Related papers: Semi-classical Analysis of Spin Systems near Criti…

Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schr\"odinger operator on the real line, $W(x)$ be a bounded observable depending only on the coordinate and $k$ be a fixed integer. Suppose that an energy level $E$ intersects the potential $V(x)$…

The spectral properties of a tractable collective model Hamiltonian are studied. The potential energy is truncated up to quartic terms in the quadrupole deformation variables, incorporating vibrational, $\gamma$-independent rotational and…

The dynamics and the thermodynamics of particles/spins interacting via long-range forces display several unusual features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model, a Hamiltonian system of…

We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S.…

The Spin-1/2 Heisenberg Model (HM) is investigated using a block-spin renormalization approach on Kagome and triangular lattices. In both cases, after coarse graining the triangles on original lattice and truncation of the Hilbert space to…

Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. Here, we show that for nonadiabatic dynamics with two…

The electron motion in rather strong magnetic fields (when only the lowest Landau level is populated) is considered. In this case the electron kinetic energy is frozen out and the electrons are guided by slowly varied potential. Using the…

In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of…

We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $d\geq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String…

We present a method to show that low-energy states of quantum many-body interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its…

We consider a two-parameter $(\bar c, \tilde c)$ family of quantum integrable Hamiltonians for a chain of alternating spins of spin $s=1/2$ and $s=1$. We determine the thermodynamics for low-temperature $T$ and small external magnetic field…

Semiclassical electrodynamics is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be…

Motivated by recent work on Heisenberg antiferromagnetic spin systems on various lattices made up of triangles, we examine the low-energy properties of a chain of antiferromagnetically coupled triangles of half-odd-integer spins. We derive…

This survey gives a short and comprehensive introduction to a class of finite-dimensional integrable systems known as hypersemitoric systems, recently introduced by Hohloch and Palmer in connection with the solution of the problem how to…

We study the thermodynamics and critical behavior of su($m|n$) supersymmetric spin chains of Haldane-Shastry type with a chemical potential term. We obtain a closed-form expression for the partition function and deduce a description of the…

Energy spectrum and thermodynamics of the pseudospin-electron model introduced at the consideration of the anharmonicity effects in high-$T_c$ superconductors are investigated in the dynamical mean field approximation ($d=\infty$ limit). In…

A sixth-order quadrupole boson Hamiltonian is used to describe the states $0^+$ and $2^+$ identified in several nuclei by various types of experiments. Two alternative descriptions of energy levels are proposed. One corresponds to a…

We develop a semi-classical approximation to electron spin resonance in quantum spin systems, based on the rotor or non-linear sigma model. The classical time evolution is studied using molec- ular dynamics while random initial conditions…

We derive a spin-dependent Hamiltonian that captures the symmetry of the zone edge states in silicon. We present analytical expressions of the spin-dependent states and of spin relaxation due to electron-phonon interactions in the…

We investigate a two-level system in resonant contact with a larger environment. The environment typically is in a canonical state with a given temperature initially. Depending on the precise spectral structure of the environment and the…