Related papers: Multicenter integrals involving complex Gaussian t…
We revisit quantum state preparation of an oscillator by continuous linear position measurement. Quite general analytical expressions are derived for the conditioned state of the oscillator. Remarkably, we predict that quantum squeezing is…
The electron repulsion integrals over the Slater-type orbitals with non-integer principal quantum numbers are considered. These integrals are useful in both non-relativistic and relativistic calculations of many-electron systems. They…
A new type of basis functions is proposed to describe a two-electron continuum which arises as a final state in electron-impact ionization and double photoionization of atomic systems. We name these functions, which are calculated in terms…
Multicritical Ising models and their perturbations are paradigmatic models of statistical mechanics. In two space-time dimensions, these models provide a fertile testbed for investigation of numerous non-perturbative problems in…
The current understanding of finite temperature phase transitions in QCD is reviewed. A critical discussion of refined phase transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in…
A charged particle in a magnetic field possesses discrete energy levels associated with particle rotation around the field lines. A bound complex of particles with a nonzero net charge possesses an analogous levels associated with its…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
Nuclear physics seeks to describe both bound and unbound states within a unified predictive framework. While coordinate-space Quantum Monte Carlo (QMC) methods have successfully computed bound states for systems with $A \leq 12$, their…
We present a statistical model of non-interacting individual classical particles that may lead to a microscopic implementation of quantum mechanics. The model requires the action of a special type of detector that detects and records…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…
A quasi classical approximation to quantum mechanical scattering in the Moeller formalism is developed. While keeping the numerical advantage of a standard Classical--Trajectory--Monte--Carlo calculation, our approach is no longer…
The nonrelativistic many-electron system in the forward, exchange and BCS approximation is considered. In this approximation, which is still quartic in the annihilation and creation operators, the model is explicitly solvable for arbitrary…
A new computational method is presented for study suspensions of charged soft particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins and porous particles…
We provide a rigorous derivation of a quantum filter for the case of multiple measurements being made on a quantum system. We consider a class of measurement processes which are functions of bosonic field operators, including combinations…
Quantum coherence is one of the clearest departures from classical physics, exhibited when a system is in a superposition of different basis states. Here the coherent superposition of three motional Fock states of a single trapped ion is…
We demonstrate the existence of finite-system multicriticality in a qubit-boson model where biased qubits collectively coupled to a single-mode bosonic field. The interplay between biases and boson-qubit coupling produces a rich phase…
In any ab initio molecular orbital (MO) calculations, the major task involves the computation of the so-called molecular multi-center integrals. Multi-center integral calculations is a very challenging mathematical problem in nature.…
We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…
We demonstrate that a conditional wavefunction theory enables a unified and efficient treatment of the equilibrium structure and nonadiabatic dynamics of correlated electron-ion systems. The conditional decomposition of the many-body…