedom, to the fermionic Hubbard model with repulsive interactions on the honeycomb lattice.…

Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…

The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form $(-\Delta)^\alpha\partial_t u$, $\alpha\in(0,\frac{1}{2})$, in bounded smooth domains of $\Bbb R^3$. It appears that to…

We extend the study of finite-entanglement scaling from one-dimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size…

The perturbation expansion for a general class of many-fermion systems with a non-nested, non-spherical Fermi surface is renormalized to all orders. In the limit as the infrared cutoff is removed, the counterterms converge to a finite limit…

We study spectral properties of Schr\"odinger operators on $\RR^d$. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in $\ZZ^d$, with the property that frequencies of finite patterns are…

There is convincing numerical evidence that fractional quantum Hall (FQH)-like ground states arise in fractionally filled Chern bands (FCB). Here we show that the Hamiltonian theory of Composite Fermions (CF) can be as useful in describing…

We use the numerical renormalization group method to investigate the spectral properties of a single-impurity Anderson model with a gap {\delta} across the Fermi level in the conduction-electron spectrum. For any finite {\delta} > 0, at…

In this paper, we consider the inverse problem of recovering a doubly periodic Lipschitz structure through the measurement of the scattered field above the structure produced by point sources lying above the structure. The medium above the…

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

We consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the system of 5 linear ODEs for periods of the corresponding Abelian integrals of first, second, and third kind, as functions of the parameters of the…

This paper consists of four parts. It begins by using the authors's generalized Schauder formula, [50], and the algebraic multiplicity, $\chi$, of Esquinas and L\'opez-G\'omez [18,17,40] to package and sharpening all existing results in…

We study Schr\"{o}dinger operator $H=-\Delta+V(x)$ in dimension two, $V(x)$ being a limit-periodic potential. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this…

In continuation of our previous works J. Phys. A: Math. Gen. 35, 9355-9365 (2002), J. Phys. A: Math. Gen. 38, 7851 (2005) and Eur. Phys. J. D 72, 172 (2018), we investigate a class of generalized coherent states for associated Jacobi…