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We introduce variational wave functions to evaluate the ground-state properties of spin-phonon coupled systems described by the Su-Schrieffer-Heeger model. Quantum spins and phonons are treated on equal footing within a Monte Carlo…
We obtain new results about the high-energy distribution of resonances for the one-dimensional Schr\"odinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular…
In this paper, we consider Schr\"odinger operators on $L^2(0,\infty)$ given by \begin{align} Hu=(H_0+V)u=-u^{\prime\prime}+V_0u+Vu,\nonumber \end{align} where $V_0$ is real, $1$-periodic and $V$ is the perturbation. It is well known that…
Given a self-adjoint operator H, a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure is defined such…
In this paper, we study self-adjointness and spectrum of operators of the form $$H=\displaystyle -\frac{d^2}{dx^2}+Fx, F>0 \quad\text{on} \quad \mathcal{H}=L^{2}(-L,L).$$ $H$ is called Stark operator and describes a quantum particle in a…
We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form $H = H_V - i C^* C$, where $H_V = H_0 + V$ is self-adjoint and $C$ is a bounded operator. We study the wave operators…
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…
We consider the spectral problem for the two-dimensional Schr\"odinger operator for a charged particle in strong uniform magnetic and periodic electric fields. The related classical problem is analyzed first by means of the…
We consider the self-energy and quasiparticle spectrum, for both electrons interacting with phonons, and composite fermions interacting with gauge fluctuations. In both cases we incorporate the singular structure arising from Landau level…
We analyze spectral properties of two mutually related families of magnetic Schr\"{o}dinger operators, $H_{\mathrm{Sm}}(A)=(i \nabla +A)^2+\omega^2 y^2+\lambda y \delta(x)$ and $H(A)=(i \nabla +A)^2+\omega^2 y^2+ \lambda y^2 V(x y)$ in…
In the presence of spin-orbit coupling two branches of the energy spectrum of 2D electrons get shifted in the momentum space. Application of in-plane magnetic field causes the splitting of the branches in energy. When both, spin-orbit…
We analyze the (discrete) spectrum of the semirelativistic ``spinless-Salpeter'' Hamiltonian H = \beta \sqrt{m^2 + p^2} + V(r), beta > 0, where V(r) represents an attractive, spherically symmetric potential in three dimensions. In order to…
This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate…
We discuss spectral properties of the self-adjoint operator \[ -d^2/dt^2 + (t^{k+1}/(k+1)-\alpha)^2 \] in $L^2(\mathbb{R})$ for odd integers $k$. We prove that the minimum over $\alpha$ of the ground state energy of this operator is…
For Schr\"odinger operators with potentials that are asymptotically homogeneous of degree $-2$, the size of the coupling determines whether it has finite or infinitely many negative eigenvalues. In the latter case the asymptotic…
We study the electron addition spectrum of the one-dimensional extended Hubbard-Su-Schrieffer-Heeger (HSSH) model in the dilute limit using the density matrix renormalization group method. In addition to the expected renormalization to the…
We are interested in the nature of the spectrum of the one-dimensional Schr\"odinger operator $$ - \frac{d^2}{dx^2}-Fx + \sum_{n \in \mathbb{Z}}g_n \delta(x-n) \qquad\text{in } L^2(\mathbb{R}) $$ with $F>0$ and two different choices of the…
We consider asymptotic behavior of $e^{-itH}f$ for $N$-body Schr\"odinger operator $H=H_0+\sum_{1\le i<j\le N}V_{ij}(x)$ with long- and short-range pair potentials $V_{ij}(x)=V_{ij}^L(x)+V_{ij}^S(x)$ $(x\in {\mathbb R}^\nu)$ such that…
We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond-phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling…
We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We…