Related papers: Comparing energy levels in isotropic and anisotrop…
The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with…
We consider asymptotics of the ground state energy of heavy atoms and molecules and derive it including Schwinger and Dirac corrections. We consider also related topics: an excessive negative charge, ionization energy and excessive negative…
We carry out a model study on two-atom interactions and bound states in quasi-two dimensional traps. The interactions are modeled by two-parameter potentials with parameters being the range $r_0$ and the $s$-wave scattering length $a_s$. We…
We show that the rational Calogero model with suitable boundary condition admits quantum states with non-equispaced energy levels. Such a spectrum generically consists of infinitely many positive energy states and a single negative energy…
Energy gap, the difference between the energy of the ground state of a given Hamiltonian and the energy of its first excited state, is a parameter of a critical importance in analysis of phase transitions and adiabatic quantum computation.…
For interacting electrons in solids, Heisenberg's equation is used to calculate the distribution in energy of transitions induced by adding an electron to an atomic-like spin orbital. This is the projected density of transitions which…
We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of…
The quantum-classical correspondence between local minima on the classical energy landscape and excited eigenstates in the energy spectrum is studied within the context of many-body quantum spin systems. In mean-field approximations of a…
Quantum chemistry is one of the important applications of quantum information technology. Especially, an estimation of the energy gap between a ground state and excited state of a target Hamiltonian corresponding to a molecule is essential.…
Passive states are special configurations of a quantum system which exhibit no energy decrement at the end of an arbitrary cyclic driving of the model Hamiltonian. When applied to an increasing number of copies of the initial density…
In this paper we investigate the energy distribution of states of a linear scalar quantum field with arbitrary curvature coupling on a curved spacetime which fulfill some local thermality condition. We find that this condition implies a…
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in…
Geometric and topological bounds are obtained for the first energy level gap of a particle constrained to move on a compact surface in 3-space. Moreover, geometric properties are found which allows for stationary and uniformly distributed…
We analyze differences in dynamics and in properties of the sampled potential energy landscape between different equilibrium trajectories, for a system of rigid water molecules interacting with a two body potential. On entering in the…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
We report experiments on the energy structure of antidot-bound states. By measuring resonant tunneling line widths as function of temperature, we determine the coupling to the remote global gate voltage and find that the effects of…
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger…
We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications…
We establish an asymptotic formula for the ground-state energy of the spherical pure $(p,q)$-spin glass model for $p,q\ge 97$. We achieve this through understanding the concentration of the complexity of critical points with values within a…
We consider ground state energies (GSE) of multipartite $p$-spin models. Relying on partially lifted random duality theory (pl RDT) concepts we introduce an analytical mechanism that produces easy to compute lower and upper GSE bounds for…