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Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
We show how the dynamics of a specific subset of states can be separated from the dynamic of the total quantum state via a time-dependent projector-based formalism of adiabatic elimination. Within our formalism, we assume explicit time…
Dielectrically confined Coulomb systems are widely employed in molecular dynamics (MD) simulations. Despite extensive efforts in developing efficient and accurate algorithms for these systems, rigorous and accurate error estimates, which…
We study a scheme for implementing a controlled-Z (CZ) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground…
It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy…
Quantum adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the…
Isothermal and self-gravitating systems bound by non-conducting and conducting walls are known to be unstable if the density contrast between the center and the boundary exceeds critical values. We investigate the equilibrium and dynamical…
In the adiabatic approximation, most of the effects of quark-antiquark loops on spectroscopy can be absorbed into a static interquark potential. I develop a formalism which can be used to treat the residual nonadiabatic effects associated…
The concept of the partial osmotic pressure of ions in an electrolyte solution is critically examined. In principle these can be defined by introducing a solvent-permeable wall and measuring the force per unit area which can certainly be…
In ab initio calculations of superconducting properties, the Coulomb repulsion is accounted for at the GW level and is usually computed in RPA, which amounts to neglecting vertex corrections both at the polarizability level and in the…
We show how to significantly reduce the number of energy bands required to model the interaction of light with crystalline solids in the velocity gauge. We achieve this by deriving analytical corrections to the electric current density.…
An antiadiabatic approach is proposed to model how the refractive index of the surrounding medium affects optical spectra of molecular systems in condensed phases. The approach solves some of the issues affecting current implementations of…
Coherent transport by adiabatic passage has recently been suggested as a high-fidelity technique to engineer the centre-of-mass state of single atoms in inhomogenous environments. While the basic theory behind this process is well…
We study the electron-energy loss spectra of strongly correlated electronic systems doped away from half-filling using dynamical mean-field theory ($d=\infty$). The formalism can be used to study the loss spectra in the optical (${\bf…
We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…
The local approach to computing electrostatic interactions proposed by Maggs and adapted by Pasichnyk for molecular dynamics simulations is extended to situations where the dielectric background medium is inhomogeneous. We furthermore…
The absence of thermalization in certain isolated many-body systems is of great fundamental interest. Many-body localization (MBL) is a widely studied mechanism for thermalization to fail in strongly disordered quantum systems, but it is…
We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated…
We derive the effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) in the asymptotic limit where the restoring forces tend to infinity. In contrast to…