Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1111.3748

Feynman Diagrams for Dispersion Interactions Out of Equilibrium -- Two-Body Potentials for Atoms with Initial Excitation

Harald R. Haakh·Jürgen Schiefele·Carsten Henkel
View original source ↗Read source document ↗Export metadata ↓

Abstract

Diagrammatic techniques are well-known in the calculation of dispersion interactions between atoms or molecules. The multipolar coupling scheme combined with Feynman ordered diagrams significantly reduces the number of graphs compared to elementary stationary perturbation theory. We review calculations of van der Waals-Casimir-Polder forces, focusing on two atoms or molecules one of which is excited. In this case, calculations of the corresponding force are notorious for mathematical issues connected to the spontaneous decay of the excitation. Treating such unstable states in a full non-equilibrium theory provides a physical interpretation of apparent contradictions in previous results and underlines the importance of decay processes for the intermolecular potential. This may have important implications on reactions in biological systems, where excited states may be relatively long-lived and the resonant intermolecular force may result in directed Brownian motion.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Harald R. Haakh, Jürgen Schiefele, Carsten Henkel. 2011-11-16. Feynman Diagrams for Dispersion Interactions Out of Equilibrium -- Two-Body Potentials for Atoms with Initial Excitation. https://doi.org/10.1142/s2010194512007465

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Programmable digital quantum simulation of 2D Fermi-Hubbard dynamics using 72 superconducting qubits

Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to ${6\times 6}$ using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware.

quant-ph↗
arXiv2026

Beyond Penrose tensor diagrams with the ZX calculus: Applications to quantum computing, quantum machine learning, condensed matter physics, and quantum gravity

We introduce the Spin-ZX calculus as an elevation of Penrose's diagrams and associated binor calculus to the level of a formal diagrammatic language. The power of doing so is illustrated by the variety of scientific areas we apply it to: permutational quantum computing, quantum machine learning, condensed matter physics, and quantum gravity. Respectively, we analyse permutational computing transition amplitudes, evaluate barren plateaus for SU(2) symmetric ansätze, study properties of AKLT states, and derive the minimum quantised volume in loop quantum gravity. Our starting point is the mixed-dimensional ZX calculus, a purely diagrammatic language that has been proven to be complete for finite-dimensional Hilbert spaces. That is, any equation that can be derived in the Hilbert space formalism, can also be derived in the mixed-dimensional ZX calculus. We embed the Spin-ZX calculus inside the mixed-dimensional ZX calculus, rendering it a quantum information flavoured diagrammatic language for the quantum theory of angular momentum, i.e. SU(2) representation theory. We diagrammatically derive the fundamental spin coupling objects - such as Clebsch-Gordan coefficients, symmetrising mappings between qubits and spin spaces, and spin Hamiltonians - under this embedding. Our results establish the Spin-ZX calculus as a powerful tool for representing and computing with SU(2) systems graphically, offering new insights into foundational relationships and paving the way for new diagrammatic algorithms for theoretical physics.

quant-ph↗
arXiv2026

Density of states of quantum systems from free probability theory: a brief overview

We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random matrix Hamiltonian, which can be written as a sum of two non-commutating operators, one can obtain an expression for the density of states of the Hamiltonian from the known density of states of the two component operators by assuming that these operators are mutually free and by using the free additive convolution. In many examples of interacting quantum systems and random matrix models, this procedure is known to provide a reasonably accurate approximation to the exact numerical density of states. We review some of the examples that are known in the literature where this procedure works very well, and also discuss some of the limitations of this method in situations where the free probability approximation fails to provide a sufficiently accurate description of the exact density of states. Subsequently, we describe a perturbation scheme that can be developed from the subordination formulas for the Cauchy transform of the density of states and use it to obtain approximate analytical expressions for the density of states in various models, such as the Rosenzweig-Porter random matrix ensemble and the Anderson model with on-site disorder.

quant-ph↗